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Course contents

Algebra M001(2+2+0) – 6 ECTS credits

Course objective. The objective of the course is to define and study some basic algebraic structures.

Prerequisites. Geometry of plane and space. Linear algebra I and II.

Course contents.
1. Groups. Groupoid, semigroup, monoid, group. Homomorphisms and isomorphisms. Finite groups. Lagrange's theorem. Normal subgroups and quotient groups. Cyclic groups. Solvable groups. Sylow's theorems.

2. Rings and modules. Rings. Examples. Multiplicative group of a ring. Subring. Ideal. Quotient ring. Homomorphisms and isomorphisms. Skew fields and fields. Polynomial ring. Modules. Submodules and quotient modules. Vector spaces.

3. Integral domains. Definition. Maximal ideals. Characteristic. Simple fields. Fields of fractions. Polynomial and rational functions.

4. Principal ideal rings. Definition. Finitely generated modules over principal ideal rings. Classificaton of finite Abelian groups. Connection with the theory of linear operators.

5. Field extensions. Definition of field extensions. Finite extensions. Degree of an extension. Algebraic extensions. Transcendental elements of an extension. Purely transcen-dental extensions. Minimal polynomial. Simple extensions. Algebraic closure.

6. Fundamental theorem of algebra. Sketch of a proof using the notion of loops and their winding numbers.

7. Extensions of the field of rational numbers. Algebraic and transcendental numbers. Gauss lemma. Eisenstein's criterion of ireducibility of a polynomial. Gauss field and Gauss integers. Algebraic integers. Quadratic extensions. Constructibility by ruler and compass.

8. Galois theory. Splitting fields. Automorphisms of a field. Galois group of a field exten-sion. Galois group of a polynomial. Separable polynomials and separable extensions. Basic theorems of Galois theory. Normal extensions. Fundamental theorem of Galois theory.

9. Equations of third, fourth and higher degrees. Cardano formulas. Solubility by radicals. Solutions of a fourth degree equation. Fifth degree equation insoluble by radicals.

Teaching methods and student assessment. Attending lectures and exercises is compulsory. The examination consists of both written and oral part after completing lectures and exercises. During the semester students can take tests which replace the written part of the examination.

Literature:
Recommended literature:
[1] G. Birkhoff, S. Mac Lane, A survey of modern algebra, Macmillan, New York, 1965
[2] S. Lang, Algebra, AddisonWesley, Reading, Mass., 1965
Additional literature:
[3] B.L. van der Waerden, Algebra I,II, Springer Verlag, 1971
[4] T.W. Hungerford, Algebra, Rinehart&Winston, New York, 1974
[5] I.Stewart, Galois theory, Chapmann and Hall, London, 2004

Analytic geometry M002 (1+1+0) – 2 ECTS credits

Course objective. To make students familiar with fundamentals and practical applications of analytic geometry.

Course contents.
Rectangular (Cartesian) coordinate system (in plane and space). The distance between points. Vectors in plane and space: operations with vectors, linear independence, scalar product of vectors, vector product of vectors. Analytic geometry in plane: line, circle, ellipse, hyperbola, parabola. Polar coordinates. Plane section of cone. The theory of conic sections. Analytic geometry of space: line, plane, curves, surfaces of second order (ellipsoid, hyperboloid, paraboloid, cylindric and conic surfaces). Cylindrical and spherical coordinates.

Teaching methods and student assessment. Attendance is mandatory in terms of both lectures and exercises. The final assessment consists of the written and oral examination, which can be taken upon completion of lectures and exercises. During the semester students can take two tests, which then replace the written examination.

Literature:
Recommended literature:
[1] B. Pavković, D. Veljan, Elementarna matematika II, Školska knjiga, Zagreb, 1994
Additional literature:
[2] Secondary school textbooks and workbooks.

Analysis of company business E001 (2+2+0) – 4 ECTS credits

Course objective. This course will introduce students to fundamental fields of financial analysis, with the emphasis placed on the methodological and instrumental aspect and the application of mathematical and statistical methods and models.

Prerequisites. None.

Course contents.
1. Analysis of business potentials: Concept, objectives, methodology. Financial analysis („hard facts“) and management system analysis („soft facts“). Sector analysis. Region analysis.
2. Financial analysis: concept, objectives.
3. Methods of financial analysis: primary methods (methods of discrimination, comparison and correlation) and secondary methods (methods of relative efficiency, scoring models, mathematical and statistical methods). Balance analysis, income statement analysis, cash flow analysis.
4. Instruments of financial analysis: horizontal analysis, vertical analysis, business indicators, system of business indicators.
5. Early warning system: single diagnostic and prognostic indicators, systems of indicators, early warning systems: Altman, Kralicek, Beermann, Taffler.
6. Solvency rating: application of mathematical and statistical methods.

Teaching methods and student assessment. Lectures and seminars (mostly by using computers). Students' knowledge referring to the application of various methods is continuously assessed through tests and projects. The final examination consists of the written and the oral examination.

Literature:
Recommended literature:
[1] E.A.Helfert, Tehnike financijske analize, HZRFD, Zagreb, 1997
Additional literature:
[2] N. Osmanagić Bedenik, Kriza kao šansa, Školska knjiga, Zagreb, 2003
[3] J.Tintor, Poslovna analiza, HIBIS, Zagreb, 2000

Business data analysis E002 (2+0+2) – 5 ECTS credits

Course objective. The aim of the course is to qualify each student for the application of statistical methods to solving economical problems on a micro and a macro level. The emphasis is put on understanding the context of business decisions making. Students are required to understand statistical methods. The course is organised such that fundamentals are made up of consideration of an economical problem, after which there follows application of statistical methodology aiming at analysis and development of a solution to the given problem.

Prerequisites. Probability, Statistics.

Course contents.
Application of statistical methods in solving certain financial problems. Analysing outstanding accounts (invoices) and charging for those accounts. Testing the influence of different factors on equity price. Control of money supply. Credit rate testing. Analysing IBM’s equity prices.
Application of statistical methods in production control process: Testing product quality. Testing the production process. Testing production quality. Anticipating the number of working hours required for finishing the work. Modelling (forming) the expected duration of a machine.
Application of statistical methods in marketing: Promotion efficiency in product sale. Influence of different ways of product advertising. Anticipating the market value of a product. Choosing hotel location. Testing the influence of media on public opinion. Modelling the product sale per month. Testing the influence on product sale. Testing the influence of advertising on profit rate.
Application of statistical methods in management: Testing the efficiency of training programmes for managers. Comparison of managers’ efficiency in making business. Testing the efficiency of sale strategies.
Application of statistical methods in planning: Planning future constructive (structural) projects. Planning construction of a new plant. Planning the retail trade based on a month data analysis.
Application of statistical methods in certain macroeconomic problems: Testing the difference between unemployment rates in different areas. Analysing the index of consumer goods as part of GDP. Monitoring the month prices of gold on the world market. Product consumption in relation to average retail prices in a certain period of time. Relation between month salary and productivity. Phillips curve. Cobb-Douglas curve of production. Analysing personal goods and personal income. Forming product demand. Analysing work force considering age, gender, education, unemployment rate and its changes. Predicting equity prices. Demand and supply function. Company’s investing attitude. Analysing product spending per capita. Analysing an increase in country’s’ revenue. Modelling the average spending as a function of average revenue.

Teaching methods and student assessment. Teaching methods used in this course are: lectures, exercises, group discussions and case studies. Attendance and activity are required. Continuous student assessment is carried out through tests and assignments during the semester. In addition, each student has to develop a project assignment consisting of the data analysis worked out on one actual economical problem. For that purpose, students will use statistical programmes SAS and Statistica (StatSoft). The final examination consists of the written and the oral part.

Literature:
Recommended literature:
[1] J.T.McClave, P.G.Benson, T.Sincich, Statistics for Business and Economics, Prentice Hall, 2001
[2] A.H.Studenmund, Using Econometrics, Harper Collins Publishers, New York, 1992
Additional literature:
[3] A.A.Afifi, V.Clark, Computer-Aided Multivariate Analysis, Chapman&Hall, Washington, D.C., 2000
[4] D.N.Gujarati, Basic Econometrics, McGraw-Hill, Inc., New York, 1998
[5] J.Kmenta, Počela ekonometrije, MATE, Zagreb, 1997

Time series analysis M003 (2+1+1) – 6 ECTS credits

Course objective. The objective of this course is to make students familiar with the fundamental concepts and results of time series analysis. Students will be introduced to classical and modern methods in modelling real-life time series. Special attention will be dedicated to the applications of time series models in economics and financial mathematics. In the practical part of the course students are supposed to learn necessary techniques and apply them on computers.
Prerequisites. Probability. Statistics. Random processes.

Course contents.
1. Introduction. Examples of time series. Trend and seasonality. Autocorrelation function. Hilbert spaces. Linear and nonlinear forecasting.
2. Spectral analysis. Complex random variables. Spectral density. Spectral representation of stationary processes. Periodogram.
3. ARMA processes. Strong and weak stationarity. Linear processes. ARMA models. Causality and invertibility of ARMA processes. Estimation of autocorrelation function and the mean. Modelling and forecasting for ARMA processes. Asymptotic behaviour of the sample mean and the autocorrelation function. Parameter estimation for ARMA processes.
4. Other time series models. Nonstationary models of time series. GARCH models. State space models.
5. Practical part. Analysis of time series using software. Simulation of time series models.

Teaching methods and student assessment. Classes will be carried out in a series of lectures, exercises and practical classes at the computer lab. Grading will be based on the final examination (oral or written), assignments during the semester and/or project work.

Literature:
Recommended literature:
[1] P.J.Brockwell, R.A.Davis: Introduction to time series and forecasting. Second edition. Springer Verlag, New York, 2002
[2] P.J.Brockwell, R.A.Davis: Time series: theory and methods. Second edition. Springer Series in Statistics. Springer-Verlag, New York, 1991
[3] Neil Shephard: Statistical aspects of ARCH and stochastic volatility. In Time Series Models with Econometric, Finance and Other Applications, edited by D.R.Cox, D.V.Hinkley and O.E.Barndorff-Nielson, 1-67, London: Chapman and Hall, 1996
Additional literature:
[4] C.Alexander: Market Models: A Guide to Financial Data Analysis
[5] P.Embrechts,C.Klueppelberg,T.Mikosch: Modelling extrernal events. For insurance and finance, Springer-Verlag, Berlin, 1997
[6] C.Gourieroux: ARCH Models and Financial Applications, Springer, 1997
[7] J.D.Hamilton: Time Series Analysis. Princeton University Press, 1994
[8] T.C.Mills: The Econometric Modelling of Financial Time Series. Cambridge University Press, 1999
[9] A van der Vaart: Time Series. Unpublished lecture notes.

Databases I001 (2+2+0) – 5 ECTS credits

Course objective. Students should learn about different data models, principles of database modelling, and acquire skills required to use databases. Through exercises they should gain an insight into database management systems (MS Access, MS SQL and MySQL) and basic database administration.

Prerequisites. Introduction to computer science. Introduction to programming.

Course contents.
1. Data management in information society.
Basic concepts: data, database, information, knowledge. Data processing systems. Formatted and unformatted data records. Transaction and analytic databases. Information systems.
2. Methodological foundations of database modelling.
System theory and system analysis. Models and descriptive modelling. Submodels of database management systems. Data models. Database models. Databases.
3. Physical data modelling.
Principles of physical data recording on external memory data carriers. Physical data organisation: successive, direct and index. Methods of data search. Distributed databases.
4. Conceptual data model.
Data model concepts. Entities-relationship model. Graphic representation of entities-relationship model. Design of entities-relationship model and a design example.
5. Logical data models.
Relationships between data. N-ary. Hierarchical data model. Network data model. Relational data model. Relational algebra. Integrity rules in relational model. Database shaping. SQL – non-procedural language for working with a relational database. Translating an entities-relationship model into a relational model. Object model. UML. File model.
6. Logical modelling of analytic data.
Data warehouse. Dimensional model of data warehouse. Methods of data warehouse design. Operations in a dimensional model. Analytical data processing. Discovering knowledge out of data.
7. Structured databases.
Database management systems. Codd's rules and relational databases. Data safety. Log of transactions. Basic administration of database management systems. Guidelines for connecting programme application and database. XML and integration of heterogenous data sources.
8. Semi-structured databases.
Textual and multimedial databases (document bases). Document management. Web as a base of semi-structured data. Search methods. Portals – usage and design.

Teaching methods and student assessment. Lectures and exercises are obligatory. Students' progress is assessed regularly during the semester through preliminary tests and homework assignments. At the end of the course students take the examination consisting of a written and an oral part.
Literature:
Recommended literature:
[1] Varga, M.: Baze podataka, Konceptualno, logičko i fizičko modeliranje podataka, DRIP, Zagreb, 1994
[2] Tkalac, S.: Relacijski model podataka, DRIP, Zagreb, 1993
[3] R. Elmasri, S. Navathe, Fundamentals of Database Systems; 3rd edition, The Benjamin/Cummings Publishing Company, Inc., 2000
Additional literature:
[1] Helman, P.: The Science of Database Management, IRWIN, Illinois., 1994
[2] Williams H. E. , Lane D. , Web Database Applications with PHP and MySQL, O'Reilly UK, 2002
[3] Welling, L., Thomson, L., PHP and MySQL Web Development, Sams, 2003
[4] Mesarić, J., Zekić-Sušac, M., Dukić, B.: PC u uredskom poslovanju, Sveučilište J.J. Strossmayera, Ekonomski fakultet Osijek, Osijek, 2001

Computational Geometry I025(1+0+1) - 4 ECTS credits

Computational geometry is a recent field of computer science, originating around 1978, that studies geometric problems from an algorithmic or complexity-theoretic point of view. Results of interest in this field include efficient algorithms and lower bounds for the following example classes of problems:
Content:
1. Perform a geometric construction, e.g., compute the convex hull or Voronoi diagram of a given set of points.
2. Generate additional geometric structure, e.g., triangulate or otherwise mesh a given set of points or polygon.
3. Extract geometric information from given data, e.g., find the closest pair of points in a given set of points.
4. Preprocess input into a data structure to support fast queries, e.g., range queries or point location.
5. Maintain information about data subject to a sequence of updates and queries, e.g., collision detection. Computational geometry is also closely tied to discrete geometry, which is more broadly interested in determining properties of geometric figures and operations, even if they do not immediately lead to algorithms (although frequently they do).

Computational geometry is also closely tied to discrete geometry, which is more broadly interested in determining properties of geometric figures and operations, even if they do not immediately lead to algorithms (although frequently they do).

Expected work: Throught the semester several projects will be assigned, some involving programming skills. The projects are normally undertaken by individuals. Each project is followed by a class presentation.

Grading: Homeworks and Projects (40%), Finalterm (60%).

References:
[1] M.D. Berg, M.V. Kreveld, M. Overmars, O. Schwarzkopf, Computational Geometry, Algorithms and Applications, 2nd rev. Ed., Springer-Verlag, Berlin, 2000.
[2] Computer Aided Geometric Design, Elsevier, Amsterdam, ISSN:0167-8396

Didactics P001 (1+0+1)+ (1+0+1) – 4 ECTS credits

Course objective. Make students familiar with basic cognitions in didactics referring to organisation of teaching in primary school, develop skills necessary for application, realisation and evaluation of the teaching process. Become familiar with the development of didactical thoughts. Understand basic methods of research in didactics. Develop critical opinion towards the application of methods, forms and ways of teaching. Become familiar with the structure and importance of curriculum; preparation, realisation and evaluation of teaching; teaching as communication; teaching systems – from a theoretical and a practical viewpoint. Usage and a critical approach to teaching technologies. Educational pluralism – alternative schools.

Prerequisites. Psychology.

Course contents.
Structure of didactics. Didactic thought. Subject and scope of didactics. Didactics and other sciences. Fundamental concepts in didactics. Pupil-centered teaching. Teacher-centered teaching.
Methodology of didactics. Subject. Research in didactics.
Teaching process. Goals – tasks. Syllabus, curriculum. Sources. Classes as communication. Verbal communication. Asymmetric teaching communication. Rules of optimal communication. Teaching communication principles. Factors – subjects of the teaching process: pupil, teacher – parent – other subjects. Phases of the teaching process – working dynamics: learning process phases. Preparation. New contents. Revision and exercise. Checking - change. Evaluation - assessment.
Teaching systems. Lecturing. Heuristic teaching. Programming teaching. Exemplary teaching. Teaching problem solving.
Methods, forms, procedures. Methods of teaching. Forms of teaching. Teaching procedures.
Teaching aids and technology. Teaching aids. Technology used in teaching – media. Application of teaching aids: blackboard and flanelograph. Audio technology - radio, tape recorder. Visual aids: slide projector, epiprojector, overhead projector. Audio-visual aids – cinema projector, VCR, TV. Teaching documentation.
Organisation and articulation of teaching. External and internal organisation. Working in small schools and schools with combined classes. Differentiation in teaching and learning. Team work.
Teacher’s preparation for classes. School: Macroorganisation of school. Didactic organisation of school. Modern tendencies in the teaching process reform, schools in Croatia and abroad. Alternative and free schools. Internal educational reform.
Seminar and exercises in didactics. Seminar paper. Primary school curriculum. Syllabus. Formulation of concrete and operating tasks. Assessing and grading pupils – analysis and exercises.

Teaching methods and student assessment. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises.

Literature:
Recommended literature:
[1] A.Bežen, F.Jelavić, N.Kujundžić, V.Pletenac, Osnove didaktike, NIRO Školske novine, Zagreb, 1991
[2] L.Bognar, M.Matijević, Didaktika, Školska knjiga, Zagreb, 1994
[3] A.Peko, A.Pintarić, Uvod u didaktiku (hrvatskoga jezika), Sveučilište J.J.Strossmayera, Osijek, 1999
Additional literature:
[4] W.Glasser, Kvalitetna škola, Educa, Zagreb, 1994
[5] H.Gudjons, R.Teske, R.Winkel (Eds.), Didaktičke teorije, Educa, Zagreb, 1994
[6] F.Jelavić, Didaktičke osnove nastave, Naklada Slap, Jastrebarsko, 1995
[7] L.Legrand, Obrazovne politike, Educa, Zagreb, 1993
[8] J.Lesourne, Obrazovanje i društvo, Educa, zagreb, 1993
[9] A.Madlain, Osloboditi školu, Educa, Zagreb, 1995
[10] M.Matijević, Alternativne škole, Institut za pedagogijska istraživanja, Zagreb, 1994
[11] C.J.Marsh, Kurikulum: Temeljni pojmovi, Educa, Zagreb, 1994
[12] V.Mužić, A.Peko (Eds.), Vrednovanje obrazovnog procesa programa, ostvarivanja, učinka, Pedagoški fakultet, Osijek, 1996

Differential calculus M004 (3+3+0) – 7 ECTS credits

Course objective. At the introductory level students should be introduced to fundamental ideas and methods of mathematical analysis, which represent the basis for many other courses. During lectures basic terminology would be explained in an informal way, their utility and applications would be illustrated. During exercises students should master an adequate technique and become trained for solving concrete problems. The programme is the same for all branches.
Prerequisites. High-school knowledge.

Course contents.
1. Introduction. Real numbers, supremum and infimum of a set, absolute value, intervals. Complex numbers.
2. Functions. Definition of a function, representation and basic properties of functions. Composition of functions and the inverse function. Elementary functions.
3. Sequences. Definition of a sequence. Some special sequences. Convergent sequence. The number e.
4. Limit and continuity of a function. Limit of function. Properties of limit. One-sided limits. Infinite limits and limits at infinity. Asymptotes. Continuous functions.
5. Differential calculus. Tangent line and velocity problems. Concept of derivative. Differentiation rules and derivatives of elementary functions. Implicit differentiation. Parametric differentiation. Lagrange's mean-value theorem. Higher-order derivatives. Taylor's theorem.
6. Applications of the derivatives. Differentials. Newton's method of tangents. L'Hospital’s rule. Applications of the derivatives (tangent and normal, increase and decrease of a function, local extrema, convexity and concavity of a graph, points of inflection, sketching the graph of a function, curvature of a curve).

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students can take 2 tests that replace the written examination.

Literature:
Recommended literature:
[1] W.Rudin, Principles of Mathematical Analysis, Mc Graw-Hill, Book Company, 1964
[2] D. Jukić, R. Scitovski, Matematika I, Odjel za matematiku, Osijek, 2000
Additional literature:
[3] S. Kurepa, Matematička analiza 1 (diferenciranje i integriranje), Tehnička knjiga, Zagreb, 1989
[4] S. Kurepa, Matematička analiza 2 (funkcije jedne varijable), Tehnička knjiga, Zagreb, 1990
[5] B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke, Tehnička knjiga, Zagreb, 1986

Graduation seminar Z001 (0+0+2) + (0+0+2) – 8 ECTS credits

Course objective. The goal of this course is to make students familiar with the structure of their graduation theses (contents, introduction, body of the text, literature, summary) as well as appropriate graphic design (page layout, typeface, reference and citation, formulae, diagrams, figures, tables, etc.). Prior to the thesis defense, every student is obliged to present his/her thesis to second-year Master level students of mathematics and fifth-year Master level students obtaining a degree in mathematics and computer education.

Teaching methods and student assessment. Students’ active participation in the seminar is required. Their regular attendance is confirmed by the signature of the seminar lecturer.

e-Business I002 (2+0+2) - 4 ECTS credits

Course objective. To make students familiar with changes in business influenced by information and Internet technology. Basic terms, principles and models important for e-business will be described during the course lectures. The case study method will also be used by analysing the advantages and limitations of e-business strategies in companies that use B2C and B2B models. Students will be able to analyse assigned cases and propose an e-business strategy of a company through project assignments. The course will provide an insight into possibilities of Internet and information technology in business, as well as its impact to business successfulness.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Definition of electronic business (e-business) and electronic commerce (e-commerce). Basic terms: digital economy, globalisation, virtualisation, information (new) economy, technology support to information economy.
2. History of e-business. Forerunners of e-business: ERP systems, CRM systems, EDI, logistics, portals. Basic economic terms in e-business: product branding and pricing, markets, auctions. Changes caused by e-business. Traditional company vs. dot.com company. Case studies: Amazon.com, Yahoo.com, and others.
3. Concept of e-business. Areas of e-business application. On-line sale, electronic commerce, electronic banking, on-line financial transactions, Internet banking, electronic publishing. Concept of "webocentric" company.
4. Strategy of e-business. Managing the transition from traditional business to e-business. Key factors that influence the strategy of e-business. Technology, branding, services and market segmentation strategy as key factors for achieving competitive advantage.
5. Security of e-business. Security of information, security standards. Tactics of solving security problems and security policy. Public keys.
6. Tactics of e-business. Model selection. Broker or commision models, advertising models, mediator models, commerce models, manufacturing models, collaborative or affiliation models, virtual organisation models, subscriber models, accessory service models, and others. How to build a successful tactic from the strategy.
7. Operations of e-business. Corporation web site: design, implementation, maintainance and managment, performance measurement.
8. Architecture of e-business: software applications for e-business. Integration of business processes – customer relationship management (CRM), supply chain management and sale chain management (SCM), enterprise resourse planning (ERP). Business intelligence systems.
9. Integration of business applications by using intranet. Connecting Internet, intranet, and extranet.
10. Global infrastructure in e-business: Internet access, network infrastructure, security infrastructure, payment transactions infrastructure.
11.Future of e-business.

Teaching methods and student assessment. Lectures and seminars are obligatory. Student knowledge is examined during the semester through homework and project assignments. There is also a final examination (written and oral).

Literature:
Recommended literature:
[1] Ž. Panian, Izazovi elektroničkog poslovanja, Narodne novine, Zagreb, 2002
[2] M. Spremić, Menadžment i elektroničko poslovanje, Narodne novine, Zagreb, 2004
Additional literature:
[1] R. Kalakota, M. Robinson, e-Poslovanje 2.0, Mate, Zagreb, 2001
[2] J. Reynolds, The Complete E-Commerce Book: Design, Build, and Maintain a Successful Web-Based Business, CMP Books, 2004
[3] J. Reedy, S. Schullo, K. Zimmerman, Electronic Marketing, The Dryden Press, Forth Worth, 2000

General physics I F001 (2+2+0) - 4 ECTS credits

Course contents.
Mathematics in physics. Introduction to physics. Physical quantity units. Motion; velocity, acceleration, free-fall, slope, vertical projectile motion, slant projectile motion, circular motion. Dynamics; Newton’s laws. Conservation of linear momentum. Gravitation. Dynamics law for two systems in relative motion. The Galilean transformations, circular motion, Coriolis force, elastic force. Friction force. Work and kinetic energy. Conservation of mechanical energy. Statics; the center of mass, handle, rigid body rotating about a fixed axis, parallel axis theorem, conservation of angular momentum, rigid body rotating about a free axis. Oscillations; mathematical pendulum, Lissajous figures, damped simple harmonic motion, forced harmonic oscillator, the physical pendulum. Fluids at rest; hydraulic pressure, buoyant force, atmospheric pressure, surface tension of liquids, capillarity. Fluids in motion; the equation of continuity, Bernoulli's equation, viscosity, flow of real fluids within tube, motion of body in fluids. Viscosity measurements, errors of measurements. Thermodynamics: laws. Thermal properties of matter. Carnot cycle. Kinetic theory of gases.

Literature:
Recommended literature:
[1] J. Planinić, J., Osnove fizike 1, Školska knjiga, Zagreb, 2005
[2] J. Planinić, Osnove fizike I - MEHANIKA, Pedagoški fakultet Osijek, 2003
[3] C. Kittel, W.D. Knight, M. A. Ruderman, Udžbenik fizike Sveučilišta u Berkleyu, Svezak 1 (Mehanika) Tehnička knjiga, Zagreb, 1992
[4] M. Paić, Predavanja iz opće fizike Part I and Part II, Sveučilište u Zagrebu, Zagreb, 1975
Additional literature:
[5] N.Cindro, Fizika 1, Školska knjiga, Zagreb, 1992
[6] I.V.Saveljev, Physics, A general course, Vol. I, (Mechanics, Molecular Physics) MIR Publishers, Moscow, 1980 (in Russian and English)
[7] E.Babić, R. Krsnik i M. Očko, Zbirka riješenih zadataka iz fizike, Školska knjiga, Zagreb, 1982

General physics II F002 (2+2+0) - 4 ECTS credits

Course contents.
Fundamentals of electrostatics and electrodynamics. Networks and Kirchhoff’s rules. Magnetic field and magnetic force. Induction. Alternating currents. Maxwell's equations; light. Relativistic mechanics. Lorentz transformations, length contraction, time dilation, relativistic conservation of momentum, relativistic energy. Optics; basic laws of geometrical optics. Physical optics. Structure of atoms. Spectrum of black body radiation. Planck law of black body radiation. Atomic line spectra and energy levels. Bohr's model. The Pauli exclusion principle. Periodic table. Schrödinger wave equation.

Literature:
Recommended literature:
[1] J. Planinić, J., Osnove fizike 1, Školska knjiga, Zagreb, 2005
[2] J.Planinić, Osnove fizike I - MEHANIKA, Pedagoški fakultet Osijek, 2003
[3] E.M.Purcell, Udžbenik fizike Sveuč. u Berkleyu, Sv.II (Elektricitet i magnetizam) Tehnička knjiga, Zagreb, 1988
[4] M.Paić, Predavanja iz opće fizike III / IV dio, skripta Sveučilišta u Zagrebu, Zagreb, 1975
Additional literature:
[5] N.Cindro, Fizika 2, Školska knjiga, Zagreb, 1992
[6] I.V.Saveljev, Physics, A general course, Vol. I & III (Electricity and magnetism, Waves, Optics, Quantum Phenomena) MIR Publishers, Moscow, 1980 (in Russian and English)
[7] E.Babić, R.Krsnik, M.Očko, Zbirka riješenih zadataka iz fizike, Školska knjiga, Zagreb, 1982

Elementary geometry M005 (2+2+0) - 5 ECTS credits

Course objective. The objective of this course is to systematise, consolidate and deepen the knowledge of the elementary primary-school geometry, without giving axiomatic of geometries. Classical geometrical contents will be updated by demonstrations on computers.

Prerequisites. Not necessary.

Course contents.
1. Introduction to the planimetry. Basic objects of geometry in plane (points and straight lines). Axioms of Euclidean geometry plane. Axioms about paralleles. (The axioms will be given only as information and dealt with very elementary.)
2. Prominent sets of points in the plane. Half-line. Segment. Convex sets in the plane. Half-plane. Angle. Measure of angle. Vertical angles. Angles with parallel arms and angles with perpendicular arms. Angles along transversal. Triangle. Sum of angles in a triangle. Relation of triangle. Quadrangle. Diagonal of a quadrangle. Trapezoid. Parallelogram. Rhomb. Rectangle. Square. Quadrangles with perpendicular diagonals. Multiangles. Circumference and circle. (Only proofs referring to angles will be dealt with in detail; all other concepts will be only defined.)
3. Congruence of a triangle. Definition of triangle congruence. Triangle congruence theorems. Perpendicular bisector theorem. Four basic constructions of a triangle. Characterisation of a parallelogram and a rhomb. The midline of a triangle theorem. Four characteristic points of a triangle. Circumcircle and incircle of a triangle. The midline of a trapezoid theorem. Theorem about the bisector of an angle.
4. Perimeter and area. Perimeter and area of a polygon. Areas of square, parallelogram, triangle, trapezoid, quadrangle with perpendicular diagonals. Heron's formula. Connection between the area of a triangle and its sides and the radius of its escribed circles. Area of a circle. Length of a circumference.
5. Similarity of triangles. Thales' theorem of proportion. Theorem about bisector of an interior angle in a triangle. Definition of similarity of triangles. Pythagorean theorem (some proofs) and its converse. Euclidean theorem.
6. Theorems about circumference. Theorem about peripherical and central angle. Thales' theorem about angle on a diameter. Circumscribed and inscribed quadrilateral.
7. Plane mapping. Isometries of a plane. Axial and central symmetry. Rotation. Translation. Homothety. Eulerean line. Mapping of similarity.
8. Introduction to stereometry. Basic objects of geometry of space (points, lines and planes). Axioms of Euclidean geometry of space. Determination of plane and a line in the space. Halfspace. Parallel lines and planes. Perpendicular lines and planes. Theorem of three normals.
9. Angles between lines and planes. Angle between two lines. Angle between line and plane. Angle between two planes.
10. Distance in the space. Distance from point to plane. Distance from point to line. The shortest distance between skew lines. Symmetral planes of a segment and of a couple of planes. Dihedrons and trihedrons.
11. Polyhedra. Idea of polyhedron. Some kinds of polyhedra (pyramid, bipyramid, prism). Eulerean formula for polyhedra. Regular polyhedra (Platonean bodies). Volume and surface area of a polyhedron - rectangular parallelepiped, parallelepiped, prism, pyramid and truncated pyramid. Cavalieri's principle.
12. Round bodies. Cylindar. Cone. Sphere. Volume and surface of round bodies - volume and surface area of cylinder, cone, sphere.
Teaching methods and student assessment. Students are obliged to be present in classes and participate actively in the practical part. Students’ knowledge is assessed during the semester through tests and homework. Written part of the final examination can be replaced by tests.

Literature:
Recommended literature:
[1] B. Pavković, D. Veljan, Elementarna matematika l, Školska knjiga, Zagreb, 2003
[2] D. Palman, Trokut i kružnica, Element, Zagreb, 1994
[3] D. Palman, Planimetrija, Element, Zagreb, 1999
Additional literature:
[4] A.Marić, Planimetrija - zbirka riješenih zadataka, Element, Zagreb, 1998
[5] Primary and secondary school textbooks and exercise books in mathematics

Elementary mathematics I M006 (2+2+0) - 6 ECTS credits

Course objective. To refresh and broaden students' knowledge of elementary mathematics, which is necessary as a strong base for further study. Educational contents of this course are equal for all study branches.

Prerequisites. Not required.

Course contents.
1. Elements of mathematical logic. Notion of proposition. Operations on propositions. Basic mathematical propositions. Types of theorem proofs.
2. Sets. Notion of a set (subset, equality of sets, power set). Operations on sets (union, intersection, difference, complementary set). Cartesian product of sets. Finite and infinite set.
3. Functions-basic notions (equality of functions, composite function, bijective function, inverse function).
4. Relations (relation of equivalence; relation of ordering).
5. Numbers - properties. Set of natural numbers. Set of integers and set of rational numbers. Axioms of the set of real numbers. Complex numbers.
6. Basic elementary functions - properties. Polynomials (divisibility, Horner's scheme, Euclid's algorithm). Rational functions and irrational functions (roots). Exponential functions. Logarithmic functions. Trigonometric and inverse trigonometric functions. Algebraic equations (zeros of polynomials). Inequations.

Teaching methods and student assessment. Attending lectures and auditory exercises is obligatory. During the semester knowledge of students is assessed by tests, which, if done successfully, influence the final grade and can replace the written part of the final examination. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] B. Pavković, D. Veljan: Elementarna matematika I, Tehnička knjiga, Zagreb, 1992
Additional literature:
[2] Elementary mathematics textbooks and exercise books, secondary school textbooks and exercise books in mathematics

Elementary mathematics II M007 (2+2+0) -6 ECTS credits

Course objective. To refresh and broaden students' knowledge of elementary mathematics, which is necessary as a strong base for further study. Educational contents of this course are equal for all study branches.

Prerequisites. Not required.

Course contents.
1. Axioms of Euclidean geometry in the plane.
2. Isometric mapping (axial symmetry, rotation, central symmetry, translation). Homothety and similarity. Angles (degrees, radians).
3. Geometry of triangle (congruence; center of gravity of triangle, orthocenter, center of circumcircle and of incircle; similarity of triangles; right triangle).
4. Area and perimeter of polygons and other geometrical figures in the plane.
5. Applications of trigonometry (sine and cosine theorem for triangle, trigonometric equalities in a right triangle, in other geometrical figures).
6. Stereometry – volumes and surface areas of some geometric solids in the space.

Teaching methods and student assessment. Attending lectures and auditory exercises is obligatory. During the semester knowledge of students is assessed by tests, which, if done successfully, influence the final grade and can replace the written part of the final examination. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] B. Pavković, D. Veljan: Elementarna matematika I, Tehnička knjiga, Zagreb, 1992
[2] B. Pavković, D. Veljan: Elementarna matematika II, Školska knjiga, Zagreb, 1995
Additional literature:
[3] Elementary mathematics textbooks and exercise books, secondary school textbooks and exercise books in mathematics

English for mathematics / computer science students I Z002 (0+0+2) - 6 ECTS credits

Course objective. Students should acquire fundamental terminology from the fields of mathematics and computer science as well as apply structures typical of ESP (English for Specific Purposes). They should be taught and trained how to read various pieces of literature from the fields of mathematics and computer science as well as to carry out conversation referring to some basic topics in their fields of study.

Prerequisites. High-school knowledge of the English language

Course contents.
Mathematics. Numbers. The number system. Sets of numbers. Arithmetical operations on numbers. Reading mathematical formulae. Fractions. Ratio, proportion and percentage. Powers and roots. Factors. Equations and formulae. Lines and angles. The triangle. The circle. More 2-dimensional figures. 3-dimensional figures.
Introduction to computer science terminology. Computer applications: What can computers do? What is a computer? What's inside a microcomputer? About the keyboard. Point and click. Types of printers. Optical disks: pros and cons.
Grammar: Parts of speech. Word order. Tenses. Modals. Participles. Relative clauses. Passive voice. Conditional clauses. Irregular plural. Word building – prefixes, suffixes. Comparison of adjectives. Acronyms. Connectors and modifiers. Antonyms and synonyms.

Teaching methods and student assessment. This course is organised through seminars which are obligatory for all students. Various audio-visual teaching aids are used in the course (LCD, PC, DVD), as well as numerous professional journals and books available in the Department’s library. From time to time students are assigned homework or small project tasks, which might affect their final grade. Students’ knowledge is continuously assessed by four tests, two per each semester, and the oral part of the examination takes place at the end of academic year.

Literature:
Recommended literature:
[1] I.Ferčec, A Course in Scientific English: Mathematics, Physics, Computer Science, Odjel za matematiku/Elektrotehnički fakultet, Osijek, 2001
[2] R.Murphy, English Grammar in Use, CUP, Cambridge, 1999
Additional literature:
[3] C. Clapham, The Concise Dictionary of Mathematics, OUP, Oxford, 1996
[4] D. Koračin, Čitanje matematičkih formula, Element, Zagreb, 1996
[5] M. Krajnović, Rječnik matematičkih naziva, Matematičko-fizički list, (izvanredni broj), Zagreb, 1999-2000
[6] Oxford Dictionary of Computing (ed. V. Illingworth), OUP, Oxford, 1996

English for mathematics / computer science students II Z003 (0+0+2) - 6 ECTS credits

Course objective. Students should acquire vocabulary in the fields of mathematics and computer science as well as apply structures typical of ESP (English for Specific Purposes). They should be taught and trained how to read and understand various pieces of literature pertaining to mathematics and computer science, discuss topics in their fields of study and translate simple ESP texts from Croatian into English. Students should also be taught how to individually present a selected topic in English.

Prerequisites. English for mathematics / computer science students I

Course contents.
History of mathematics: Ancient mathematics, Greek mathematics, Medieval and Renaissance mathematics, Islamic and Indian mathematics, Mathematics since the 16th century (17th-20th century), Current mathematics. Number systems. Algebra. Analytic geometry. Etimology of numbers from 0 to 9. Idioms with numbers 0-9. Fibonacci and Lucas numbers. Thales of Miletus. Ludolph van Ceulen and pi.
Storage devices: Floppies. Hard drives. Basic software: Operating systems. The graphical user interface. A walk through word processing. Spreadsheets. Databases. Faces of the Internet. Creative software: Graphics and design. Desktop publishing. Multimedia. Jobs in computing. Computers tomorrow.
Grammar: Principles and techniques used in writing an abstract of a scientific paper. Revision of tenses. Sequence of tenses. Noun Clauses. Questions. Polite questions. Question tags. Reported speech. Reported questions. Articles. Compounds. Word formation. Prepositions.

Teaching methods and student assessment. This course is organised through seminars which are obligatory for all students. Various audio-visual teaching aids are used in the course (LCD, PC, DVD), as well as numerous professional journals and books available in the Department’s library. From time to time students are assigned homework or small project tasks, and every student should individually present a selected ESP topic, which altogether affects their final grade. Students’ knowledge is continuously assessed by four tests, two per each semester, and the oral part of the examination takes place at the end of academic year.

Literature:
Recommended literature:
[1] I. Ferčec, A Course in Scientific English: Mathematics, Physics, Computer Science, Odjel za matematiku/Elektrotehnički fakultet, Osijek, 2001
[2] R. Murphy, English Grammar in Use, CUP, Cambridge, 1999
Additional literature:
[3] C. Clapham, The Concise Dictionary of Mathematics, OUP, Oxford, 1996
[4] Oxford Dictionary of Computing (ed. V. Illingworth), OUP, Oxford, 1996
[5] E. Remacha, Infotech - English for Computer Users, CUP, Cambridge, 2002
[6] Scientific and professional papers from the fields of mathematics and computer science

Mathematics of finance and actuarial mathematics M008 (2+0+2) - 4 ECTS credits

Course objective. Students will learn basic concepts (terms, idea, knowledge), symbols and principles of mathematics of finance and actuarial mathematics through lectures, tutorials and special assignments.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
I Mathematics of finance.
The idea of interest. Simple and compound interest. Effective and nominal rate of interest. Discount rate. Accumulation factors. Present values. The force of interest. Present value of cash flows. Valuing cash flows. Interest income. The equation of value and the yield on a transaction. Annuities-certain: present value and accumulation. Deferred, increasing, continuously payable annuities. General loan schedule. Interest payable m times a year. Annuities payable m times a year. Discounted cash flow. Capital redemption policy. The Zillmerized reserve.
II Actuarial mathematics.
The mortality tables (basic function and relationship). The force of mortality. Approximation of the force of mortality. Some simple mortality laws. Selected and ultimate mortality tables. Pure endowment. Life annuities (whole, temporary, deferred). Present value and accumulation. Whole life insurance. Term life insurance. Endowment insurance. Net and gross premium. Life annuities payable m times a year. Premiums payable m times a year. Policy value. Premium reserve.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. Exercises are auditory and laboratory, at which students use Mathematica and/or MatLab software packages. Students may take an examination only after having attended all lectures and exercises. The final examination consists of the written and the oral part. Students may take tests during the semester which replace the written part of the final examination. Students may also prepare special assignments during the semester which may add a certain number of points to their final grade.

Literature:
Recommended literature:
[1] J. J. McCutcheon, W. F. Scott, An Introduction to the Mathematics of Finance, Institute and Faculty of Actuaries, Butterworth - Heinemann, 1986
[2] A. Neill, Life contigencies, Heinemann, 1977
Additional literature:
[3] M. Crnjac, D. Jukić, R. Scitovski, Matematika, Ekonomski fakultet, Sveučilište u Osijeku,
Osijek, 1994
[4] H.U. Gerber, Life Insurance Mathematics, Springer-Verlag Berlin Heidelberg and Swiss Association of Actuaries Zürich, 1990
[5] V. Hari, Financijska matematika, Matematički odjel, Zagreb, 2001
[6] E. Caprano, A. Gierl, Finanzmathematik, Verlag Franz Vahlen, München, 1992
[7] L. Kruschwitz, Finanzmathematik, Verlag Franz Vahlen, München, 1989
[8] B. Relić, Gospodarska matematika, Računovodstvo i financije, 1996

Financial markets E004 (2+0+2) - 3 ECTS credits

Course objective. In this course students should acquire fundamental knowledge of how the financial system and its markets function. Basic participants and their influence on interest rates and security prices will be considered. Students should solve basic categories in financial systems. In seminars they should analyse stock prices and interest rates and calculate yields for these investments.

Prerequisites. Macroeconomics.

Course contents.
The economy and the financial system. The role of markets in the economic system. Type of markets. Financial markets and the financial system. Types of financial markets. The dynamics of the financial system.
Financial assets, money and financial transactions. The creation of financial assets. Lending and borrowing in the financial system. Money as a financial asset. Types of financial transactions.
Interest rates in the financial system. Functions of the rate of interest in the economy. The classical theory of interest rates. The liquidity preference theory. The loanable fund theory.
Relationship between interest rates and security prices. Units of measurement for interest rates and security prices. Measurement of yield on a loan or security. Yield-price relationships.
Inflation, yield curve, duration and default risk influence on interest rate.
The money market. Characteristics of the money market. The interest rates in the money market. Money market securities.
Bond market. Principal features of corporate bonds. Basic characteristics of corporate bonds. Yields on corporate bonds.
Stock market. Characteristics of stocks. Stock exchanges.

Teaching methods and student assessment. Students are obliged to attend lectures and seminars. They will be continuously assessed during the semester through tasks and two tests. The final examination consists of the written and the oral part.

Literature:
Recommended literature:
[1] B.Novak, Financial markets and institution. Faculty of Economics in Osijek, Osijek, 2005
[2] S.Peter Rose, Money and Capital Markets. Homewood Il., Boston, 1989
[3] V.Veselica Financial system in economy. Inženjering biro, Zagreb, 1995

Functions of several variables M009 (2+2+0) - 6 ECTS credits

Course objective. In this course students are informed about differential calculus and integral calculus of functions of several variables and of vector functions. Situations in which a geometric view helps are primary analysed, i.e. real functions of two or three variables, and the functions from R in R2 and R3. Lectures introduce and analyse basic notions, which are illustrated by examples, while during exercises students adopt corresponding techniques of approaching particular concrete problems and solving them.
Prerequisites. Differential calculus, Integral calculus, Linear algebra I.

Course contents.
1. Real functions of several variables. Space Rn . Level-curve and level-surface. Limit and continuity.
2. Partial derivatives and differentiability of functions of several variables. Partial derivatives of implicit functions and composite functions. Partial derivatives and differentials of higher order.
3. Vector functions. Vector function of one variable – derivative and integrating. Differentiability of vector function of several variables; Jacobi’s matrix.
4. Applications of differential calculus of functions of several variables. Equation of tangent plane to the surface. Taylor’s formula. Extrema and conditional extrema.
5. Multiple integrals. Double integral – notion, properties, calculation, substitution of variables (polar coordinates), applications. Triple integrals (cylindrical and spherical coordinates).
6. Line integrals (of the first and the second kind). Notion, properties, calculation, applications.
7. Surface integrals (of the first and the second kind). Notion, properties, calculation, applications.
8. Scalar and vector fields. Directional derivative of a scalar field. Gradient of a scalar field. Divergence of a vector field. Rotation (curl) of a vector field. Theorem of Gauss-Ostrogradsky. Stokes’ theorem.

Teaching methods and student assessment. Lectures and exercises are obligatory for all students. During the semester students can take tests that can replace the written examination. The final examination consists of both a written and an oral part and can be taken after the completion of lectures and exercises.

Literature:
Recommended literature:
[1] S.Kurepa, Matematička analiza 3: Funkcije više varijabli, Tehnička knjiga, Zagreb, 1984
[2] P.Javor, Matematička analiza 2, Element, Zagreb, 2000
[3] Š.Ungar, Matematička analiza u Rn, Golden marketing-Tehnička knjiga, Zagreb, 2005
[4] B.P.Demidovič, Zadači i upražnjenja po matematičeskomu analizu, FM Moskva, 1963
Additional literature:
[5] G.N.Berman, Zbornik zadač po kursu matematičesko analiza, Nauka, Moskva, 1972
[6] S.Lang, Calculus of Several Variables, Springer, New York, 1987
[7] M.Lovrić, Vector Calculus, Addison-Wesley Publ.\ Ltd., Don Mills, Ontario, 1997

Geometry of plane and space M010 (2+3+0) - 7 ECTS credits

Course objective. The objective of the course at the introductory level based on geometry of plane and space is to make students familiar with fundamentals of linear algebra.

Prerequisites. None.

Course contents.
1. Vectors in plane and space. Operations with vectors. Linear dependence and independence of vectors. Basis of vector spaces. Coordinate system. Norm of vectors. Distance between two points. Cauchy - Schwarz - Buniakowsky inequality. Vector dot (scalar) product. Direction cosine. Projection of vector to the straight line and plane. Gramm - Schmidt orthogonalization process.
2. Square matrix of the second and third order. Square matrix of the second and third order and their determinants. Orientation  right and left basis and coordinate systems. Vector cross product. Algebraic properties of the vector product. Geometrical properties of the cross product. Multiple vector-vector product. Jacobi identity. Straight line and plane in space.
3. Linear operators in plane. Examples of operators: axial symmetry, central symmetry, homothety, orthogonal projection, rotation. Basic properties of the linear operator. Operations with linear operators  vector space L(X(M)). Products and power of the linear operator. Matrix of the linear operator. Algebra of the matrix of the second order. Contraction and dilatation of the plane  eigenvectors and eigenvalues of the linear operator. Symmetric linear operator in the plane. Orthogonal linear operator in plane. Diagonalization of the symmetric linear operator. Quadratic forms. Curves of the second order.
4. Linear operators in space X_0(E). Transfer of all definitions from plane. Existence of eigenvectors and eigenvalues. Orthogonal linear operator. Symmetric linear operator. Surfaces of the second order.
Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students are encouraged to take 4 or more tests that replace the written examination.

Literature:
Recommended literature:
[1] D.Jukić, R.Scitovski, Matematika I, Odjel za matematiku, Sveučilište u Osijeku, Osijek, 2004
[2] S. Kurepa, Uvod u linearnu algebru, Školska knjiga, Zagreb, 1978
Additional literature:
[3] D.Blanuša, Viša matematika I/1, Tehnička knjiga, Zagreb, 1963
[4] D.M. Bloom, Linear algebra and geometry, Cambridge University Press, Cambridge, 1988
[5] L. Čaklović, Zbirka zadataka iz linearne algebre, Školska knjiga, Zagreb, 1992
[6] N.Elezović, Zbirka zadataka. Linearna algebra, Element, Zagreb, 2003
[7] K.W. Gruenberg, A.J. Weir, Linear geometry, Springer Verlag, Berlin, 1977

Oral and written communication Z005 (1+1+0) – 3 ECTS credits

Course objective. Make students familiar with nonverbal and verbal forms of communication. Train students towards better oral and written communication in the forms necessary for everyday and professional activities.

Prerequisites. Not required.

Course contents.
Introduction – culture and communication.
Linguistic skills – speaking, listening, reading, writing, translating. Listening as a skill that can be improved. Types of reading, improvement of reading (speed and understanding).
Oral communication. Talking. What makes a good speaker / errors. Types of utterances.
Written communication. Functional styles. Types of errors.
Linking speaking to writing, reading and listening.

Teaching methods and student assessment. Fundamentals of communications are based upon interactive learning and interpersonal communication which is realised both in lectures and in exercises. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. The final grade is influenced by the following two segments: seminar paper and other students’ communication activities. To the final oral examination students bring portfolios with all contributions written in that year.

Literature:
Recommended literature:
[1] I.Škarić, Temelji suvremenoga govorništva, Školska knjiga, Zagreb 2000
[2] S.Neil, Neverbalna komunikacija u razredu, EDUCA, Zagreb 1994
Additional literature:
[3] S.Težak, Teorija i praksa nastave hrvatskoga jezika, Školska knjiga, Zagreb, 1996
[4] J.Biškup, Osnove javnog komuniciranja, Školska knjiga, Zagreb, 1990
[5] P.Brajša, Umijeće razgovora, C.A.S.H., Pula, 2000
[6] D.Pavić, B.Sirovica, Čitajte brže, pamtite bolje, NIZMH, Karlovac, 1995
[7] A.Pease, Govor tijela, AGM, Zagreb, 2002
[8] K.K.Reardon, Interpersonalna komunikacija, Alineja, Zagreb, 1998

Computer architecture I009 (2+2+0) ) - 5 ECTS credits

Course objective. The goal of this course is to introduce students to microcontroller (microprocessor) programming, to make them understand working principles, embedding and programming of computers in process control, as well as to practice C-a and PIC programming. Lectures focus on working principles and microcomputer programming and their connection in distributed systems. During exercises students deal with techniques referring to programming and design of computers in process control.
Prerequisites. Introduction to computer science, Programming languages.

Course contents.
1. Introduction. Computer organisation: CPU, buses, input/output. Bit-operations. Logic algebra.
2. Programming. Assembler. Programmable logic devices. Linking of assembler and C++ modules. Development System for PIC and Atmel.
3. Interfaces and converters. Process control: digital and analog control. Sensors. Interface between computer and environment. A/D and D/A conversion. Conversion errors.
4. Distributed systems. Microcontroller networks. Modularity, scalability, safety. Multiprocessor systems (bus based, switched, homogeneous, heterogeneous).
5. Multimedial interface. Interface to process. Standard programming tools in industry. Communication protocols.

Teaching methods and student assessment. Lectures and exercises are obligatory. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] J. Iovine, S. Grillo, PIC Microcontroller Project Book, McGraw-Hill Education, New York, 2000
[2] D. W. Smith, PIC in Practice: An Introduction to the PIC Microcontroller, Butterworth-Heinemann, London, 2002
Additional literature:
[3] T. Wilmshurst, An Introduction to the Design of Small-scale Embedded Systems: With Examples from PIC, 80C51 and 68HC05/08 Microcontrollers, Palgrave, New York, 2001
[4] M. A. Mazidi, J. Mazidi, The 8051 Microcontroller and Embedded Systems, PHIPEs, New York, 1999
[5] G. Rizzoni, Principles and Applications of Electrical Engineering, McGraw-Hill, New York, 2000

Graphs MO11 (2+2+0) ) - 6 ECTS credits

Course objective. Make students familiar with basic ideas and methods of graph theory. Basic components will be taught and some of their applications will be given in lectures. In exercises students will master techniques and methods of solving tasks and apply them to real problems. The course is the same for all branches.

Prerequisites. Calculus I, Calculus II , Combinatorial and discrete mathematics.

Course contents.
Basic concepts and motivation. Trees. Eulerian graphs and Hamiltonian cycles. Connectivity. Graph colourings. Planar graphs. Matchings on graphs. Domination on graphs. Digraphs and transport netwoks.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] D. Veljan, Kombinatorika s teorijom grafova, Školska knjiga, Zagreb, 1989
Additional literature:
[2] J.Gross, J. Yellen, Graph Theory and its Applications, CRC Press, Washington, 1999
[3] G. Chartrand, L. Lesniak, Graphs & Digraphs, Chapman & Hall, London, 1996
[4] F.S: Roberts, Graphs Theory and Its Applications to Problems of Society, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1978

Integral calculus M012 (2+3+0) - 7 ECTS credits

Course objective. At the introductory level students should be introduced to fundamental ideas and methods of mathematical analysis, which represent the basis for many other courses. During lectures basic terminology will be explained in an informal way, their utility and applications will be illustrated. During exercises students should master an adequate technique and become trained for solving concrete problems.
Prerequisites. Differential calculus.

Course contents.
1. Riemann integral. An area problem. Definition and properties of the Riemann integral. Integrability of monotone and continuous functions. Mean-value theorem for definite integrals. Newton-Leibniz formula. Indefinite integral. Methods and techniques of integration. Applications of the definite integral: area, volume, rectification, work, moment, center of mass. Improper integral. Numerical integration (rectangular rule, trapezoidal rule, Simpson’s rule).
2. Series. Definition of a series. Convergent series. Tests for convergence and divergence of series.
3. Series of functions. Uniform convergence. Power series. Taylor's series of elementary functions. Exponential and logarithmic function.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students can take 2 tests that replace the written examination.

Literature:
Recommended literature:
[1] W.Rudin, Principles of Mathematical Analysis, Mc Graw-Hill Book Company, New York, 1964
[2] D. Jukić, R. Scitovski, Matematika I, Odjel za matematiku, Osijek, 2000
Additional literature:
[3] S. Kurepa, Matematička analiza 1 (diferenciranje i integriranje), Tehnička knjiga, Zagreb, 1989
[4] S. Kurepa, Matematička analiza 2 (funkcije jedne varijable), Tehnička knjiga, Zagreb, 1990
[5] B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke, Tehnička knjiga, Zagreb, 1986

Financial law and financial science Z004 (2+0+1) - 2 ECTS credits

Course objective. Students will become familiar with basic principles and models of the financial law and financial science. State revenues and incomes will also be analysed, as well as instruments of financing. Since the Department of Mathematics envisaged the branch Financial and business mathematics as giving students knowledge of this field from various aspects, the objective of this course is to supplement the study programme by providing fundamental knowledge in the field of law and financial science.

Prerequisites. Not required.

Course contents.
1. General part. State economy. Public finances. Financial law (status-financial legal standards, substantive-financial legal standards, formally-financial legal standards). Subject of the study of the contemporary financial science. Satisfying public needs.

2. State revenues. Generally about incomes. Kinds of state revenues. Fiscal incomes. Legal basis for the acquisition of income. Taxes. The concept and characteristics of taxes. The tax terminology – elements of taxation. Taxpayer. Base tax. Tax rate. Border of taxation. Justification of levying taxes. Aims of taxation. Effects and functioning of taxes. Tax evasion, tax shifting and double taxation. Tax division. Principles of taxation. The tax system. Taxation system in the Republic of Croatia. Taxation of income, Taxation of profit. Contemporary economic theory and practice of income taxation. Financing of the units of local self-government. Purchase tax. Value added tax. The single purchase tax, excise duties, excises. Rights and real property transfer tax and. Tax on inheritances and gifts. Surveillance and controls. The new system of state administration. Financial police. Government audit. Commercial revision. Other public revenues. Customs - the customs system of the Republic of Croatia. Contributions. Fees. Concept of fees in the Republic of Croatia. Parafiscal incomes. Nonfiscal incomes. Financing local and regional self-government.

3. Public loan. The concept of public loan and its characteristics. Kinds of public loans. Conversion and reprogramming of public loans.

4. Public expenditures. Concept and characteristics of public expenditures. Kinds of state expenditures. Principles of public expenditures. Causes of the growth of public expenditures. Structure of public expenditures.

5. Instruments of financing. Budget. Concept, development and characteristics. Legal nature of the budget. Budget principles. Calculating and passing the budget. Budget revision. Surveillance and budgetary control. Funds.

6. Monetary law. Types of banks. Banking operations. Bank system of the Republic of Croatia. Loss of monetary souvereignity. International monetary institutions.

Teaching methods and student assessment. All students are obliged to attend lectures and exercises. Students are occasionally assigned homework which influences their final grade. They should also prepare a seminar paper and present it to other fellow students. The final examination that can be taken at the semester end consists of a written and an oral part.

Literature:
Recommended literature:
[1]V.Srb, R.Perić, Financiranje javnih potreba, Pravni fakultet, Osijek, 1999
[2]B.Jelčić, Financijsko pravo i financijska znanost, Zagreb, 1998
Additional literature:
[3]B.Jelčić, O.Lončarić – Horvat, J.Šimović, H.Arbutina, Financijsko pravo - posebni dio, Zagreb, 1994
[4]D. C. Nice: Public Budgeting, Washington State University, 2002

Equations of mathematical physics M013 (1+1+0) - 3 ECTS credits

Course objective. Introduce students to basic applications of methods in simple mathematical models. Students will be able to use basic results of mathematical physics, which will allow them to apply numerical methods for calculation in some simple mathematical models. Dynamical systems with one and more than one degree of freedom will be considered.

Prerequisites. First-cycle degree study programme in mathematics.

Course contents.
1. Equilibrium equations. Structures in equilibrium with finite degrees of freedom. Positive definitness and minimum principles. Structures in equilibrium with rigid connections.
2. Energy approach to the equilibrium problem. Estimate of the equilibrium for the symmetric chain. Stationary flow in electrical networks. Heat transfer. Truss.
3. Oscillations. Small one-dimensional oscillations. Oscillations with more degrees of freedom. Small oscillations and eigenvalue problem (eigenvalues and dynamical systems).
4. Eigenvalue problem. Some properties of the eigenvalue problem. Practical solving of the eigenvalue problem. Nonstationary heat transfer. Damped oscillations.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. During exercises students will become trained for solving concrete problems from the fields of biology, chemistry, physics and engineering by using ready-made software packages or by making their own programmes. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] I.Aganović, K.Veselić, Uvod u analitičku mehaniku, Matematički odjel PMF-a, Zagreb, 1990
[2] I.Aganović, K.Veselić, Matematičke metode i modeli, Odjel za matematiku, Sveučilište J.J. Strossmayera u Osijeku, in preparation.
Additional literature:
[3] G.Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press, Wellesley 1986
[4] J.W.Demmel, Applied Numerical Algebra, SIAM, Philadelphia, 1997
[5] N. Truhar, K. Veselić, Optimizing the solution of the Lyapunov equation, Seminarberichte aus dem Fachbereich Mathematik, Fernuniversitaet Hagen 73 (2002)
[6] N. Truhar, K. Veselić, On some properties of the Lyapunov equation for damped systems, Mathematical Communications. Vol. 9. No.2. 189.--197 (2004)

Combinatorial and discrete mathematics M014 (2+2+0) - 5 ECTS credits

Course objective. Make students familiar with basic structures and methods of combinatorial and dicrete mathematics. Basic components will be taught and some of their applications will be given in lectures. In exercises students will master techniques and methods of solving tasks and apply them to real problems. The course is the same for all branches.

Prerequisites. Calculus I, Calculus II.

Course contents.
Dirichlet principle and generalisations. Basic rules of recount. Permutations on sets. Combinations on sets. Permutations and combinations on multisets. Binomial and multinomial coefficients. Some linear recurrences. Fibonacci numbers. Inclusion - exclusion principle. Generating functions. Recurrence and generating functions. Basic concept of graph theory. Cycles and trees.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] D. Veljan, Kombinatorika s teorijom grafova, Školska knjiga, Zagreb, 1989
[2] D. Veljan, Kombinatorna i diskretna matematika, Algoritam, Zagreb, 1989
Additional literature:
[3] J. Anderson, J. Bell, Discrete Mathematics with Combinatorics, Prentice Hall, New York, 2000
[4] J. Matoušek, J. Nešetril, Invitation to Discrete Mathematics, Oxford University Press, Oxford, 1998

Complex analysis M015 (2+2+0) - 6 ECTS credits

Course objective. Today necessary, classical and relatively simple theory of functions of complex variable can be presented in a such a way that a student adopts it as a completed unity as well as a tool for solving a series of problems in applications.

Prerequisites. Differential calculus, Integral calculus.

Course contents.
Complex numbers and elementary functions. Polynomials, roots, exponential functions, logarithms, trigonometric and hyperbolic functions.
Analyticity. Cauchy-Riemann's conditions. Conformal mapping. Moebius transformation, fields around cylinders. Streaming around plane wing. Harmonic functions.
Series of functions. Series of elementary functions. Taylor series. Radius of convergence.
Integral of the function of complex variable. Singular points and Cauchy's theorems. Laurent series. Residue theorems. Calculation of integrals.
Laplace transformation. Basic properties. Mellin formula. Calculation of inverse transformation by means of residues.
Systems of differential equations. Systems of linear homogeneous equations with constant coefficients. Stability and asymptotics.

Teaching methods and student assessment. Complex analysis related exercises should be mostly auditory. Strict proofs will be mainly avoided. Lectures and exercises are obligatory. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] H. Kraljević, S. Kurepa, Matematička analiza 4/I, Funkcije kompleksne varijable, Tehnička knjiga Zagreb,1986
[2] R.Galić, Funkcije kompleksne varijable za studente tehničkih fakulteta. Osijek, 1994
[3] I. Ivanšić, Funkcije kompleksne varijable. Laplaceova transformacija. Liber, Zagreb, 1978
Additional literature:
[4] M.A. Lavrentjev, B.V. Šabat, Metody teorii funkcii kompleksnogo peremennogo. Fizimatgiz, Moskva, 1958
[5] Ž. Marković, Uvod u višu analizu II. Školska knjiga Zagreb, 1952
[6] A.I. Markuševič, Teorija analitičeskih funkcij, 1-2, Nauka, Moskva, 1967

Concrete mathematics M016 (2+2+0) - 6 ECTS credits

Course objective. To develop techniques for discrete objects in analogy with techniques for continuous objects. Concrete mathematics is a blending of CONtinuous and disCRETE mathematics. More precisely, it is a controlled manipulation of mathematical formulas using a collection of techniques for solving problems. The course is important in computer science for the analysis of algorithms, since it deals with a collection of fundamental mathematical facts. (A quote by I.M.Gelfand says: “Theories appear and vanish but examples remain”).

Prerequisites. A certain level of mathematical maturity is necessary, no knowledge of combinatorics is required, since everything is developed from the first principle.

Course contents.
Basic notations. Reccurent problems (Towers of Hanoi , lines in a plane). Sums (notations for sums, sums and recurrences, transformations of sums, multiple sums, general summation methods, indefinite/definite sums, partial summation). Integer functions (floor and ceiling functions); "mod" as a binary operation, floor and ceiling sums. Binomial coefficients (Basic identities, basic methods, special methods, generating functions, hypergeometric functions, partial hypergeometric sums – Gosper's algorithm, mechanical summation).

Teaching methods and student assessment. Lectures are based on selected topics from the [1] (containing a number of additional topics accesible to those students who wish to broaden their knowledge). Exercises will be carefully selected from [1] (and given to students in advance). Book [1] includes more than 500 exercises, divided into six categories (complete answers are provided for all exercises, except for research problems, making the book particularly valuable for self-study). From time to time summation techiques will be illustrated by using packages MAPLE and MATHEMATICA. The examination will be written and oral. Student’s knowledge is continuously assessed during the semester by means of tests and homework. Tests can replace the written part of the final examination. Students are also encouraged to prepare seminar papers which influence the final grade.

Literature:
Recommended literature:
[1]Graham, Ronald L.; Knuth, Donald E.; and Patashnik, Oren. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994
Additional literature:
[2] Comtet, Louis. Advanced Combinatorics: The Art of Finite and Infinite Expansions, Dordrecht, Netherlands: Reidel, 1974
[3] Knuth, Donald E. The Art of Computer Programming,Volume 1 Fundamental Algoritms Reading, Mass. : Addison-Wesley,1997
[4]. Petkovšek ,M.,Wilf , H.S. , Zeilberger D. A=B, Peters, AK, Limited, 1996
[5] Rosen, Kenneth H. (Ed.). Handbook of Discrete and Combinatorial Mathematics. Boca Raton, FL: CRC Press, 2000
[6] Ross, Sheldon M. Topics in Finite and Discrete Mathematics. Cambridge, England: Cambridge University Press, 2000
[7] Stanley, Richard P. Enumerative Combinatorics, Vol. 1. Cambridge, England: Cambridge University Press, 1999 ( Enumerative Combinatorics, Vol. 2)
[8] J. H. Van Lint and R.M. Wilson (CU, QA164 .L56 1992), A Course in Combinatorics, Paperback - (July 1992), Cambridge Univ Press.
[9] Veljan D.: Kombinatorna i diskretna matematika,. Zagreb, Algoritam, 2001

Constructive geometry M017(1+1+0) – 3 ECTS credits

Course objective. Most important topics of Euclidean geometry from the point of constructive methods are treated in this course with necessary theoretical preliminaries. Most of these subjects are covered from the analytical and synthetical point of view in courses Analytic geometry and Elementary geometry. Special stress in this course is put on the application of constructive methods in geometric parts of teaching in primary and secondary schools. During exercises students use computer software with geometry contents.

Prerequisites. Selected topics from the courses Analytic geometry and Elementary geometry.

Course contents.
1. Euclidean constructions. Constructive task. Methods of solving. Algebraic method. Method of intersection. Method of transformation.
2. Isometries of Euclidean plane. Axes and central symmetries. Translations and rotations. Glide symmetries. The group of isometries and some of its subgroups.
3. Homothety and similarity. Power of the point with respect to the circle. Potential axis and potential center. Inversion.
4. Projective mappings of the Euclidean plane. Double ratio. Perspective collineations. Perspective affinity.
5. Conic sections. Ellipse, parabola and hyperbola. The plane intersection of the cone and cylinder. Pascal and Brianchon theorem. Conic sections as the perspective images of the circle. Ellipse as the perspective affine image of the circle.
6. Constructions by means of limited instruments. Constructions by means of the ruler. Constructions in a limited part of a plane. Constructions by means of the ruler with the given auxiliary figure. Steiner constructions. Construction by means of two-side ruler. Hilbert-Bachman constructions. Mohr-Mascheroni constructions.
7. Non-elementary constructions. Constructibility by means of a ruler and a compass. Duplication of the cube and angle trisection. Non-elementary solutions of the duplication of the cube and angle trisection. Quadrature of the circle. Approximative solutions of three classical problems.
8. Elements of descriptive geometry.

Teaching methods and student assessment. Lectures are auditory. Exercises are performed in groups in the computer lab using computer software with contents in the field of geometry. The final examination consists of both the written and the oral part.

Literature:
Recommended literature:
[1] D. Palman, Geometrijske konstrukcije, Element, Zagreb, 1996
Additional literature:
[2] D. Palman, Trokut i kružnica, Element, Zagreb, 1994
[3] B.I.Argunov, M.B.Balk, Elementarnaja geometrija, Prosveščenie, Moskva 1996 (Chapter V, Geometričeskie postroenija, pp. 265-354)

Cryptography and computer system security I004 (2+2+0) - 6 ECTS credits

Course objective. Teach basic notions in cryptography and protection of computer systems. Exercise projecting of cryptography schemes. Make students familiar with multi-user and multitask operating systems (UNIX, Linux, XP). Make students familiar with notions from cryptography and protection of operating systems. Students will learn various cryptography schemes and implement them as well as analyse security of operating systems and databases.

Prerequisites. First-cycle degree study programme in mathematics.

Course contents.
1. Introduction. Cryptography. Modelling, design and verification of security protocols.
2. Data encryption. Pseudo random number generators. Encryption schemes. RSA.
3. Authentication. Key management. PKI - public-key infrastructure. Digital signatures.
4. Models of security control. Model analysis using Petri nets. Unreliable parts of system.
5. Protection. Multi-level Secure Databases. Network security and safety measures. Firewall.

Teaching methods and student assessment. Lectures and exercises are mandatory. Student’s knowledge is regularly assessed during the semester by means of homework and tests. The final examination consisting of a written and an oral part, is taken at the end of the semester.

Literature:
Recommended literature:
[1] D. R. Stinson: Cryptography. Theory and Practice, CRC Press, Boca Raton, 1996 (first edition), 2002 (second edition).
[2] N. Koblitz: A Course in Number Theory and Cryptography, Springer-Verlag, New York, 1994
Additional literature:
[3] B. Schneier, Applied Cryptography: Protocols, Algorithms and Source Code in C, John Wiley & Sons Inc., 1995
[4] F. Piper, S. Murphy, Cryptography: a Very Short Introduction, Oxford Paperbacks, 2002
[5] F.L. Bauer, Decrypted Secrets: Methods and Maxims of Cryptology, Springer-Verlag Berlin and Heidelberg GmbH & Co., 2002
[6] B. Schneier, Secrets and Lies: Digital Security in a Networked World, John Wiley & Sons Inc, 2000

Linear algebra I M018 (2+3+0) - 7 ECTS credits

Course objective. Introduction to basic ideas and problems of linear algebra.

Prerequisites. Geometry of plane and space.

Course contents.
I. Matrix Operations
1. Vectors and Linear Combinations. Column vectors. Vector spaces.
2. Linear Operators. Matrices. Composition. Associativity.
3. Dot product. Transpose matrix. Inverses. Right and left inverses.
4. Gauss – Jordan Elimination. Inverse matrices. Elementary matrices. Pivots.
5. Groups. Permutations. Transpositions.
6. Block Matrices. Block multiplication. Block elimination.
II.Vector Spaces and Linear Systems
7. Subspaces. Linear dependence and independence. Nullspace and left nullspace.
8. Homogeneous Systems. Pivot and free variables. Special and complete solutions.
9. Bases and Dimension. The four subspaces. Row space and column space. Direct and orthogonal sums.
10. The Theorem of Rank and Defect. Dimensions of the four spaces. Projections. The Gram – Schmidt process.
11. General Systems. Particular solutions. The complete solution.
12. Particular Cases. Full column rank. Full row rank. Right and left inverses revisited.

Teaching methods and student assessment. Attendance of classes and exercises is obligatory. Knowledge assessment consists of three parts:
1. Points obtained through three preliminary tests held during the semeste
2. Points obtained at the final examination
3. Oral part of the examination

Literature:
Recommended literature:
[1] S. Kurepa., Uvod u linearnu algebru, Školska knjiga, Zagreb, 1987
[2] S. Kurepa, Konačnodimenzionalni vektorski prostori i primjene, Tehnička knjiga, Zagreb, 1967
Additional literature:
[3] K. Horvatić, Linearna algebra, 9. izdanje, Tehnička knjiga, Zagreb, 2003
[4] S. Lang, Introduction to Linear Algebra, Springer – Verlag, 1980
[5] S. Lang, Linear Algebra, Springer – Verlag, 2004
[6] G. Strang, Introduction to Linear Algebra , Cambridge Press, 1998

Linear algebra II M019 (2+2+0) - 6 ECTS credits

Course objective. Introduction to basic ideas and problems of linear algebra.

Prerequisites. Linear algebra I.

Course contents.
I. Determinants
1. The Pivot Formula. Definition of determinants as a linear function of rows separately. Elementary properties.
2. The Permutation or Big Formula. The cofactor formula. The Cramer’s rule. The Binet – Cauchy theorem.
II. Linear Operators
3. Change of Bases. Similar matrices.
4. Adjoint Operators. Dot products in new bases. The four subspaces of an operator.
5. Eigenvalues and Eigenvectors. The invariant subspaces. Diagonalising a matrix. Jordan matrices.
6. Symmetric Matrices. Positive definite and semidefinite matrices. Quadratic forms.
7. Complex Eigenvalues and Eigenvectors. Orthonormal matrices. Complex dot product.
8. Unitary and Hermitian Matrices. Diagonalizing a Hermition Matrix.
III. Matrix Polynomials
9. The Characteristic Equation and Characteristic Polynomial. The Hamilton – Cayley theorem.
10. The Minimal Polynomial. Definition and properties. Applications.

Teaching methods and student assessment. Attendance of classes and exercises is obligatory. Knowledge assessment consists of three parts:
1. Points obtained through three preliminary tests held during the semester
2. Points obtained at the final examination
3. Oral part of the examination

Literature:
Recommended literature:
[1] S. Kurepa., Uvod u linearnu algebru, Školska knjiga, Zagreb, 1987
[2] S. Kurepa, Konačnodimenzionalni vektorski prostori i primjene, Tehnička knjiga, Zagreb, 1967
Additional literature:
[3] K. Horvatić, Linearna algebra, 9. Izdanje, Tehnička knjiga, Zagreb, 2003
[4] S. Lang, Introduction to Linear Algebra, Springer – Verlag, 1980
[5] S. Lang, Linear Algebra, Springer – Verlag, 2004
[6] G. Strang, Introduction to Linear Algebra – Cambridge Press, 1998

Linear programming M020 (2+1+1) - 4 ECTS credits

Course objective. To introduce students with observation, modelling, solving and interpretation of real problems of optimisation. To analyse the basic method for solving linear programming problem – simplex method and to apply it as much as possible to real problems from practice, using thereby a computer and software Winqsb. Stress will be placed on observing a problem, modelling and interpreting of results.

Prerequisites. First-cycle degree study programme in mathematics.

Course contents.
1. Introduction: information about problems in practice, modelling a linear programming problem. Defining determination variables, objective function and constraints (a set of feasible solutions and its properties). A standard problem of maximum.
2. Graphical solving of linear programming problem (the problem of minimum and maximum). Example of unique optimal solution, example of alternative optimal solution, example when the set of feasible solutions is empty, example when the set of feasible solutions is unbounded.
3. Simplex method. Standard problem of maximum. Charnes' M-procedure.
4. Dual problem. Connections between primary and dual problem. Interpretation.
5. Sensibility analysis by coefficients of objective function (with basic and nonbasic variables) and by coefficients of the right-hand side of constraints. Interpretation.
6. Transport problem. Assignment problem. Problems on nets (problem of the least path, problem of minimum spanning tree, problem of maximum flux).
7. Dynamic programming.
8. Continuous multicriterial programming.

Teaching methods and student assessment. Lectures and exercises are obligatory. The course is carried out in the form of theoretical classes, by solving tasks and cases from practice during exercises, as well as by working on computers and using software package Winqsb. Students' knowledge is assessed by means of homework, a written and an oral part of examination.

Literature:
Recommended literature:
[1] K.G. Murty, Linear and Combinatorial Programming, John Wiley & Sons, Inc., 1983
[2]L.Neralić, Uvod u matematičko programiranje 1, Element, Zagreb, 2003
Additional literature:
[3] G. Sierksma, Linear and Integer Programming, Marcel Dekker, Inc., Nemhauser, 1999
[4] D.Kincaid, W.Cheney, Numerical Analysis, Brooks/Cole Publishing Company, New York, 1996
[5] A.Schrijver, Theory of Linear and Integer Programming, John Wiley & Sons, Inc., NY, SAD, 1999

Macroeconomics E005 (2+1+0) + (2+1+0) - 8 ECTS credits

Course objective. The course aims to develop understanding of the economy’s behaviour over time, exploring the causes of fundamental macroeconomic problems and evaluating the effects of macroeconomic policy (primarily monetary and fiscal) on the economy’s behaviour and performance. This course encourages the application of system and model approach in the analysis of economic activities, problems and evaluation of macroeconomic performance and policy.

Course contents.
1. An introduction to macroeconomics. Macroeconomic performance. Economics as a science.
2. Organisation and dynamics of an economy. Measures of economic activities. Introduction to macroeconomic policies.
3. Macroeconomic problems. Business cycles. Unemployment. Inflation. Deficit.
4. Macroeconomic theories and models. AS-AD model. AD and the goods market. AE model. Classical model. Money and financial sector. Money market. IS-LM model. AS and the labor market. Exogenous supply shocks. The effects of fiscal policy. The effects of monetary policy. Unemployment and inflation.
5. Open economy macroeconomics. Open economy models. Balance of payments.
6. Macroeconomic policy: synthesis and extensions.
7. Economic growth.

Teaching methods and student assessment. Class attendance is mandatory. Students are encouraged to actively participate in class discussions and use Internet. Students’ knowledge is assessed continuously through in-class participation and tests. The final examination is composed of an oral and a written part.

Literature:
Recommended literature:
[1] Đ. Borozan, Makroekonomija, EFO, Grafika d.o.o., Osijek, 2001 (new edition in press)
Additional literature:
[2] Đ. Borozan, Priručnik iz makroekonomije, EFO, Grafika d.o.o., Osijek, 2001
[3] Đ. Borozan, Prezentacijski materijali iz makroekonomije, EFO, Osijek, 2005
[4] O. Blanchard, Makroekonomija, Mate, Zagreb, 2005
[5] M. Babić, Makroekonomija, XII. izdanje Mate d.o.o., Zagreb, 2004
[6] N.G. Mankiw, Principles of Macroeconomics, the Dryden Press, Fort Worth, 1998

Mathematical biology M021 (1+0+1) - 2 ECTS credits

Course objective. The course is focused on studying mathematical models used for description and research of various phenomena in biology. These and/or similar models are used in other fields such as medicine, psychology, ecology, etc.

Prerequisites. Bachelor level degree in mathematics. Ordinary differential equations.

Course contents.
Continuous and discrete population models for single species. Continuous models for interacting populations. Discrete growth models for interacting populations. Enzyme kinetic. Biological oscillators and switches. Epidemic models and the dynamics of infectious diseases.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students are encouraged to prepare a seminar paper, which, if successful, affects the final grade and can replace the written examination.

Literature:
Recommended literature:
[1] J.D. Murray, Mathematical Biology, Springer, Berlin, 1993
Additional literature:
[2] D. Burghes, M. Borrie, Modelling with Differential Equations, Ellis Horwood Ltd, Chichester, 1982
[3] D. Mooney, R. Swift, A Course in Mathematical Modelling, Mathematical Association of America, 1999
[4] M. S. Klamkin (Ed.), Mathematical Modelling: Classroom Notes in Applied Mathematics, SIAM, Philadelphia, 1987

Mathematical logic M022 (2+2+0) - 6 ECTS credits

Course objective. At the introductory level make students familiar with ideas and methods of mathematical logic. Basic components will be taught and some of their applications will be given in lectures. In exercises students will master techniques and methods of solving tasks and apply them to real problems. The course is the same for all branches.

Prerequisites. Calculus I and Calculus II.

Course contents.
Propositional logic: Introduction. Syntax. Semantics. Normal form. Theorem of compactness. Tests of worthiness. Adjustment of proposition. Consistency. Natural deduction. Some other axiomatics of propositional logic.
First order logic: Introduction. Syntax. Interpretations and models. Main test. Adjustment of theories of first order. Theorem of completeness. Some examples of first order theory.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] M. Vuković, Matematička logika 1, Zagreb, 1999
Additional literature:
[2] E. Mandelson, Introduction to mathematical logic, D. von Nostrand Company, 1987
[3] L.A. Kalužnin, Što je to matematička logika, Školska knjiga Zagreb, 1975
[4] V. Devide, Matematička čitanka, Školska knjiga Zagreb, 1991

Mathematical theory of computer science I013(2+2+0) - 4 ECTS credits

Course objective. Familiarise students with fundamentals of language theory as well as syntax and semantic approaches to analysis of programming languages.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
Syntax. Languages. Regular expressions and regular languages. Arden’s Lemma. Residuals. Characterisation of regular languages. Deterministic Finite Automata (DFA). Languages recognised by DFA. Characterisation of DFA. Pumping Lemma for Regular Languages (RL). Nondeterministic Finite Automata (NFA). NKA=DKA. Right Linear Grammar and Languages. Context Free Languages (CFL). Closure properties of CFL. Closure properties of RL. Derivation Tree. Pumping Lemma for Right Linear Languages. Push Down automata (PDA).
Semantics. Introduction. Operational semantics of arithmetic and logic expressions. Operational semantics of while programming language.

Teaching methods and student assessment. Lectures and exercises are mandatory. Students' knowledge is assessed by means of tests. The final examination which consists of a written and an oral part takes place at the end of the semester.

Literature:
Recommended literature:
[1] J. E. Hopcroft, R. Motwani, J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison–Wesley, 2001, Reading, Massachusetts, Boston
[2] Moll, Arbib, Kfoury, Introduction to Formal Language Theory, Springer Verlag 1988, New-York, Heidelberg, Berlin
Additional literature:
[3] G.Winskel, The Formal Semantics of Programming Languages, MIT Press 1993
[4] K.R.Apt, E.-R.Olderog, Verification of Sequential and Concurrent Programs, Springer, Berlin, 1991

Mathematical finance M023 (2+2+0) - 8 ECTS credits

Course objective. The course objective is to introduce students to the fundamental concepts and methods in modern financial mathematics. Students will be introduced to theory of martingales and stochastic differential equations. Attention will be placed on the applied examples and the intuitive and informal understanding of models and theory. In the practical part of the course students are supposed to learn the necessary techniques and solve concrete problems using computers.
Prerequisites. Probability. Statistics. Random processes.

Course contents.
1. Discrete time martingales Conditional expectation. Random walk. Definition and basic properties of martingales. Doob's inequalities. Stopping times. Martingale convergence theorem. Uniform integrability. Examples.
2. Continuous time martingales. Brownian motion. Covariance and characteristic function. Basic properties.
3. Stochastic integrals and Ito's formula. Comparison with Riemann integral. Ito's integral. Basic properties. One-dimensional Ito's formula. Examples. Multidimensional Ito's formula. Local time of Brownian motion.
4. Martingale representation theorem.
5. Stochastic differential equations. Weak and strong solutions. Diffusion processes.
6. Transformations of diffusion processes. Feynman-Kac formula. Cameron-Martin formula.
7. Black-Scholes model. European call option. Arbitrage. Completness. Examples.

Teaching methods and student assessment. Teaching will be performed in a series of lectures, exercise classes and practical classes in the computer lab. Grading will be based on the final examination (oral or written), homework assignments during the semester and/or project work.

Literature:
Recommended literature:
[1] D.Williams: Probability with martingales. Cambridge University Press, Cambridge, 1991
[2] J.M.Steele: Stochastic calculus and financial applications. Springer-Verlag, New York, 2001
[3] M.Baxter,A.Rennie: Financial Calculus: An Introduction to Derivative Pricing. Cambridge University Press, 1996
Additional literature:
[4] B.Øksendal: Stochastic differential equations. An introduction with applications. Fifth edition. Springer-Verlag, Berlin, 1998
[5] F.den Hollander,M.Loewe,H.Maassen: Stochastic analysis. Unpublished manuscript.
[6] A.Etheridge: A Course in Financial Calculus. Cambridge University Press. 2002
[7] T.Mikosch: Elementary Stochastic Calculus With Finance in View. World Scientific. 1998
[8] K.L.Chung,R.J.Williams: Introduction to stochastic integration. Second edition. Birkhäuser Boston, Inc., Boston, MA. 1990
[9] T.Bjork: Arbitrage Theory in Continuous Time. Oxford University Press. 1999
[10] J.C.Hull: Options, Futures, and Other Derivatives. Prentice Hall. 5th edition. 2002
[11] P.Kloeden,E.Platen: Numerical Solution of Stochastic Differential Equations. Springer Verlag; 2nd edition. 1995
[12] I.Karatzas,S.E.Shreve: Methods of Mathematical Finance. 1998
[13] I.Karatzas,S.E.Shreve: Brownian Motion and Stochastic Calculus. 1988.
[14] P.J.Hunt,J.E.Kennedy: Financial Derivatives in Theory and Practice. 1998.
[15] L.C.G.Rogers,D.Williams: Diffusions, Markov Processes and Martingales: Volumes 1 and 2. Cambridge University Press. 2000
[16] A.N.Shiryaev: Essential of Stochastic Finance. World Scientific. 1999

Mathematical aspects of electoral systems M024 (1+0+1) - 3 ECTS credits

Course objective. To introduce students to some elementary mathematical aspects of electoral systems, such as evaluation and forming of the electoral systems, models of electoral systems, basic methods of assignments, etc.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
Classification and properties of electoral systems. Well-known paradoxes. Basic properties of electoral methods – majority and proportional system. Over-representation and under-representation. Designing electoral units. Examples of procedures of a social choice (majority, Borda count, dictatorship).

Teaching methods and student assessment. One part of classes refers to classical lecture-type classes with basic notions, characteristics, mathematical aspects and problems of electoral systems explained and seminar paper topics proposed. The other part of classes encompasses presentations of student seminar papers covering topics falling into the scope of mathematical aspects of electoral systems. The final examination consists of a written and an oral part, and a seminar paper, which, if successful, affects the final grade and can replace the oral examination either partially or completely.

Literature:
Recommended literature:
[1] P.G.Cortona et al.: Evaluation and Optimization of Electoral Systems, SIAM, Philadelphia, 1999
[2] A.D.Taylor: Mathematics and Politics – Strategy, Voting, Power and Proof, Springer-Verlag, New York, 1995

Mathematical models M025 (1+0+1) - 3 ECTS credits

Course objective. Through lectures and seminar papers students will become familiar with some classical mathematical models described by ordinary differential equations used in various fields of human activity (physics, engineering, economy, medicine, biology, agriculture).

Prerequisites. Bachelor level degree in mathematics. Ordinary differential equations.

Course contents.
1. Models described by first-order linear differential equations. Exponential growth model. Logistic growth model. Gompertz growth model. Applications (population dynamic, drug absorption, water heating and cooling, rocket flight, Torricelli's law, spread of technological innovations, neoclassical economic growth, exploited fish populations, tumor growth).
2. Models described by second-order linear differential equations. Mechanical oscillations, electrical networks, Testing for diabetes. National economy model.
3. Models described by second-order nonlinear differential. Planetary motions. Chemical kinetics. Pursuit curves.
4. Models described by systems of differential equations. Predator-pray model. Epidemic models. Two-oscillator model. Mathematical theories of war (Richardson's theory of conflict, Lanchester combat models and the battle of Iwo Jima).

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students are encouraged to prepare a seminar paper, which, if successful, affects the final grade and can replace the written examination.

Literature:
Recommended literature:
[1] M.Braun, Differential Equations and Their Applications, Springer, New York, 1993
[2] D.Mooney, R.Swift, A Course in Mathematical Modelling, Mathematical Association of America, 1999
Additional literature:
[3] D.Burghes, M.Borrie, Modelling with Differential Equations, Ellis Horwood Ltd, Chichester, 1982
[4] M.S.Klamkin (Ed.), Mathematical Modelling: Classroom Notes in Applied Mathematics, SIAM, Philadelphia, 1987
[5] I.Ivanšić, Fourierovi redovi. Diferencijalne jednadžbe, Odjel za matematiku, Osijek, 2000
[6] M.Alić, Obične diferencijalne jednadžbe, PMF-Matematički Odjel, Zagreb, 1994

Mathematical practicum M027 (2+0+2) - 6 ECTS credits

Course objective. The objective of the course is to introduce students to methodology of scientific research. After having attended the course and passed the examination students should be able to independently solve a given problem, research literature, write and present their papers in an interesting way.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
Since every year several new topics are introduced, we will mention several topics presented so far: Data generation and presentation. Floating-point arithmetic. Interpolation. Linear and cubic least squares spline. Best L_p (p \geq 1) approximation. L_p (p \geq 1) distance between a point and a straight line and between a point and a curve. Best least squares and best total least squares straight line. Solving special systems of linear equations. LU decomposition of a three-diagonal matrix. Iterative methods for solving large systems of linear equations. Eigenvalue problem. Power method. Solving the equation f(x)=0. Method for solving the system of nonlinear equations. Horner's algorithm. Gauss-Newton method. One-dimensional minimisation. Multiple dimensional minimisation. Golden section search, parabolic interpolation and Brent's method. Application of Nelder-Mead algorithm. Numerical method for solving differential equations. Magic squares. Teaching methods and student assessment. During lectures students are introduced to scientific-research and professional activities by means of small projects. Every topic is dealt with by doing the following: motivation and mathematical elaboration, derivation of basic formulas, laying foundations for a design of a Mathematica or Matlab program, programming and program testing. Exercises are laboratory. They are done by using computers and LCD projectors supported by Mathematica and Matlab software. During classes students can take several tests. Every student is also individually assigned a seminar paper. Students should first study the topic by using some fundamental literature, then search additional literature (books, articles from journals and on the Internet) after which they explain the topic in front of their teachers and fellow students. After that the topic and the way of preparation are defined in detail. Seminar papers should be written in \LaTeX, with an abstract both in Croatian and English, key words in Croatian and English and AMS Mathematical Classification (2000). The text should be divided into sections and subsections, and the cited formulas should be marked appropriately. Literature, which is mentioned at the end of the paper, should be listed in accordance with AMS regulations and cited at least once in the text. Finally, students are obliged to present their papers to teachers and other students. A successful seminar paper replaces the written part of the examination, and during seminar paper presentation in front of all other students, the oral examination takes place. Successful presentation of high quality guarantees a high grade. The paper will be put on the Department's web page and enter into competition for one of the awards (e.g. Rector's Award).

Literature:
Recommended literature:
[1] R.Scitovski, K.Sabo, Matematički praktikum, Odjel za matematiku
[2] R.Scitovski, Numerička matematika, Odjel za matematiku, Sveučilište u Osijeku, Osijek, 2004
[3] The College Mathematical Journal, Mathematical Association of America
[4] Mathematics Magazine, Mathematical Association of America [5] The Mathematical Inteligencer, Springer-Verlag Additional literature:
[6] J.W.Demel, Applied Numerical Linear Algebra, SIAM, Philadelphia, 1997
[7] P.Dierckx, Curve and Surface Fitting with Splines, Oxford Univ. Press, New York, 1993 [8] W.Gautschi, Numerical Analysis: An Introduction, Birkhäuser, Boston, 1997
[9] P.E.Gill, W.Murray and M.H.Wright, Practical Optimization, Academic Press, 1981 [10] G.H.Golub, C.F.vanLoan, Matrix Computations, The J. Hopkins University Press, Baltimore and London, 1989
[11] F.Jare, J.Stoer, Optimierung, Springer-Verlag, Berlin, 2004
[12] D.Kincaid, W.Cheney, Numerical Analysis, Brooks/Cole Publishing Company, New York, 1996 [13] P.Lancaster, K.Salkauskas, Curve and Surface Fitting; An Introduction, Academic Press, London, 1986 [14] Z.Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1996 [15] W.H.Press, B.P.Flannery, S.A.Teukolsky, W.T.Vetterling, Numerical Recipes, Cambridge University Press, Cambridge, 1989
[16] H.R.Schwarz, Numerische Mathematik, Teubner, Stuttgart, 1986 [17] H.Späth, Numerik, Vieweg, 1994 [18] G.W.Stewart, Afternotes goes to Graduate School, SIAM, Philadelphia, 1998 [19] J.Stoer, R.Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, New York, 1993 [20] J.Stoer, R.Bulirsch Numerische Mathematik I,II, Springer-Verlag, Berlin, 1999
[21] L.N.Trefethen, D.Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997

Optimisation methods M028 (2+1+1) - 6 ECTS credits

Course objective. The objective of this course is to make students familiar with the main methods of one-dimensional and multidimensional minimisation with or without constraints. Minimisation methods of nondifferentiable functions will be analysed in particular. Thereby proving theorems will be avoided, except in case of some constructive proofs which themselves refer to the construction of ideas or methods.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. Local and global minimum. Illustrated examples from applications. Convex functions.
2. One-dimensional minimisation. Golden section search, parabolic interpolation and Brent's method. Newton's method and its modifications.
3. Multidimensional minimisation without constraints. Gradient method. Steepest descent method. Newton's method and its modifications. Quasi-Newton methods. Conjugate gradient method. Least squares problems. Examples and applications. Graphical interpretations of an iterative procedure.
4. Multidimensional minimisation without constraints of nondifferentiable functions (Searching methods). Method of coordinate relaxation. Nelder-Mead downhill simplex method. Powell's method. Methods of random search.
5. Nonlinear programming. Motivation and examples. Basic methods.
Teaching methods and student assessment. Lectures will be illustrated by ready-made software packages and graphics using a PC and an LCD projector by means of Mathematica or Matlab. Exercises are partially auditory and partially laboratory, and students will use PCs and an LCD projector by means of the aforementioned software systems. The final assessment consists of both the written and the oral examination that can be taken after the completion of all lectures and exercises. During the semester students are given homework. They can also take 2-4 tests that completely cover course contents. Successful tests replace the written examination. Students are encouraged to prepare seminar papers. Successful seminar papers influence the course final grade.

Literature:
Recommended literature:
[1] C.T.Kelley, Iterative methods for optimization, SIAM, Philadelphia, 1999
[2] P.E.Gill, W.Murray and M.H.Wright, Practical Optimization, Academic Press, 1981
[3] F.Jare, J.Stoer, Optimierung, Springer-Verlag, Berlin, 2004
Additional literature:
[4] J.E.Dennis, Jr, R.B.Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, 1996
[5] J.E.Dennis Jr., J.J.More, Quasi-Newton methods, motivation and theory, SIAM Review, 19(1977), 46-89
[6] Z.Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1996
[7] J.M.Ortega, W.C.Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, SIAM, Philadelphia, 2000
[8] W.H.Press, B.P.Flannery, S.A.Teukolsky, W.T.Vetterling, Numerical Recipes, Cambridge University Press, Cambridge, 1989
[9] R.Scitovski, Numerička matematika, Odjel za matematiku, Sveučilište u Osijeku, Osijek, 2002
[10] J.Stoer, R.Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, New York, 1993

Teaching computer science I005 (2+2+0) ) - 5 ECTS credits

Course objective. To make students familiar with current approaches to lecture structure and organisation, teaching aids, and procedures used in teaching computer science. To teach students how to acquire knowledge on the basis of which they will be able to keep up with a rapid and pervasive development of computer science and communications as well as to introduce new procedures and aids in teaching computer science.

Prerequisites. First-cycle degree program in mathematics.

Course contents.
1. Introduction. Fundamental teaching issues – syllabus, teaching aids, methods of lecture preparation and delivery. Relation between teaching and instructional methodology – teaching content and units, objectives, visualisation methods and basic foreknowledge. Special demands and diversity of computer science teaching in relation to other education areas.
2. Problems in computer science teaching. Comprehensive presentation of topics in computer science and classification into thematic units. Dynamics and pervasiveness as main characteristics of information technologies. Influence of methodological and didactic nonflexibility of other teaching areas to computer science courses, possible solutions. New guidelines referring to computer science curriculum.
3. Methods of computer science teaching. Planning individual lecture content and order of their delivery. Structure and type of a session (lesson/exercise). Teaching methods. Raising pupil’s interest. Principles of didactic theory and their use in teaching computer science. Cybernetics methods. Heuristic, programming and problem-oriented teaching. Analysis and synthesis, analogy, algorithmic approach to problem solution. Adapting computer science content and available teaching aids to psychology and the age of respective pupils. Demands and forms of lecturer’s preparation. Lecture analysis. Continuous assessment of pupil’s progress and talent. Testing the acquired knowledge. Pupil’s independent work.
4. Establishing conditions for computer science teaching. Relation between lecture content, teaching aids and methods. Lecturer’s qualification with respect to fast changes in lecture content and teaching methods. Literature for lecture preparation. Computer classroom equipment, classroom - laboratory. Computer as a teaching aid. Application software for preparation, presentation and distribution of teaching materials (MS Word, PowerPoint), as well as for pupil’s evaluation and assessment (Excel, Access). Internet technology in teaching computer science (FrontPage, WebCT). Media for storage and distribution of teaching materials (CD-R, CD-RW, DVD).
5. Teaching computer science through topics. Adapting methodological and didactic principles to teaching topics. Computer and Internet as teaching aids. Lecture preparation by means of a computer, delivery by using a presentation tool and software environment. Theoretical overview – introduction to topics in computer science, deepening of pupil’s knowledge, examples and solutions as fundamentals of teaching all topics in computer science. Computer system and personal computer. Network and Internet. Cybernetic and heuristic approach by using examples. Computer animation of historical review and basic computer principles. Fundamentals of mathematical logic, computer architecture, information representation by analogy models and simulation tools. Algorithmic thinking with examples. Programming language of a corresponding level of complexity. Programming solutions of simple problems. Using computers for complex problem solving (depending on profession and age - individual and team work).

Teaching methods and student assessment. Lectures and exercises are obligatory. Lectures are aimed at pointing out to methodological and didactic principles applicable to computer science teaching, and linking them to available tools and software solutions. Laboratory exercises and seminar papers are directed towards solving real problems in a (computer) classroom based upon the mentioned principles. The final examination consists of a written and an oral part. During the semester students can choose one of the proposed topics for their seminar paper that should be relative to the course contents. A successfully prepared and presented seminar paper represents an equal part in defining the final grade.

Literature:
Recommended literature:
[1] L.Cassel, R.Reis, Informatics Curricula and Teaching Methods, Kluwer Academic Publishers,2003
[2] L.Budin, Informatika za 1. razred gimnazije, Element, Zagreb, 1996
Additional literature:
[3] M.Pavleković, Metodika nastave matematike s informatikom I and II, Element, Zagreb, 1997, 1999
[4] Teaching materials for primary and secondary schools
[5] Conference Proceedings of ACM SIGCSE Symposia
[6] IEEE Transactions on Education, IEEE Press, 1999-2005

Teaching mathematics I M029 (2+1+1) +(2+1+1) - 12 ECTS credits

Course objective. To introduce methods of teaching primary and secondary school mathematics and develop teaching skills.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
Guiding principles in teaching mathematics (respect, preparation, clarity, active learning).
Teaching forms (frontal, individual, work in groups, work in pairs, tutorial work; individual and team projects, work on problems, work with text and other media, etc. ).
Inductive vs. deductive method.
The role of mathematical theory. (How to introduce a new notion in order to satisfy prescribed aims and objectives and pupils' age, theorems and proofs in teaching mathematics)
Exercises. (Methodology of solving different types of excesses - algebra, geometry, problem, etc.)
Homework.
Assessment in mathematics (State of pupils' knowledge at the beginning, assessing pupils' progress – observations and checklists, test construction, assessing a teacher)
Integrating technology in mathematics instructions. (Models, overhead projector, videos, computer technology and internet)
Planning. (Planning a course, unit planning, lesson planning, reflecting on a lesson)
Examples of teaching mathematics (Attend and analyse several lessons at primary and secondary schools, discuss ideas about teaching methods referring to specific mathematical topics)

Teaching methods and student assessment. Students should attend lectures and prescriptive classroom activities in primary and secondary school, do their homework and seminar. The final examination is oral. The final grade is a combination of grades obtained in seminars, homework and the final examination.

Literature:
Recommended literature:
[1] M.Pavleković, Metodika nastave matematike s informatikom I, Element, Zagreb, 2001
[2] M.Pavleković, Metodika nastave matematike s informatikom II, Element, Zagreb, 1999
Additional literature:
[3] D.J. Brahier, Teaching Secondary and Middle School Mathematics, Allyn and Bacon, Boston – Singapore, 2000
[4] Primary school textbooks and other didactic materials
[5] Journals: Matka, Matematičko-fizički list, Matematika i škola, Osječka matematička škola, Poučak
[6] S.Posamentier, J.Stepelman, Teaching Secondary School Mathematics: Techniques and Enrichment Units, Prentice Hall, 1998
[7] S.G.Krantz, How to teach mathematics, Amer. Math. Soc., Boston, 1999
[8] T. Leuders, Mathematik-Didaktik, Praxishandbuch für die Sekundarstufe I und II, Cornelsen, Berlin, 2003
[9] T. Leuders, Qualität im Mathematikunterricht der Sekundarstufe I und II, Cornelsen, Berlin, 2001

Teaching mathematics II M030 (1+2+1) + (1+2+1) - 11 ECTS credits

Course objective. The objective of this course is to educate and train students to be able to apply modern and traditional didactic strategies and methods in teaching primary school mathematics. The possibility of applying some strategies and teaching methods in dependence of mathematical subjects necessary to be learnt, will be studied, by combining lectures, practice and individual projects depending on the age and ability of students, as well as the aims of secondary schools in question. Special stress is placed on working with pupils showing special interest in mathematics, competitions in mathematics, working with pupils having difficulties in mathematics and visualisation of mathematics.

Prerequisites. Teaching mathematics I.

Course contents.
Methodology and subjects of the work with gifted pupils. Competitions in mathematics. Reporting from professional-methodic journals and journals for the secondary school pupils. Preparation for writing a professional paper the subject of which falls into the scope of working with pupils showing special interest in mathematics. Preparation for the presentation of a paper at professional conferences the topic of which falls into the scope of working with pupils showing special interest in mathematics. Creating project tasks which can be used in project teaching. Inventing materials which can be used in programmed teaching. Making posters, presentations and some other materials for the purpose of visualisation and popularisation of mathematics. Methodology of special subjects in vocational secondary schools of e.g. commerce, civil, mechanical engineering, etc. Analysis of subjects and other materials for teaching mathematics in other countries.

Teaching methods and student assessment.
Lectures and exercises are obligatory. Exercises are performed in co-operation with secondary schools. Students must attend, analyse and perform the arranged lectures led by the course assistant co-operating with the secondary shool maths teacher as a tutor. Student assessment is carried out regularly. Mathematical classes students perform at schools are also assessed. The final assessment consists of the oral examination that can be taken after the completion of all lectures and exercises.

Literature:
Recommended literature:
[1] M.Pavleković, Metodika nastave matematike s informatikom I, Element, Zagreb, 2001
[2] M.Pavleković, Metodika nastave matematike s informatikom II, Element, Zagreb, 1999
Additional literature:
[3] D.J. Brahier, Teaching Secondary and Middle School Mathematics, Allyn and Bacon, Boston – Singapore, 2000
[4] Primary school textbooks and other didactic materials
[5] Journals: Matka, Matematičko-fizički list, Matematika i škola, Osječka matematička škola, Poučak
[6] S.Posamentier, J.Stepelman, Teaching Secondary School Mathematics: Techniques and Enrichment Units, Prentice Hall, 1998
[7] S.G.Krantz, How to teach mathematics, Amer. Math. Soc., Boston, 1999
[8] T. Leuders, Mathematik-Didaktik, Praxishandbuch für die Sekundarstufe I und II, Cornelsen, Berlin, 2003
[9] T. Leuders, Qualität im Mathematikunterricht der Sekundarstufe I und II, Cornelsen, Berlin, 2001

Metric spaces M031 (2+2+0) - 6 ECTS credits

Course objective. Make students familiar with the structures of metric and topological spaces.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
Basic and more complex examples from mathematical analysis and motivation for the concept of metric space. Metric spaces. Examples, open and closed sets, equivalent metrics, continuous mappings.
Topological spaces. Topological structures, basis, subbasis, subspaces, product of spaces, quotion space, homeomorphism. Hausdorff's spaces. Examples, properties, continuous mapping on compact space, compactness in Rn , uniform continuous mappings and compactness.

Teaching methods and student assessment. Students should regularly attend lectures and exercises. The final assessment which consists of the written and the oral part can be taken after the completion of lectures and exercises.

Literature:
Recommended literature:
[1] S.Mardešić, Matematička analiza u n-dimenzionalnom realnom prostoru I, Školska knjiga, Zagreb 1974
Additiopnal literature: [2] Š.Ungar, Matematička analiza 3, Matematički odjel PMF, Zagreb 1992
[3] E.T.Copson, Metric Spaces, Cambridge Univ. Press, Cambridge 1968
[4] W.Rudin, Real and Complex Analysis, McGraw-Hill, New York 1966

Microeconomics E006 (2+2+0) - 4 ECTS credits

Course objective. This course covers the core concepts and methods of microeconomic analysis, using some mathematics in modeling and explication. By the end of the course unit students should be able to understand and apply basic microeconomic principles to the economic decisions of households and firms under a variety of market conditions. The aim of this unit is to enable students to deepen their analytical ability in microeconomics so that they can use theory to generate predictions and explanation with respect to economic phenomena.

Prerequisites. None.

Course contents.
1. Introduction. The concept and topics of microeconomic theory. Microeconomic entities.
2. Market determinants of micro economy. Products and services market. The concept and factors of demand. Elasticity of demand. Supply in competition. The supply changes factors. Elasticity of supply. Dynamics of competition. Labor market. Capital market.
3. Production functions. Allocation of economic resources. Production possibilities curve. Short run production function. Total, average and marginal return of the production resource. Law of diminishing returns. Three stages of production function. Combining production resources.
4. Costs of production. Opportunity and actual costs. Economic and accounting concept of costs. Theory of costs in the short run. Fixed costs. Variable costs. Total costs function. Average and marginal costs. Short run costs curve. Costs in the long run.
5. Profit maximisation. Total, average and marginal revenue. Production and revenue interaction. Profitability of resource investment. Normal and economic (pure) profit. Total and average profit. Marginal revenue and marginal profit. Maximal profit and market prices. Costs and revenues in different market structures. Break-even point. Concept and application of marginal analysis.
6. Theory of investment. Concept of investment. Static and dynamic decision models. Demand of the firm for investments. Decisions under subjective risks. Risk identification. Risk measurement. Valuation of risky investment projects. Decision under uncertainty. Risk analysis using simulation.

Teaching methods and student assessment. Students are required to attend lectures and exercises on a regular basis. During the course students will be continuously assessed by means of homework and tests. The final examination which consists of the written and the oral part can be taken after the completion of lectures and exercises.

Literature:
Recommended literature:
[1] M.Karić, Mikroekonomika, Ekonomski fakultet, Osijek 2003
[2] M.Karić, Ekonomika poduzeća, Ekonomski fakultet, Osijek 2001
Additional literature:
[3] P.A.Samuelson, W.Nordhaus, Ekonomija, MATE, Zagreb 1992
[4] M. Babić, Mikroekonomska analiza, MATE, Zagreb 1997
[5] A. Koutsoyiannis, Moderna mikroekonomija, MATE, Zagreb 1996

New product diffusion models E007 (1+0+1) - 3 ECTS credits

Course objective. The objective of the course is to make students familiar with basic principles and models of new product diffusion. Features of the given models will be analysed and fundamental methods for parameter estimation in models will be presented.

Prerequisites. Bachelor level degree in mathematics. Ordinary differential equations. Microeconomy.

Course contents.
1. Introduction. Diffusion models in marketing theory. Marketing-decision. Marketing-models.
2. Mathematical models. Input growths and parameters. Fourt-Woodlock model. Bass model, Easingwood-Mahajan-Muller model. Logistic model. Nelder-Lewandowsky model. Nonsymmetric logistic model. Other new product diffusion models.
3. Parameter estimation methods. Least squares method. Quasilinearisation method – initial value approach. Finite difference method. Integration of data method. Moving least squares method. Methods for estimation the best L_p (p\geq 1) approximation.
4. Statistical description of results. Confidence intervals for parameters in the model. 5. Model operationalisation in practice.

Teaching methods and student assessment. Lectures will be illustrated by ready-made software packages and graphics using a PC and an LCD projector by means of Mathematica or Matlab. The final assessment which consists of the written and the oral part can be taken after the completion of lectures and exercises. During seminars students will be assigned small projects for independent work that have to presented either to other students or at some professional or scientific conferences. The final examination can be taken after the completion of lectures and presentation of the seminar paper that has to be presented to students and teachers prior to taking the examination.

Literature:
Recommended literature:
[1] M.Meler, R.Scitovski, Matematički modeli difuzije novog proizvoda, u: T.Hunjak, Lj.Martić, L.Neralić, Zbornik radova V. konferencija iz operacijskih istraživanja, Zagreb, 1995, 194-203.
[2] R.Scitovski, M.Meler, Solving Parameter Estimation Problem in New Product Diffusion Models, Applied Mathematics and Computation 127(2002) 45-63
Additional literature:
[3] D.Barković,. Analitika novog proizvoda, Ekonomski fakultet u Osijeku, Osijek 1998
[4] V.Mahajan, E.Muller and F.M.Bass, New Product Diffusion Models in Marketing: A Review and Directions for Research, Journal of Marketing, 54(1990), 1-26
[5] F.M.Bass, A new product growth model for consumer durables, Management Science 15(1969), 215-227
[6] V.Mahajan, C.H.Mason and V.Srinivasan, An evaluation of estimation procedures for new product diffusion models, in: V.Mahajan and Y.Wind (eds), Innovation Diffusion Models of New Product Acceptance, 203-232, Cambridge: Ballinger publ., 1986
[7] R.Scitovski, Numerička matematika, Odjel za matematiku, Osijek, 2000

Multimedia systems I006 (1+1+0) - 4 ECTS credits

Course objective. To introduce students to basic concepts in multimedia programming and to help them understand COM, .NET objects and ActiveX controls. To exercise programming (Visual C, Flash) of multimedia content in visual environment. Lectures present graphics, animation, text and sound. Data compression algorithms as well as data streaming algorithms are taught. During laboratory exercises students should master techniques of visual programming.

Prerequisites. Bachelor level degree in mathematics or electrical engineering.

Course contents.
1. Introduction. User interface. Window, icon, interaction, events.
2. MS ActiveX and COM objects. Implementation of controls and objects in program code. Object properties – settings, change, fetching.
3. Visual programming. Macromedia Flash. MS Visual C, J, Basic. Programming sound effects. Video. Animation.
4. Data compression. Longitudinal coding, prediction, Move-to-Front and Huffman algorithm, arithmetic coding, Lempel-Ziv and Wheeler's block compression.
5. WEB applications. Video streaming. Searching for multimedia contents.

Teaching methods and student assessment. Lectures and exercises are obligatory. During the semester students’ knowledge is continuously assessed by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] F.Balena, Programming Microsoft Visual Basic .NET (Core Reference), Microsoft Press, 2002
[2] C.Rey, B.Schneier, Macromedia Flash MX: Training from the Source, Peachpit Press, San Francisco, 2002
Additional literature:
[3] S.M.Alessi, S.R.Trollip, Multimedia for Learning: Methods and Development (3rd Edition), Allyn & Bacon, Boston, 2000
[4] R.M.Jones, Introduction to MFC Programming with Visual C++, Prentice Hall PTR, New York, 1999
[5] D.Vandevoorde, N.M.Josuttis, C++ Templates: The Complete Guide, Addison Wesley Professional, Boston, 2002
[6] Sybex Inc., Security Complete, Sybex International, London, 2001

Multivariate analysis M032 (2+1+1) - 4 ECTS credits

Course objective. To introduce basic notions and results of multivariate statistical procedures and develop skills in their applications.

Prerequisites. Probability, Statistics.

Course contents.
Multivariate linear regression and applications. Estimation. Hypothesis - testing. Classical assumption violations. Model building: variable selection. Variable transformation. Categorical variable (design matrix, ANOVA). Sensitivity analysis, robust estimators.
Generalised linear models. Poisson regression. Dichotomous dependent variable.
Factor analysis.

Teaching methods and student assessment. Students should attend lectures, do their homework and seminars. The final examination is oral. The final grade is a combination of grades obtained in seminars, homework and the final examination.

Literature:
Recommended literature:
[1] G.A.F. Seber, Linear Regression Analysis, J. Wiley & Sons., New York, 1977
[2] F.E. Harrell, Ir. Regression Modelling Strategies with Applications to Linear Models, Logistic Regression and Survival Analysis, Springer, New York, 2001
[3] A. Basilevsky, Statistical Factor Analysis and Related Models: Theory and Applications, Wiley-Interscience, New York, 1994
Additional literature:
[4] L. Fahrmeier, G. Tutz, Multivariate Statistical Modelling Based on Generalized Linear Models, Springer, New York, 2001
[5] R.C. Mittelhammer, Mathematical statistics for economics and business, Springer, 1996
[6] P. McCullagh, J.A: Nelder, Generalized Linear Models, CRC Press, 1989
[7] R.L. Gorsuch, Factor Analysis, Lawrence Erlbaum Assoc. 1983

Numerical linear algebra M033 (2+1+0) - 5 ECTS credits

Course objective. Make students familiar with the basic idea and methods of numerical linear algebra which can be applied to solving linear systems, least squares problems, eigenvalue and singular value problems. Further, through lectures students will be introduced to the usage of dense and sparse matrices, floating point arithmetics and different matrix factorisations as well as to the corresponding algorithms for solving different problems in applications. Through exercises students will deal with techniques for solving concrete problems by using ready-made software packages or their own programmes.

Prerequisites. Differential calculus, Integral calculus, Functions of several variables, Linear algebra I, II.

Course contents.
1. Introduction. Basic algorithms, usage of structures, vectorisation. Floating point arithmetics.
2.Matrix analysis. The basic ideas of linear algebra. Matrix and vector norms. Ortogonalisation and SVD. Matrix condition and sensitivity of quadratic linear systems.
3. Solving linear systems. Triangular systems, LU factorisation, Gaussian elimination, pivoting.
4. Linear least square problem. Householder and Givens matrices, QR-decomposition. The full rank linear least square problem.
5. The eigenvalue problem. The eigenvalue problem, properties and decompositions. The symmetric eigenvalue problem, properties and decompositions. Iterative methods for eigenvalue determination.
6. Iterative methods for linear systems. Standard iterations (Jacobi and Gauss-Seidel). Relaxation methods. Large and sparse linear systems.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. During exercises students will become trained for solving problems from the fields of biology, chemistry, physics and engineering by using ready-made software packages or by making their own programmes. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] G.Golub, C.F.Van Loan, Matrix Computations, Johns Hopkins Univ. Pr., 3rd edition, 1996
[2] R.Scitovski, Numerička matematika, Odjel za matematiku, Sveučilište u Osijeku, Osijek, 1999
Additional literature:
[3] J.W.Demmel, Applied Numerical Algebra, SIAM 1997
[4] D.Kincaid, W.Cheney, Numerical Analysis, Brooks/Cole Publishing Company, New York, 1996 [5] G.W.Stewart, Matrix Algorithm, SIAM 1998

Numerical mathematics M034 (2+2+0) - 6 ECTS credits

Course objective. The objective of this course is to make students familiar with the main methods of numerical mathematics, whereby proving theorems will be avoided, except in case of some constructive proofs which themselves refer to the construction of ideas or methods.

Prerequisites. Differential calculus, Integral calculus, Functions of many variables, Linear algebra I, II.

Course contents.
1. Introduction. Error Analysis. Significant digits. Floating point arithmetic. Error of the function. Inverse problem in Error Analysis.
2. Interpolation. Spline interpolation. Interpolation problem. The interpolation formula of Lagrange. The interpolation formula of Newton. Error estimation. Linear spline interpolation. Cubic spline interpolation. 3. Solving nonlinear equations. Bisection method. Method of simple iteration. Newton method and modifications. Solving methods for nonlinear system of equations: Newton method, quasi-Newton methods. 4. Approximation of functions. Best L_2 approximation. Orthogonal polynomial. Chebyshev's polynomial. Best L_\infty approximation. 5. Least squares problems. Introduction and examples. Nonlinear lest squares problems. Gauss-Newton method. 6. Numerical integration. Trapezoidal rule. Newton-Cotes formula. Simpson rule. 7. Numerical methods for solving ordinary differential equations. Euler method. Runge – Kutta method. Difference methods for solving boundary value problems.
8. Numerical methods for solving partial differential equations.
Teaching methods and student assessment. Lectures will be illustrated by ready-made software packages and graphics using a PC and an LCD projector by means of Mathematica or Matlab. Exercises are partially auditory and partially laboratory, and students will use PCs and an LCD projector by means of the aforementioned software systems. The final assessment consists of both the written and the oral examination that can be taken after the completion of all lectures and exercises. During the semester students are given homework. They can also take 2-4 tests that completely cover course contents. Successfully passed tests replace the written examination. During their studies students are encouraged to prepare seminar papers. Successful seminar papers influence the course final grade.

Literature:
Recommended literature:
[1] R.Scitovski, Numerička matematika, Odjel za matematiku, Osijek, 2000
Additional literature:
[2] G.Dalquist, A.Björck, Numerische Methoden, R.Oldenbourg Verlag, München, 1972 (there is an English translation as well)
[3] D.Kincaid, W.Cheney, Numerical Analysis, Brooks/Cole Publishing Company, New York, 1996
[4] J.Stoer, R.Bulirsch, Introduction to Numerical Analysis, 2^{nd} Ed.,Springer Verlag, New York, 1993

Njemački jezik u struci I Z002 (0+0+2) - 6 ECTS bodova

Cilj predmeta: Usvajanje osnovne terminologije iz područja matematike i računarstva te što korektnija primjena gramatičkih struktura koje su karakteristične za jezik u struci. Osposobljavanje studenata za čitanje stručne literature i vođenje razgovora o nekim osnovnim temama vezanim uz struku.

Potrebna predznanja. Znanje njemačkog jezika iz srednje škole

Sadržaj predmeta.
Mathematik (Zahlen, Grundrechnungsarten). Potenzieren und Wurzelrechnung. Klammern. Brüche. Lesen mathematischer Formeln. Gleichungen. Geometrische Grundbegriffe (Dreieck, Vier- und Vielecke, Kreis).
Was ist Informatik? Kurze Geschichte des Computers. PC-Aufbau. Speicher. Die Peripherie: Ein- und Ausgabegeräte: Die Tastatur. Der Bildschirm. Der Drucker. Scanner. Die Maus.
Grammatik: Temporalsätze, Konditionalsätze mit und ohne die Konjuktion wenn, Imperativ, Partizip I und Partizip II, Das Passiv, Die Adjektivdeklination, Das erweiterte Attribut, Relativsätze, Wortzusammensetzungen.

Izvođenje nastave i vrednovanje znanja. Nastava za ovaj predmet predviđena je obliku seminara koji su obvezni za sve studente. U nastavi se koriste audiovizuelna nastavna pomagala (LCD, PC, DVD), te brojni stručni časopisi i knjige koje su dostupne u knjižnici Odjela za matematiku. Studenti povremeno dobivaju domaće zadaće ili manje projektne zadatke, što utječe na konačnu ocjenu iz predmeta. Znanje studenata prati se kontinuirano putem četiri kolokvija, po dva u semestru, a usmeni dio ispita slijedi na kraju akademske godine.

Literatura:
Osnovna literatura:
[1] H. Binder/R. Buhlmann, Hinführung zur mathematisch-naturwissenschaftlichen Fachsprache, Teil 1: Mathematik, Max Hueber Verlag, München, 1981.
[2] Dreyer-Schmitt, Lehr- und Übungsbuch der deutschen Grammatik, Max Hueber Verlag, München, 2000.
[3] J. Ortmann, Einführung in die PC-Grundlagen, Tandem Verlag, Herne, 1993.
Literatura koja se preporučuje:
[4] D. Koračin, Čitanje matematičkih formula, Element, Zagreb, 1996.
[5] M. Krajnović, Rječnik matematičkih naziva, Matematičko-fizički list (izvanredni broj), Zagreb, 1999-2000.

German for mathematics / computer science students I Z002 (0+0+2) - 6 ECTS credits

Course objective. Students should acquire fundamental terminology from the fields of mathematics and computer science as well as apply structures typical of GSP (German for Specific Purposes). They should be taught and trained how to read various pieces of literature pertaining to mathematics and computer science as well as to carry out conversation referring to some basic topics in their fields of study.

Prerequisites. high-school knowledge of the German language

Course contents.
Mathematik (Zahlen, Grundrechnungsarten). Potenzieren und Wurzelrechnung. Klammern. Brüche. Lesen mathematischer Formeln. Gleichungen. Geometrische Grundbegriffe (Dreieck, Vier- und Vielecke, Kreis).
Was ist Informatik? Kurze Geschichte des Computers. PC-Aufbau. Speicher. Die Peripherie: Ein- und Ausgabegeräte: Die Tastatur. Der Bildschirm. Der Drucker. Scanner. Die Maus.
Grammatik: Temporalsätze, Konditionalsätze mit und ohne die Konjuktion wenn, Imperativ, Partizip I und Partizip II, Das Passiv, Die Adjektivdeklination, Das erweiterte Attribut, Relativsätze, Wortzusammensetzungen.

Teaching methods and student assessment. This course is organised through seminars which are obligatory for all students. Various audio-visual teaching aids are used in the course (LCD, PC, DVD), as well as numerous professional journals and books available in the Department’s library. From time to time students are assigned homework or small project tasks, which might affect their final grade. Students’ knowledge is continuously assessed by four tests, two per each semester, and the oral part of the examination takes place at the end of academic year.

Literature:
Recommended literature:
[1] H. Binder/R. Buhlmann, Hinführung zur mathematisch-naturwissenschaftlichen Fachsprache, Teil 1: Mathematik, Max Hueber Verlag, München, 1981
[2] Dreyer-Schmitt, Lehr- und Übungsbuch der deutschen Grammatik, Max Hueber Verlag, München, 2000
[3] J. Ortmann, Einführung in die PC-Grundlagen, Tandem Verlag, Herne, 1993
Additional literature:
[4] D. Koračin, Čitanje matematičkih formula, Element, Zagreb, 1996
[5] M. Krajnović, Rječnik matematičkih naziva, Matematičko-fizički list (izvanredni broj), Zagreb, 1999-2000

German for mathematics / computer science students II Z003 (0+0+2) - 6 ECTS credits

Course objective. Students should acquire vocabulary in the fields of mathematics and computer science as well as apply structures typical of GSP (German for Specific Purposes). They should be taught and trained how to read and understand various pieces of literature pertaining to mathematics and computer science, discuss topics in their fields of study and translate simple GSP texts from Croatian into German. Students should also be taught how to individually present a selected topic in German.

Prerequisites. German for mathematics / computer science students I

Course contents.
Mengen. Menge der rationalen Zahlen. Aussagen über Produkte. Menge der reelen Zahlen. Gleichungen. Hinreichende und notwendige Bedingung. Beweismethoden. Abbildungen. Funktionen.
Das Betriebssystem. Anwendersoftware. Programmierung. Vernetzung und Kommunikation. Datensicherheit und Computerviren.
Grammatik: Wortbildung. Pronominaladverbien. Die Arten der Sätze (einfache und zusammengesetzte Sätze). Infinitivkonstruktionen.

Teaching methods and student assessment. This course is organised through seminars which are obligatory for all students. Various audio-visual teaching aids are used in the course (LCD, PC, DVD), as well as numerous professional journals and books available in the Department’s library. From time to time students are assigned homework or small project tasks, and every student individually presents a selected GSP topic, which altogether affects their final grade. Students’ knowledge is continuously assessed by four tests, two per each semester, and the oral part of the examination takes place at the end of academic year.

Literature:
Recommended literature:
[1] Autorengruppe, Deutsch – Ein Lehrbuch für Ausländer – Mathematik, VEB Verlag Enzyklopädie Leipzig, 1978
[2] Dreyer-Schmitt, Lehr- und Übungsbuch der deutschen Grammatik, Max Hueber Verlag, München, 2000
Additional literature:
[3] H. Binder/R. Buhlmann, Hinführung zur mathematisch-naturwissenschaft- lichen Fachsprache, Teil 1: Mathematik, Max Hueber Verlag, München, 1981
[4] J. Ortmann, Einführung in die PC-Grundlagen, Tandem Verlag, Herne, 1993
[5] Scientific and professional papers from the fields of mathematics and computer science

Ordinary differential equations M035 (2+2+0) - 6 ECTS credits

Course objective. To make students familiar with the concept and a geometrical sense of an ordinary differential equation. To show basic types and methods for solving. To make students familiar with the existence and uniqueness theorems by giving motivation only, without any precise proof. To present the concept and basic methods for solving partial differential equations. To illustrate concepts and methods by using numerous geometric and practical examples by means of a computer.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. Problems associated with differential equations (Growth and decay problems, temperature problems, falling body problems, electrical circuits, orthogonal trajectories). General and particular solution. Initial value problem. Geometric interpretation. Sensitivity problem to the perturbation of initial conditions.
2. Ordinary differential equations of the first order. Solution. Field of directions. Existence and uniqueness theorem. Some types of ordinary differential equations of the first order (Exact equations, homogenous equations, linear equations, Bernoulli equations, Lagrange equations, Clairaut equations, Riccati equations). Examples and applications.
3. Ordinary differential equations of the second order. Some special types. Linear differential equations of the second order. Lagrange's method of the variation of the constants. Linear differential equations of the second order with constant coefficients. Laplace transformations. Examples and applications (harmonic oscillator).
4. Ordinary differential equations of the n-th order.
5. Systems of ordinary differential equations. Systems of ordinary linear differential equations with constant coefficients. Balistic problem in vacuum and in air-filled space. Examples and applications.
6. Appendix. Solving differential equations by power series. Delay differential equations – concept, examples and basic methods for solving. Partial differential equation - concept, examples and basic methods for solving.

Teaching methods and student assessment. Exercises are partially auditory and partially laboratory. Students will use PCs and an LCD projector with Mathematica or Matlab. The final assessment consists of both the written and the oral examination that can be taken after the completion of all lectures and exercises. During the course students can take 2-4 tests that completely cover course contents. Successfully passed tests replace the written examination. During their studies students are encouraged to prepare a seminar paper. Successful seminar papers influence the course final grade.

Literature:
Recommended literature:
[1] M.Alić, Obične diferencijalne jednadžbe, PMF - Matematički odjel, Zagreb, 2001
[2] I.Ivanšić, Fourierovi redovi. Diferencijalne jednadžbe, Odjel za matematiku, Osijek, 2000
Additional literature:
[3] L.E.Eljsgoljc, Differencialjnie uravnenija, Gosudarstvenoe izdateljstvo tehniko-teoretičeskoj literaturi, Moskva, 1957
[4] G.F.Simmons, J.S.Robertson, Differential Equations with Applications and Historical Notes, 2^{nd} Ed., McGraw-Hill, Inc., New York, 1991
[5] Schaum's outline series, McGRAW-HILL, New York, 1991
[6] S. Kurepa, Matematička analiza 2 (funkcije jedne varijable), Tehnička knjiga, Zagreb, 1990

Introduction to Measure Theory M036 (2+2+0) - 6 ECTS credits

Course objective. The course consists of two mutually independent units: Lebesque integral and Inequalities. The goal of the course is to make students familiar with fundamental concepts pertaining to both of these areas applicable in mathematics and engineering.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Lebesgue integral. Riemann integral. Measurable sets. Measurable functions. Lebesgue integral. Convergence and Lebesgue integral. Function space L2. Fourier series.
2. Inequalities. Basic means. Chebyshev’s, Cauchy’s, Hölder’s and similar inequalities. Power means. Convex functions and inequalities.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students can take 2 tests that replace the written examination.

Literature:
Recommended literature:
[1] H. J. Wilcox, D. L. Myers, An Introduction to Lebesgue Integration and Fourier Series, Dover, New York, 1994
[2] W.Rudin, Principles of Mathematical Analysis, Mc Graw-Hill, Book Company, 1964
[3] J. E. Pečarić, Nejednakosti, Hrvatsko matematičko društvo, Zagreb, 1996
Additional literature:
[4] J. E. Pečarić, Konveksne funkcije i nejednakosti, Naučna knjiga, Beograd, 1987
[5] S. Mardešić, Matematička analiza u n-dimenzionalnom realnom prostoru I, Školska knjiga, Zagreb, 1977
[6] I. Ivanšić, Fourierovi redovi. Diferencijalne jednadžbe, Odjel za matematiku, Osijek, 2000
[7] D.S. Mitrinovć, J.E. Pečarić, A. M. Fink, Classical and New Inequalities, Dordrecht, Netherlands: Kluwer, 1993

General pedagogy P002 (1+0+1) + (1+0+1) - 4 ECTS credits

Course objective. Make students familiar with pedagogy as a science of education. Enable students to develop their creative thinking and improve their educational practice and pedagogic theory.

Prerequisites. Not required.

Course contents.
Man, education, society. Pedagogy as a criticising and creating science. System of pedagogic sciences.Theory and practice of pedagogy. Development of pedagogy – general and national history of pedagogy. Future of pedagogy.
Pedagogic methodology. Types of research. Scheme. Hypotheses and variables. Instruments and procedures. Quantitative vs. qualitative analysis. Research.
Teaching process analysis. Goal, tasks, ideals. Models of concretising education objectives. Functional and international education.
Education. Fields of education. Educational factors and their influence. Education place and education-specific characteristics. Principles, methods, procedures, instruments and forms of education.
School, management, education policy.
The meaning and history of schools. Theories. Education systems in Croatia and abroad. Teachers and their competencies. The meaning and importance of education policy. Management theories, models and procedures.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. Every student is expected to prepare a seminar paper and conduct two exercises. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises.

Literature:
Recommended literature:
[1] M.Cindri, Profesija učitelja u svijetu i u Hrvatskoj, Persona, V.Gorica, Zagreb, 1995
[2] H.Giesecke, Uvod u pedagogiju, Educa, Zagreb, 1993
[3] H.Gudjons, Pedagogija temeljna znanja, Educa, Zagreb, 1994

Additional literature:
[4] M.Ajduković, N.Pećnik, Nenasilno rješavanje sukoba, Alinea, Zagreb, 1994
[5] D.Gossen, Restitucija preobrazba školske discipline, Alinea, Zagreb, 1994
[6] M.Matijević, Alternativne škole, Institut za pedagogijska istraživanja, Zagreb, 1994
[7] R.Winkel, Djeca koju je teško odgajati, Educa, Zagreb, 1996

Operations research M037 (1+1+0) - 3 ECTS credits

Course objective. The objective of this course is to make students familiar with fundamental operational research methods and their applications. They would also be introduced to related available software. Special stress will be placed on problem observation, modelling and interpretation of results.

Prerequisites. Bachelor level degree in mathematics or engineering.

Course contents.
1. Introduction. Introduction to problems from practice, modeling integer and mixed integer programming. Definition of decision variables, objective function and constraints (feasible set of solutions and its properties).
2. Problems known from literature. Knapsack problem, traveling salesman problem, assignment problems, machine scheduling problem (Lot Sizing Problems).
3. Theory of valid inequalities. Definitions, properties, examples of inequalities holding for certain problems.
4. Branch-and-bound algorithm using linear programming relaxation (branch criteria, stopping criteria). General cutting plane algorithm with some examples.
5. Heuristic method (local searsh, tabu - search, genetic algorithms, simulated annealing).

Teaching methods and student assessment. Lectures and exercises are obligatory. Lectures are carried out theoretically, during exercises students solve problems and cases from practice and use computers supported by the Winqsb software package. Students' knowledge is assessed by means of assignments, written and oral examination.

Literature:
Recommended literature:
[1] G. L. Nemhauser, A.Laurence, Wolsey, Integer and Combinatorial Optimization, John Wiley & Sons, Inc., 1999
[2]L.Neralić, Uvod u matematičko programiranje 1, Element, Zagreb, 2003
Additional literature: [3] G. Sierksma, Linear and Integer Programming, Marcel Dekker, Inc., 1999
[4] A.Schrijver, Theory of Linear and Integer Programming, John Wiley & Sons, Inc., NY, SAD, 1999
[5] R.Bronson, G.Naadimuth, Operation Research, Schaum's, McGraw Hill, New York, 1997
[6] H. P. Williams, Model Solving in Mathematical Programming, Wiley, 1993
[7] J. Varga, Angewandte Optimierung, F.A. Brockhaus AG, Mannheim, 1991
[8] M. S. Bazaraa, Nonlinear Programming, Theory and Algorithms, 2nd Ed., Willey, 1993
[9] C. H. Papadimitriou, H. Christos, Combinatorial Optimization, Prentice-Hall, N. J., 1982
[10] R. Horst, Nichtlineare Optimierung, Carl Hanser Verlag, Munchen, 1979

Foundations of Fourier analysis and wavelets M038 (2+2+0) - 6 ECTS credits

Course objective. To introduce students to basic ideas and applications of Fourier analysis. Lectures are presented by using examples from technology and physics. Results are given with ideas of proofs by means of graphs, frequency diagrams and geometric analogies.

Prerequisites. First-cycle degree in analysis.

Course contents.
1. Periodic Phenomena. Systems and models which generate cycles. Periodic functions. Trigonometric polynomials and series.
2. The Idea of Fourier Analysis. Approximation in vector spaces. Computing Fourier coefficients. Fourier series expansions of some simple functions. Expansions in series for odd and even functions.
3. Orthogonal Polynomials and Orthogonal Systems. Expansions in orthogonal polynomials.
4. The Fourier Integral. Fourier transformations. Laplace transformations with real parameter.
5. The Discrete Fourier Transform. The Fast Fourier transform. Approximations of the Fourier Transform.
6. Linear Filtering. Discrete filters. Continuous filters. The Z-transform. Reconstruction of signals. Daubechies filters.
7. Multiresolution Analysis. Haar wavelets. Scaling functions. The Mother Wavelet. Orthonormal Daubechies wavelet bases.

Teaching methods and student assessment. Lectures are based on examples. Exercises will be mainly laboratory ones. Students’ knowledge will be assessed continuously during lectures. Test results make 50% of the final grade. The final examination consists of the written and the oral part.

Literature:
Recommended literature:
[1] I. Ivanšić, Fourierovi redovi i diferencijalne jednadžbe, Odjel za matematiku, Osijek 2000
Additional literature:
[2] G. Kaiser, A Friendly Guide to Wavelets, Birkhaüser, 1994
[3] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992
[4] A. Popoulis, The Fourier Integral and its Applications, Mc Grow-Hill 1984

Fundamentals of management E008 (2+0+0) - 3 ECTS credits

Course objective. Students will achieve competences and skills in management, get an insight in new trends in business and management, increase effectiveness of managing career and personal professional growth, develop capabilities of managing particular business situations, and increase personal employability and personal competitive advantages on the labour market. Management is presented as a practical skill as well as a profession. The management role is often passed to the persons without economic or managerial knowledge. Therefore students will learn the basics of management in the business systems, basic skills necessary for successful functioning in the organisational settings. Some professions are highly focused on growing technical competences, while social skills remain undeveloped. This course is focused on development of social skills for future engineers who will need to initiate, develop and maintain business contacts, stimulative working conditions, personal and team motivation, attraction and managing support groups for propositions and solutions.

Prerequisites. Not required.

Course contents.
Management as a profession, theory and skill. Management skills. Fundamental function of the management in business systems: planning, organising, motivating and leading, human resource management, control. Managing communication and interpersonal skills in team; change; and conflict situations.

Teaching methods and student assessment. Students will be evaluated during the semester through exercises, simulations of business situations and case study analysis. The final examination is due at the semester end. It is a written test containing 30 questions (open type, closed type) followed by the oral examination.

Literature:
Recommended literature:
[1] E.Collins; M.A. Devanna: Izazovi menadžmenta u 21. stoljeću, Mate, Zagreb, 2002
Additional literature:
[2] M. Armstrong: Kompletna menadžerska znanja 1, 2; MEP Consult, Zagreb, 2001

Basics of artificial intelligence I007 (2+2+0) - 6 ECTS credits

Course objective. To make students familiar with the theory and application of artificial intelligence focusing on prediction, classification and pattern recognition problems. The methodology and architecture of neural networks, genetic algorithms, intelligent agents, robotics and other artificial intelligence techniques will be explained through lectures. Excercises will cover examples and usage of software tools, thus enabling students to acquire basic principles of design and evaluation of intelligent systems.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Basic terms – what is artificial intelligence (AI). Approaches of AI in solving intelectual problems. AI vs. traditional computing. AI techniques. Areas of AI application.
2. Knowledge-based systems. Definition and functioning. Designing a knowledge-based system. Knowledge acquisition and knowledge base design. Testing, analysing and evaluating the decision obtained by a system. Application of knowledge-based systems (case study and examples).
3. Neural networks. Definition and functioning (architecture, the concept of learning based on historical data). Supervised and unsupervised learning. Types of NN algorithms. Modeling the data for NN. NN architecture design. Learning process, testing and evaluating the performance of a NN. Software tools for NNs. NN application (case study and examples).
4. Other AI techniques. Genetic algorithms. Intelligent agents, Robotics. Pattern recognition. Speech recognition. Natural language processing. Hybrid AI systems.
5. Trends and future development of AI. AI application in data mining. Artificial life.

Teaching methods and student assessment. Lectures and excercises are obligatory. Student knowledge is assessed during the semester through homework and project assignments. The final examination consists of the written and the oral part.

Literature:
Recommended literature:
[1] S. J. Russell, P.Norvig, Artificial Intelligence: A Modern Approach, Prentice Hall; 2nd edition, 2002
[2] D. Mišljenčević, D. Maršić, Umjetna inteligencija, Školska knjiga, Zagreb, 1991
Additional literature:
[1] C. Bishop, Neural Networks and Machine Learning, Springer Verlag, Berlin, 1998
[2] R. R. Trippi, J.K. Lee, Artificial Intelligence in Finance & Investing, Irwin Professional Publishing, Burr Ridge, IL, 1996
[3] R. Trippi, R.R., Turban, E., Neural Networks in Finance and Investing, Probus Publishing, Chicago, IL, 1992
[4] I.H. Witten, E. Frank, Data Mining: Practical Machine Learning Tools and Techniques with Java Implementation. Morgan Kaufman Publishers, San Francisco, CA, 2000

Partial differential equations M039 (1+1+0) - 2 ECTS credits

Course objective. Introduce students with the models formed from partial differential equations which describe natural phenomena. Further, introduce them with the basic techniques for solving partial differential equations including separation of variables and expansion using the eigenfunctions. The following will also be considered: the method of characteristics, Fourier and Laplace transformations and Green function

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Partial differential equations as the models
2. Separation of variables, expansion using the eigenfunctions
3. Method of characteristics, Fourier and Laplace transformations
4. Green functions, integral equations

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. During exercises students will become trained for solving problems from the fields of biology, chemistry, physics and engineering by using ready-made software packages or by making their own programmes. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] J. David Logan, Applied Mathematics, John Wiley & Sons 2nd edition, 1996
Additional literature:
[2] E.DiBenedetto, Partial Differential Equations, Birkhauser, Boston, 1995

History of mathematics M040 (2+0+0) + (2+0+0) - 6 ECTS credits

Course objective. The course introduces students to the development of major mathematical ideas in the history. In that way they learn various examples useful for their future careers as teachers of mathematics and for the communication with people in other professions, they are introduced to connections between mathematics and other professional fields as well as the role of mathematics in the development of the human society, and they revise mathematical facts they learned before. In the first semester the development of mathematics in various cultures until the renaissance is covered mostly chronologically, and in the second semester mathematics in the period from the beginning of the 17th until the beginning of the 20th century is covered by explaining the development of major mathematical disciplines.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
First semester:
1. Early mathematics: Egyptian and Babylonian mathematics.
2. Mathematics in the Greek and Roman world: preeuclidean mathematics (Thales, Pythagoreans, etc.), Euclidean age (Euclid, Archimedes, etc.), posteuclidean mathematics (Ptolemy, Heron, etc.), mathematics in the Roman state.
3. Mathematics of Eastern cultures: Indian and Chinese mathematics.
4. Medieval mathematics: Arabian mathematics, mathematics in medieval Europe.
5. Renaissance: development of mathematical notation, solution of algebraic equations of the 3rd and 4th degree, discovery of logarithms, connections of mathematics and physics, astronomy and arts.
Second semester:
1. Development of algebra after the renaissance: beginnings of group theory, matrix theory, vector spaces; fundamental theorem of algebra; development of number theory.
2. Development of analysis after the renaissance: discovery and development of calculus; convergence, series, continuity; complex numbers.
3. Development of geometry after the renaissance: discovery of projective, analytical and non-euclidean geometries; beginnings of topology.
4. Probability theory: beginnings and development until the axiomatisation.
5. Creation of set theory.

Teaching methods and student assessment. The attendance of classes is obligatory. During the course, every student is required to prepare and present one seminar paper on a given subject. The attendance at the seminar presentations is obligatory. Plagiarism is strictly forbidden. Oral examination is taken at the semester end.

Literature:
Recommended literature:
[1] D.E.Smith: History of Mathematics - Vol. I. Dover, New York, 1958
[2] D.E.Smith: History of Mathematics - Vol. II. Dover, New York, 1953
[3] The MacTutor History of Mathematics Archives: http://www-groups.dcs.st-and.ac.uk/~history/
Additional literature:
[4] W.S.Anglin, J.Lambek: The Heritage of Thales. Springer Verlag, Berlin, 1995
[5] J.Gow: A Short History of Greek Mathematics. AMS, Boston, 1968
[6] E. Hairer, G. Wanner: Analysis by Its History. Springer Verlag , Berlin, 1996
[7] D.E.Joyce: Euclid's Elements: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html 
[8] V.J.Katz, ed.: Using History to Teach Mathematics. MAA, Washington,DC, 2000

Projecting educational computer models I014 (1+1+0) - 3 ECTS credits

Course objective. To make students familiar with the process of modelling, designing, developing, implementing, and maintaning educational software systems, especially web oriented intelligent tutoring systems. Modern information technology enables a more frequent usage of tutoring systems as an addition or a substitute of the standard way of education. Those systems are characterised with interactivity and adaptibility, including hypermedia, Internet technologies, as well as artificial intelligence. The course covers the process of designing intelligent educational systems, as well as the usage of intelligent tutoring system shells, artificial intelligence in tutoring systems, and distance learning systems. Students will incorporate the process of designing modules, such as the teacher module, the student module, the communication module (i.e. user interface). Students will therefore acquire the basic principles of design, development and implementation of educational systems, as well as the skills of evaluating such software.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Learning theories. Learning models. Educational software support – definition, goals, technologies. Approaches, integrating learning theories with information technology.
2. Information system in education. Tutoring systems. Internet usage in educational information system. Distance learning.
3. Adapting educational systems to individual students' characteristics. Usage of artificial intelligence in educational systems. Web-oriented intelligent tutoring systems.
4. Projecting educational software systems. Knowledge module, student's module, teacher's module, communication module. Designing lectures, tracking student learning process, student evaulation, communication among students and between students and teachers.
5. Developing educational software systems. Using software shells to build a tutoring system. Preparation of educational materials. Designing educational material. Designing graphic elements, sound, animation. Learning time sheduling. Designing quizzes and other ways of student evaluation. Using discussion groups (forums, mailing lists) for communication with students. Using "white board" for group learning. Using other web sources for learning: repositories, educational archives, educational portals. Organising access to educational contents, privilegies and security.
5. Methods for evaluating educational software, electronic performance support systems (EPSS).

Teaching methods and student assessment. Lectures and excercises are obligatory. Lectures will cover theories and models of learning, as well as technologies used for designing and developing educational computer models covering different topics. Exercises will cover the usage of software tools to build educational systems. Students’ knowledge is assessed during the semester through homework and project assignments. The final examination consists of a written and an oral part.

Literature:
Recommended literature:
[1] J. E. Schwartz, R .J. Beichner, Essentials of educational technology. Boston: Allyn and Bacon, 1999
Additional literature:
[2] R..E. Mayer, Multimedia learning. Cambridge, UK: Cambridge University Press, 2001
[3] D.W. Brooks, Web-teaching: A guide to designing interactive teaching for the World Wide Web. New York: Plenum, 1997
[4] M. von Wodtke, Mind over media: Creative thinking skills for electronic media. New York: McGraw-Hill, 1993

Psychology P003 (2+0+1)+ (2+0+1) - 8 ECTS credits

Course objective. Students will become familiar with various aspects of children’s growth and development as well as the structure and personality development. They will also acquire knowledge of psychology that might influence understanding of the education practice.

Prerequisites. Not required.

Course contents.
Origin and importance of psychology of education; Personality and its structure; Intelligence development, structure of intelligence; Personality and individual differences, contribution of schools; Intercultural research of mathematical achievements; Emotion and motivation; Temperament; Moral development; Building a positive self-image; Adolescence, adolescent subculture; Addiction – psychology background. Memorising and learning. Forgetting; Metamemory.

Literature:
Recommended literature:
[1] Michael J. A. Howe Psihologija učenja. Jastrebarsko: Naklada Slap. (Selected chapters) (2002)
[2] V.Andrilović, M.Čudina-Obradović Psihologija učenja i nastave. Zagreb: Školska knjiga. (Selected chapters) (1996)
[3] R.Vasta., M.Haith, S.A.Miller Dječja psihologija. Jastrebarsko: Naklada Slap. (Selected chapters) (2000)
Additional literature:
[4] T.Grgin Edukacijska psihologija. Jastrebarsko: Naklada Slap. (1997)
[5] B.Petz Uvod u psihologiju. Jastrebarsko: Naklada Slap. (2001)
[6] P.Zarevski Psihologija učenja i pamćenja. Jastrebarsko: Naklada Slap. (1998)
[7] H.Gardner, M.L.Kornhaber , K.Wake inteligencija - različita gledišta. Jastrebarsko: Naklada Slap (1999)

Psychology of gifted pupils P004 (1+0+1) - 4 ECTS credits

Course objective. Students should acquire knowledge that will help them understand, identify and develop gifted pupils.

Prerequisites. Psychology of education.

Course contents.
Giftedness and talent – definition, characteristics, fields.
Acceleration of gifted children (purpose, procedure). Support in education for gifted and talented pupils, individualisation of education, small group work. Creativity. Maturity and selection of occupations for gifted pupils.
The role of the teacher in the development of giftedness at school. Desirable qualities of teachers of gifted pupils. Creating a positive and supporting classroom atmosphere. Setting up a creative atmosphere. Teacher and class mates attitudes to gifted pupils.

Teaching methods and student assessment. Students are obliged to attend lectures and seminars. Every student is expected to prepare a seminar paper. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises.

Literature:
Recommended literature:
[1] M.Čudina Obradović, Nadarenost-razumijevanje, prepoznavanje, razvijanje. Zagreb: Školska knjiga. (1991)
[2] I.Koren, Kako prepoznati i identificirati nadarenog učenika. Zagreb: Školske novine. (1989)
Additional literature:
[3] I.Koren, Praćenje školske i profesionalne uspješnosti intelektualno nadarene omladine. Sisak: USIZ za zapošljavanje. (1986)
[4] K.A.Heller, F.J.Monks, A.H.Passow. International handbook of research and development of giftedness and talent. Oxford. Pergamon press. (1993)

Computational mathematics M042 (2+2+0) - 6 ECTS credits

Course objective. The purpose of this course is to teach students how to use highly sophisticated mathematical software and how to make their own mathematical programmes with this software (Matlab, WRI Mathematica and Mapple). Students will be introduced to different problems from mathematics, physics, economy and engineering. Through lectures they will learn about software packages and how one can write his/her own programme. Through exercises they will learn how to solve specified problems from different applications (numerical, symbolic or graphics).

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. Advantages and drawbacks of mathematical software packages. Survey of mathematical software packages and possibilities.
2. Numerical programing using MatLab. Sparse matrices. Linear Algebra. Numerical Methods.
3. Simulations in MatLab. Bibliography for Block Coding. Simulink. S-functions. Real-time workshop.
4. Symbolic calculations in Mapple. Monte Carlo method. Markov processes.
5. Programming in WRI Mathematica. Functional and procedural programming. Evaluations. Transformation rules. Interactions with incorporated rules. Graphical programming.
6. Publication on the web.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. During exercises students will become trained for solving problems from the fields of biology, chemistry, physics and engineering by using ready-made software packages or by making their own programmes. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] D. J. Higham, N.J. Higham, MATLAB Guide, SIAM, Philadelphia, 2000
[2] S. Wolfram, The MATHEMATICA ® Book, Version 4, Cambridge University, Cambridge, 1999
Additional literature:
[3] R.E. Maeder, Programming in Mathematica, 3/E, Addison-Wesley, Boston, 1995
[4] T. L. Harman, J. B. Dabney, N. J. Richert , Advanced Engineering Mathematics with MATLAB, Brooks Cole, Pacific Grove,1999
[5] E. Don, Schaum's Outline of Mathematica, McGraw-Hill Trade, NewYork, 2000
[6] R. Pratap, Getting Started With Matlab: Version 6: A Quick Introduction for Scientists and Engineers, Oxford University Press, NewYork, 2002
[7] M. Essert, Matlab-matricni laboratorij, FSB Zagreb, 2001

Computer networks and services I017 (2+1+1) - 5 ECTS credits

Course objective. Teach students basic notions about computer networks and their services. Understand web server operations and communication protocols. Practise programming skills for server-client and P2P (peer to peer) technology.

Prerequisites. Data structures and algorithms, Computer architecture.

Course contents.
1. Introduction. Intranet, Internet. OSI multi-level reference model. Communications: protocols and services, packets.
2. Understanding networking concepts. Network layers: physical link, data link, medium access. Topology of computer networks. Routers (LS and DV algorithms).
3. Protocols: TCP/IP, BGP, HTTP, SOAP.
4. Distributed systems. LAN & WAN Internet-working technologies. Models and services (file and WEB servers, client-server, RPC, P2P). Naming, security, caching.
5. Network programming. Regular expression. DOM & SAX parsers, XML transformations. Java servlets.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. Students' knowledge is continuously assessed through tests and homework. In lectures students study principles of computer networks and their services (ftp, web services, RPC, P2P). In exercises students should become able to solve programming techniques (java servlets, parsers, XSLT) and acquire some skills referring to usage of network services and protocols. They should also use this knowledge to program mobile equipment (WML/WAP) and PDA (personal digital assistant). The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises.

Literature:
Recommended literature:
[1] Tanenbaum, A.S. Computer Networks, Prentice Hall; 4th Edition (August 9, 2002), ISBN: 0130661023
[2] Comer, D.E. Internetworking with TCP/IP Vol.1: Principles, Protocols, and Architecture, Prentice Hall; 4th Edition (January 18, 2000), ISBN: 0130183806
Additional literature:
[3] E. R. Harold, Java Network Programming, O'Reilly UK, 2000
[4] E. Cerami, Web Services Essentials, O'Reilly UK, 2002
[5] Todd Lammle, CCNA: Cisco Certified Network Associate Study Guide, Third Edition, Sybex, 2002

Computers lab (practicum) I018 (2+0+2) - 6 ECTS credits

Course objective. The objective of this course is to teach students how to solve complex and network programming tasks through team work. This practicum is the link between all previously attended computer-related courses. Throughout lectures students will find out more information about relationships between mathematical tools and the web environment. In exercises they will learn how to solve two specific projects and how to publish them on the web. Projects may cover methodical problems in mathematics and physics, which enables their usage primary and secondary school education.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. Projects. Team work.
2. Matlab WEB server. Preparation of Matlab programs for WEB. Checking of local version. Localhost.
3. Web Mathematica. Preparation of WRI Mathematica programs for WEB. Mathematica server pages (MSP).
4. Testing of final versions of projects. Methods for program testing.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. During exercises students will become trained for solving concrete problems from the fields of biology, chemistry, physics and engineering by using ready-made software packages or by making their own programmes.
Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] D. J. Higham, N.J. Higham, MATLAB Guide, SIAM, Philadelphia, 2000
[2] R.E. Maeder, Programming in Mathematica, 3/E, Addison-Wesley, Boston, 1995
[3] S. Wolfram, The MATHEMATICA ® Book, Version 4, Cambridge Univ., Cambridge, 1999
Additional literature:
[4] T. L. Harman, J. B. Dabney, N. J. Richert , Advanced Engineering Mathematics with MATLAB, Brooks Cole, Pacific Grove, 1999
[5] E. Don, Schaum's Outline of Mathematica, McGraw-Hill Trade, NewYork, 2000
[6] R. Pratap, Getting Started With Matlab: Version 6: A Quick Introduction for Scientists and Engineers, Oxford University Press, NewYork, 2002

Real analysis M043 (4+2+0) - 8 ECTS credits

Course objective. The knowledge pertaining to the courses Differential calculus and Integral calculus would be broaden in a mathematically formal way.

Prerequisites. Differential calculus, Integral calculus.

Course contents.
1. Sequences. Convergent sequence. Subsequences. Upper and lower limits. Cauchy sequences. Banach’s fixed point theorem. Convergence of sequences of functions.
2. Series. Convergence. Absolute convergence. Tests for convergence and divergence of series. Series of functions. Convergence of series of functions. Uniform convergence of a series of functions
3. Continuity and limit of function. Cauchy and Heine definition of continuity. Properties of continuous functions. Monotonic functions and continuity. Continuity of elementary functions. Uniform continuity. Cauchy’s and Heine’s definition of the limit of a function. Properties of the limit.
4. Differential calculus. Derivative. Theorems on derivatives.
5. Integration. Darboux sums. Riemann integral. Riemann theorem. Mean value theorem of integral calculus. Newton-Leibniz formula. Darboux theorem.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students can take 2 tests that replace the written examination.

Literature:
Recommended literature:
[1] W.Rudin, Principles of Mathematical Analysis, Mc Graw-Hill, Book Company, 1964
[2] S. Kurepa, Matematička analiza 1 (diferenciranje i integriranje), Tehnička knjiga, Zagreb, 1989
[3] S. Kurepa, Matematička analiza 2 (funkcije jedne varijable), Tehnička knjiga, Zagreb, 1990
Additional literature:
[4] S. Mardešić, Matematička analiza u n-dimenzionalnom realnom prostoru I, Školska knjiga, Zagreb, 1977
[5] B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke, Tehnička knjiga, Zagreb, 1986

Complexity of algorithms I019 (2+2+0) - 4 ECTS credits

Course objective. Teach basic algorithms, implementation of algorithms, NP-hard problems.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. Recurrence relations. Orders of magnitude. Classification of functions by their rate of growth.
2. Classes of algorithms. Brute force. Dynamic programming. Branch and bound. Divide and Conquer.
3. Algorithms on graphs. Colouring of graphs. Hamilton cycles. Shortest path. Minimal Spanning Tree. Warshall, Floyd, Dijkstra, Prim and Kruskal's algorithms. Graph traversal algorithms. Bi-partite graphs.
4. Algorithms on strings. String matching algorithms: Knuth-Morris-Pratt, Boyer-Moore, Rabin-Karp.
3. Integer programming. Knapsack problem.
4. Sorting algorithms.
5. NP-hard problems. Travelling Salesman Problem. Genetic and evolution algorithms.

Literature:
Recommended literature:
[1] E. Horowitz, S. Sahni, S. Rajasekaran, Computer Algorithms, W. H. Freeman, 1997
[2] R. Sedgewick, Algorithms in C, Addison-Wesley, 1990
Additional literature:
[3] T.H. Cormen, C.D. Leiserson, R.L. Rivest, Introduction to Algorithms, MIT Press, 1990
[4] U. Manber, Introduction to Algorithms: A Creative Approach. Addison-Wesley, 1989
[5] D. Salomon, Data Compression: The Complete Reference. Springer, 1998

Stochastic processes M044 (2+2+0) - 6 ECTS credits

Course objective. An introduction into basic ideas and examples of stochastic processes at the level of a first course in processes. Attention is focused on models of processes in various branches of science. Lectures are to be given in an informal way, illustrating their utility and applications. Exercises should enable students to become able to master different techniques and solve particular problems.

Prerequisites. Probability theory.

Course contents.
1. Introduction. Nonnegative discrete random variables. Convolutions. Generating functions. Discrete – time random processes.
2. Basic Random Processes. Simple branching processes (Galton-Watson). Limiting distributions and the continuity theorem. Simple random walk. Stopping-times. The Wald equality.
3. Markov Chains. Construction and basic properties. Examples. Transition probabilities of higher degrees. Decomposition of the state space. The concept of dissection. Transitivity and recurrence. Periodicity. Canonical decomposition (on recurrent classes and transient states). Probability of absorption. Invariant measures and stationary distributions. Limiting distributions. Examples from genetics and simulation procedures (Monte Carlo method by Markov chains).
4. Renewal Theory. The analytic background. Counting renewals. Renewal processes with awards. The renewal equation. The Poisson process as a renewal process. Limit theorems for renewals. Regenerative processes.
5. Point Processes. The Poisson process. Transforms of the Poisson process. Marking and thinning. Ordered statistics. Laplace functionals.
6. Continuous-Time Markov Chains. Definition and construction. Stability, explosions, the Markov property. Dissection. The backward equation and the generating matrix. Stationary and limiting distributions. The Laplace transforms method. Examples.

Teaching methods and student assessment. Lectures and seminars are obligatory. During the semester students are encouraged to take tests. The final examination consists of both a written and an oral part.

Literature:
Recommended literature:
[1] S.I.Resnick, Adventures in Stochastic Processes, Birkhauser, Boston 1992
[2] G.R.Grimmet, D.R.Stirzaker, Probability and Random Processes, Clarendon Press, Oxford 1992
[3] J.R.Norris: Markov Chains, Cambridge University Press, 1998
Additional literature:
[4] R.Durret, Probability: Theory and Examples, Wadsworth & Brooks, 1991
[5] S.Karlin,H.M.Taylor: A first course in stochastic processes. Second edition. Academic press. New York-London, 1975
[6] P.Embrechts,C.Klueppelberg,T.Mikosch: Modelling extremal events. For insurance and finance, Springer-Verlag, Berlin, 1997
[7] S.M. Ross: Introduction to Probability Models, Eighth Edition. Academic Press; 8 edition. 2002
[8] S.M.Ross: Stochastic processes. Second Edition. John Wiley & Sons, Inc., New York, 1996
[9] N.Sarapa: Teorija vjerojatnosti, Školska knjiga, Zagreb 1992

Software engineering I008 (2+1+1) - 5 ECTS credits

Course objective. To unify contents of computer science courses attended during studies, especially the ones referring to programming. To study systematically methods and tools for software development, ways of managing software development projects as well as evaluation of costs.

Prerequisites. Programming languages, Data structures and algorithms, Computer networks and services, Operating systems, WEB programming.

Course contents.
1. Introduction. Software products and demands. Elements of development process. Project management.
2. Requirements and specifications. Documentation and analysis of requirements. Model of process and life-cycle model. Definitions of requirements. Prototype development. Formal and algebraic specifications. «Cleanroom» approach. Model-based specifications.
3. Design. Architecture-based design. Object-oriented design. Functional design. Design with time critical requirements. Design on the level of component. User interface. Object creation. Writing programs. Web engineering.
4. System reliability. Software reliability. Approaches to fault detection and tolerance, handling exceptions and defense programming. Software reuse. Software with increased safety.
5. Verification and evaluation. Testing method (planning, strategies). Defect targeted testing („black box“ model, structural model, interface testing). Static verification.
6. CASE (Computer-aided Software Engineering). Basic terms. Integrated CASE. Life-cycle of CASE approach. CASE evaluation tools (programming, analysis, design and testing).
7. Management of software development process. Concepts of project formation. Human resources management (employee selection, team work, working environment). Estimation of software development costs (techniques, algorithmic model, duration model, workers model). Quality management (standards, evaluation parameters, documentation). Risk analysis. Process improvement (process parameters, SEI model).
8. Design. Delivery and maintenance of software products. User-oriented configuration. Reengineering (source code transformations, program restructuring, adjustment to data, reversible approach).
9. Software engineering future. Wassermann's concept.

Teaching methods and student assessment. Lectures and exercises are obligatory. Lectures elaborate in detail methods and tools for software development as well as models of evaluation of costs. During exercises students work in project teams. On the basis of theoretical knowledge and programming skills acquired in previous courses, students carry out simpler independent tasks, which make a project as a whole. Students’ activity is continuously assessed and evaluated, and the level of their overall knowledge is tested and graded by the final oral examination.

Literature:
Recommended literature:
[1] I. Sommerville, Software Engineering (6th edition), Addison Wesley Publ. Co., USA, 2000
[2] S.L. Pfleeger, Software Engineering, Theory and Practice, Prentice Hall, USA, 2001
Additional literature:
[3] R.S. Pressman, Software Engineering, A Practitioner's Approach (5th edition), McGraw-Hill, USA, 2000
[4] I. Crnković, U. Asklund, A. Persson-Dahlquist, Implementing and Integrating Product Data Management and Software Configuration Management, Artec House Publishers, USA, 2003

Statistics M045 (2+1+1) - 6 ECTS credits

Course objective. To introduce basic notions and results of mathematical statistics in order to make students understand methods of statistical inference and to develop skills in their applications.

Prerequisites. Probability.

Course contents.
Statistical model. Random sample simulation.
Estimator and its properties (sufficient statistics, properties of estimator, Results on MVUE).
Point estimation methods (LSE (multivariate linear regression, nonlinear regression), MLE, MM).
Elements of hypothesis – testing theory (statistical hypothesis, errors, parametric hypothesis tests and test properties, Results on UMP tests).
Hypothesis – testing methods (heuristic approach, generalised likelihood ratio tests, Wald tests, tests in GLM, nonparametric tests of distributional assumptions).

Teaching methods and student assessment. Students should attend lectures, do their homework and seminars. The final examination consists of the written and the oral part. The final grade is a combination of grades obtained in seminars, homework and the final examination.

Literature:
Recommended literature:
[1] R.C. Mittelhammer, Mathematical statistics for economics and business, Springer, 1996
Additional literature:
[2] E.L. Lehman, Testing Statistical Hypothesis, Springer, 1997
[3] E.L. Lehman, G. Casella, Theory of Point Estimation, Springer, 1998
[4] J.E. Freund, Mathematical Statistics, Prentice Hall, 1992

Data structures and algorithms I011 (2+2+0) - 5 ECTS credits

Course objective. Teach student various kinds of simple and complex data structures and algorithms. Apply these structures and algorithms by means of the object-oriented programming language. Show the influence of a data structure on the design and efficiency of algorithms and computer programmes.

Prerequisites. Introduction to computer science, Introduction to programming.

Course contents.
1. Introduction. Basic notion and definitions. Data types and statements. From elementary to complex data structures - from statementsto functions and programs. Abstract structure. Algorithms.
2. Data structures. Arrays. Lists (single and double linked, circular lists). Queues. Stacks. Trees. Recursive structures. Tree traversal. Files.
3. Searching and sorting. Linear and binary searching. Priorities queues. Heap. Complex searching: R-B trees, AVL trees, hash tables. Hashing. Sorting algorithms: bubble sort, insertion sort, heap sort, selection sort, quicksort, etc.
4. Algorithms. Greedy algorithms. Recursion. Backtracking techniques. Dynamical programming.
5. Graphs. Minimum spanning trees. Traversing a graph: Breadth-First Search (BFS) and Depth-First Search (DFS). Prim's and Kruskal's algorithm. Dijkstra's algorithm.
6. NP hard problems. Introduction to network algorithms. Bi-partitive graphs. Strongly related components. Euler's and Hamiltonian travelling. The travelling salesperson problem. Game theory.

Teaching methods and student assessment. Students should attend lectures and exercises. Students learn important simple and complex data structures (lists, trees, graphs, etc.) and related algorithms (trees and graphs traversals, sorting and searching, etc.). During exercises students solve algorithm techniques by using the object-oriented programming language. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] D. Knuth, The Art of Computer Programming, Vol. 1, Fundamental Algorithms, Addison-Wesley, Reading, MA, USA, 1997
[2] S. Lipschutz, M. Lipson, Schaum's Outline of Discrete Mathematics, Mc-Graw Hill, New York, USA, 1997
[3] S. Lipschutz, Theory and Problems of Data Structures, Mc Graw-Hill, New York, USA, 1986
Additional literature:
[4] D. Flanagan, Java in a Nutshell, O'Reilly UK, 2002
[5] M.A. Weiss, Data Structures and Problem Solving Using Java, Addison Wesley, USA, 2001
[6] D. A. Bailey, Java Structures, McGraw-Hill Education, 2002

Game theory M047 (1+0+1) - 2 ECTS credits

Course objective. Make students familiar with basic ideas and methods of game theory.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. Basic concepts, motivation, definitions.
2. Strategies. Some special game theory strategies are considered as well as optimal answers to each of them. Maxmin strategy and Minmax strategy are pointed out. Various games are studied, spacially game solutions with the sum equal to zero, 2xn and mx2 games. Domination. Symmetric games and games similar to the game of poker. Minimum and maximum strategy and games with the sum which differs from zero. Mixed strategies of nonzero-sum games. Mixed Nash equilibria in 2x2 nonzero-sum games.

Teaching methods and student assessment.
Students should obligatorily attend lectures and exercises. Basic concepts will be considered and their applications illustrated. In exercises students will master techniques and methods of solving tasks and apply them to real problems. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] S.Stahl, A Gentle Introduction to Game Theory, American Mathematical Society, 1999
Additional literature:
[2] Roger B. Myerson, Game Theory: Analysis of conflict, Harvard University Press, Cambridge, London, England, 1997
[3] Martin J. Osborne, A. Rubinstein, A Course in Game Theory, MIT Press, Cambridge, USA, 1994

Decision theory M048 (1+0+1) - 4 ECTS credits

Purpose of the course. Make students familiar with basic ideas and methods in decision theory. Students will be motivated for studying standard problems of decision theory through illustrative examples. They will learn basic methods for solving standard problems of decision theory.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Decision in conditions of uncertainty. Decision tables, basic criteria for decision analysis under uncertainty, expected value. Decision tree.
2. Multi-criteria decision analysis. Ordering relations, preference relations. Methods which use the referent points, compromise ranking, TOPSIS method. Methods ELECTRE and PROMETHEE. Methods of determination of weight criteria, eigenvalue method, method of entrophy. Analytic hierarchy process (AHP method). Group decision making, methods for Group decision making.
3. Program support. Treeplan (for decision tree), Expert Choice (for AHP method), Promcalc (for PROMETHEE method), Team Expert Choice (for Group decision support).

Teaching methods and student assessment. Lectures will be illustrated by using ready-made software and an LCD projector. Students will be assigned practical seminar papers. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises. Seminar papers may replace the written part of the final examination.

Literature:
Recommended literature:
[1] S.French, Decision Theory, Ellis Harwood, Chichester. (1986)
[2] E.Triantaphyllou, Multi-Criteria Decision Making Methods: A Comparative Study, Kluwer Academic Publishers Dordrecht/Boston/London. (2000)
Additional literature:
[3] M.R..Klein, L.B.Methlie, Knowledge-based Decision Support Systems, I.Wiley&Sons (1995)
[4] T.X.Bui, Co-oP, A Group Decision Support System for Cooperative Multiple Criteria Group Decision Making, Springer-Verlag, Berlin. (1987)
[5] T.Gal, T.J.Stewart, T.Hanne (eds.): Multicriteria decision making, Advances in MCDM Models, Algorithms, Theory, and Applications, Kluwer Academic Publichers, Dordrecht/Boston/London, 1999
Journals:
European Journal of Operational Research
Journal of the Operational Research Society
Journal of Multi-Criteria Decision Analysis

Theory of Difference Schemes M055 (1+1+0) - 2 ECTS boda

Content:
For most differential equations it is unlikely that exact solutions can be found. However, numerical methods can give excellent approximations. This course introduces the basic ideas and shows how can be applied for particular cases. It covers the generation and propagation of roundoff errors, convergence criteria and efficiency of computations. Includes these topics:
1. Introduction. Examples of approximation. First-order difference operators. Second-order difference operator and its properties. The elimination method. A sample of a difference scheme.
2. Basic concepts. Introducing the difference scheme. Approximation. Correctness. Convergence. The relation between those concepts. A lot of examples.
3. Difference schemes for the heat-conduction equation. The forward scheme. The implicit scheme. Schemes with variable weight factors. Three-layer difference schemes.
4. Stability theory. Classes of difference schemes. Stability of two-layer difference schemes in various spaces. Reducing three-layer difference schemes to the two-layer ones. Stability of three-layer difference schemes. Schemes with non-autoadjoint operators.
5. Difference schemes for the transfer equation. Two-layer schemes with weight factors. Schemes with a conditional approximation.
6. Difference schemes for the vibrations of a string. Two-layer schemes with weight factors. Methods for the improvement of the approximation`s order.
7. Symmetrizable difference schemes. Classes of symmetrizable difference schemes. Criteria for stability.
8. Asymptotic stability. Criteria for the asymptotic stability of symmetrizable difference schemes. Example of stable, but not asymptotic stable schemes.

Expected work: Throught the semester several projects will be assigned, some involving programming skills. The projects are normally undertaken by individuals. Each project is followed by a class presentation.

Grading: Homeworks and Projects (40%), Finalterm (60%).

References:
[1] A.A. Samarskii, The Theory of Difference Schemes, Marcel Dekker, New York, 2001. Extra Readings:
[2] M. Schatzman, Numerical Analysis, Clarendon Press, Oxford, 2002
[3] A Kharab, R. Guenther, A Mathlab Approach, Chapman&Hall/CRC, 2002
[4] M. Spiegel, Calculus of finite differences and difference equations, McGraw-Hill, 1994.

Pupils' mathematical competitions M056 (1+0+1) - 3 ECTS credits

Course objective. The objective of this course is to prepare students – future teachers for working with advanced pupils in mathematics, as well as for working referring to preparing pupils for mathematical competitions. Through lectures and seminar papers, various fields of mathematics will be included with contents suitable for primary and secondary schools.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Arithmetics (number theory: divisibility, congruencies, number systems, diophantine equations).
2. Applications of mathematical induction.
3. Complex numbers.
4. Equations and inequations (functions, algebraic equalities and inequalities).
5. Analytic geometry in the plane and in space.
6. Planimetry (plane geometry: figures in the plane, measuring sets of points).
7. Stereometry (solid geometry: geometric solids in space, measuring sets of points).
8. Trigonometry – applications.
9. Vectors in the plane and in space.
10. Combinatorics and probability theory.

Teaching methods and student assessment. Students should attend lectures and exercises. They should present their seminar papers in which they analyse certain mathematical topics, and at the same time they choose examples and tasks intended for appropriate age of primary and secondary school pupils. Students obtain the final grade on the basis of their written seminar paper and its oral presentation, which also encompasses the oral examination.

Literature:
Recommended literature:
[1] B. Pavković, D. Veljan: Elementarna matematika I, Tehnička knjiga, Zagreb, 1992
[2] B. Pavković, D. Veljan: Elementarna matematika II, Školska knjiga, Zagreb, 1995
Additional literature:
[3] B. Pavković et al., Elementarna teorija brojeva, Mala matematička biblioteka, HMD, Zagreb, 1994
[4] B. Pavković et al., Male teme iz matematike, Mala matematička biblioteka, HMD, Zagreb, 1994
[5] Ž. Hanjš, Međunarodne matematičke olimpijade, Element, Zagreb, 1997
[6] Ž. Hanjš, S. Varošanec, Matematička natjecanja, HMD – Element, Zagreb, 1996
[7] V. Stošić, Natjecanja učenika osnovnih škola, Matkina biblioteka, HMD, Zagreb, 2000
[8] N.B. Vasiljev, A.A. Jegorov, Zbirka pripremnih zadataka za matematička natjecanja, Element,
Zagreb, 2000
[9] Journals: Matka, Matematičko-fizički list, Osječka matematička škola, Crux Mathematicorum,
Mathematics Magazine

Managing credit risk E009 (2+0+2) - 4 ECTS credits

Course objective. The objective of the course is to make students familiar with basic concepts, tools and models in credit and credit risk analysing. The course is divided into three parts: (I) Introduction – including definition of basic concepts regarding credits and credit risks; (II) Credit risk models – including the overview of certain credit risk models used in financial institutions for making better business decisions, and different input variables and methods used in establishing these models. In this part students can also find an overiew of methods used for developing models without mathematical arguments and deductions, including the explanation of the purpose of every method; (III) Implementation – including an overview of basic steps that are necessary to make in succesful model implementation.

Prerequisites. Not required.

Course contents.
1. Credit policy: Trends in amount and quality increase of credit financing. Credit trend in Croatia and in the world. Changings in population's and company's attitude towards crediting.
2. Characteristics of different credit types. Real estate credits. Commercial credits. Consumers credits.
3. Types of risks. Credit risk. Liquidity risk. Interest risk. Operational risk. Capital risk. Currency risk.
4. The concept of credit risk: Necessity of measuring credit risk. Defining credit risk. Basel accord.
5. Classic credit analysis: Credit process. Credit analysis. Evaluation of commercial credits. Evaluation of consumer credits.
6. Introduction to credit risk models: Imperfections of classic credit analysis. Need for credit risk models. Importance of credit risk models in better desicion making. Different ways in application of credit risk models.
7. Methods in creating credit risk models overview: Statistical methods. Neural networks. Decision trees. Genetic algorithms.
8. Credit risk models based on accounting data: Altman Z-score model, ZETA model. Other statistical models and neural network models.
9. Credit risk models based on equity price: Option price. EDF model. KMV model.
10. Consumers credit risk models. Criterias for different consumers credits. Role of experts in credit risk analysis. Quantitative models.
11. Smallbusiness credit risk models. Problems in creating models for smallbusiness companies. Importance and reasons for applying smallbusiness models. RMA model.
12. Testing and implementation of credit risk models. Quality of model. Stability of model. Monitoring performances of model. Usage of model in decision making process.

Teaching methods and student assessment. Teaching methods used during the course are lectures and seminars, with a combination of group discussions and case analyses. Attendance and activity at both lectures and seminars are required. Students’ knowledge will be assessed on a regular basis through tests and various assignments. Furthermore, students have to pass the final examination which will be in the written and the oral form. Students are encouraged to work on the project which will represent the application of defining models on the example, and influence the final grade.

Literature:
Recommended literature:
[1] J.B.Caouette, E.I.Altman, P.Narayanan,, Managing Credit Risk, John Wiley & Sons, New York, 1998
[2] M.Croughy, D.Galai, R. Mark, Risk Management, McGraw-Hill, New York, 2001
Additional literature:
[3] E.I.Altman, A.Saunders, Credit Risk Measurement: Development over the last 20 Years, Journal of Banking and Finance, 21, 1998, p.1721-1742.
[4] D.J.Hand, S.D.Jacka, editors, Statistics in Finance, Arnold Application in Statistics, John Wiley & Sons Inc., New York, 1998
[5] T.W.Koch, S.S.MacDonald, Bank Management, South-Western Thomson, United States, 2003

Office operations I020 (0+1+1) - 3 ECTS credits

Course objective. Develop general and specific knowledge and skills of students referring to office operations in modern business conditions. Apart from the general framework of office operations, their development, structure and processes, students should learn about the standards and norms of office operations, principles of modern business communication, and acquire skills required for practical application of digital technology in business operation systems.

Course contents.
1. Business office structure. Business administration. Types of data processing. Office information system. Computer equipment. Telematic equipment. Other equipment and premises. Human resources. Office communication and office etiquette. Integral programme systems for office operations. Organisation of office operations. Front office. Back office.
2. Business administration. Definition of business administration. Evolution of administrative subsystem. Business process administration. Administrative procedures. Administration of communications. Standardisation of administration. Appropriate behaviour in different situations. Administration organisation, management and control. Group work. Parkinson's laws.
3. Office operation automatisation. Implementation of automatic devices, computers and telematic equipment in offices. Business process theory and management. Data processing. Business reporting. Information. Time management.
4. Computers in office operations. Computers. Printers. Plotters. Scanners. Other peripheries in office operations. Computer applications. Server architectures. Integrability. Compatibility.
5. Programme equipment. Operation systems. Office tools. Design tools. Documentation tools. Databases. Organisers. Address books/lists. Communication tools. Multimedia. Videoconferencing. Message exchange. Programme tools for integrating office operations (groupware). Other programme equipment. Human resources training. Intuitiveness of programme equipment. Intelligent assistance in work.
6. Documentation. Structure and formatting of business documents. Operations by work flow. Electronic multi-purpose documents. Norms and standards. IntroNet. Computer-supported cooperation. InterNet. Remote presence and distance work. Object model of documents, hypertext and hypermedia. Processing, storing, access, exchange and operations by means of multimedia documents. Languages for description and exchange protocols for multimedia documents. Procedures for integrating office distributed applications. Browsers and editors. Document reproduction and storage. Document preservation. Document safety.
7. Communication and specialised telematic equipment. Oral (talks, meetings, presentations) and written communication (business correspondence, fax, electronic mail, SMS, MMS, Web, Internet discussions). Telematic services. Telephone. Mobile communications. Tele-text. Videotext. Fax. Telex. Short message communication.
8. Other equipment and premises. Work environment based on eOffice model. Ergonomics of office equipment and premises. Work disturbances. Noise. Light. Dynamism. Electronic pollution.
9. Office development trends. Global trends. Global growth of administration workers. Decentralisation of office operations. dOffice. eOffice. mOffice. vOffice. Globalisation and office operations. New technologies for office operations.

Teaching methods and student assessment. Exercises and seminars are obligatory. Students' knowledge is assessed during the year through assignments in which students need to solve practical problems in office operations. Each assignment is designed to cover one segment of office operations (from data processing by text processor Word, table calculator Excel, to programmes for presentations, communication, and time management MS Outlook etc.). The final grade is given on the basis of the average assignment grade and the oral examination.

Literature:
Recommended literature:
[1] V. Srića, A. Kliment, B. Knežević, Uredsko poslovanje, Strategija i koncepti automatizacije ureda, Sinergija, Zagreb, 2003
[2] Mesarić, J., Zekić-Sušac, M., Dukić, B.: PC u uredskom poslovanju, EFO, Osijek 2001
Additional literature:
[1] V.Čerić, M.Varga, H.Birolla (Eds.), Poslovno računalstvo, ZNAK, Zagreb, 1996
[2] Mosher, S., SAMS Teach Yourself Microsoft Outlook 2000 Programming, SAMS Indianapolis
[3] Kliment, Antun: Digitalne poslovne komunikacije, Ekonomski fakultet Zagreb, Mikrorad, 2000
[4] http://www.office.com

Introduction to financial engineering M053 (2+1+1) - 4 ECTS credits

Course objective. The objective of this course is to make students familiar with the main ideas and mathematical models of the money, bond and stock market. Where possible, the theory will be illustrated by practical examples from banking practice and other fields of application.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. A simple market model.
2. Risk-free assets (time value of money, money market).
3. Risky assets.
4. Discrete time market models.
5. Portfolio management.
6. Financial engineering. Variable interest rates. Stochastic interest rates.

Teaching methods and student assessment. Lectures will be illustrated by ready-made software packages and graphics using a PC and an LCD projector by means of Mathematica or Matlab. Exercises are partially auditory and partially laboratory. Students will be expected to participate in lectures by doing independent seminar papers. The final assessment consists of both the written and the oral examination that can be taken after the completion of all lectures and exercises. During the course students can take 2-4 tests that completely cover course contents. Successfully passed tests replace the written examination. During their studies students are encouraged to prepare a seminar paper. Successful seminar papers influence the course final grade.

Literature:
Recommended literature:
[1] M. Capinski, T.Zastawniak, Mathematics for Finance. An Introduction to Financial Engineering, Springer Verlag, Berlin, 2003
Additional literature: [2] L. Kruschwitz, Finanzmathematik, Verlag F. Vahlen, München, 1989
[3] B.Relić, B.Šego, Financijska matematika 2. Birotehnika, Zagreb, 1990
[4] S.B. Block, A.Conway, G.A.Hirt, Foundations of Financial Managment, A.Homewood, 1998
[5] M.Baxter, A.Rennie, Financial Calculus: An Introduction to Derivative Pricing, Cambridge Univ. Press, Cambridge, 2002
[6] M.Crnjac, D.Jukić, R.Scitovski, Matematika, Sveučilište u Osijeku, Osijek, 1994

Introduction to programming I010 (2+2+0) - 3 ECTS credits

Course objective. Teach students essentials of computer programming in a procedural programming language. Train them in producing simple algorithms and making programs based on them in a procedural programming language. Develop in students the way of thinking which will enable them to solve more complicated algorithmic and programming problems. Teach students in solving simple problems of numeric mathematical methods using self made programs.
Teach students introductory knowledge in object oriented and visual oriented programming. Give students prerequisites which will be useful in further self education on computers.

Prerequisites. Basic computer literacy. Basic knowledge on how computers work (both hardware and software). Partial knowledge of English. High-school mathematics.

Course contents.
1. Introductory part: Programme development Procedural and visual programming languages. Parts of a procedural programming language, C++ programming language features.
2. Programming. Basic (internal) programming structures (sequential, selection and iteration structures). Assignment statement and I/O statements, using files. Complex types – fields (vectors and arrays) Pointers, dynamic memory allocation.
3. Subroutines. Functions and procedures. Parameter exchange by value and by reference. Global variables. Numeric methods examples: Newton Raphson method, Simpson integration method , Fourier series. Using functions as parameters. Recursions.
4. Introduction to object oriented and visual programming. Classes and object in C++ language. Visual programming. Visual Basic examples.
Teaching methods and student assessment. Lectures and exercises are obligatory. During the course students’ knowledge will be regularly assessed by tests and homework. The final assessment consists of both the written and the oral examination that can be taken after the completion of all lectures and exercises.

Literature:
Recommended literature:
[1] B. Stroustrup, The C++ Programming Language, Addison Wesley, 2000
[2] Ortega. Grimshaw: An Introduction to C++ and Numerical Methods, Oxford University Press, New York 1999
Additional literature:
[3] M. Essert, C/C++ programski jezik, Zavodska skripta, FSB, 2000
[4] Kernighan, Ritchie: “ANSI C”, II. izdanje, Prentice Hall, Engelwood Clifs, New Jersey, 1988

Introduction to computer science I021 (2+2+0) - 6 ECTS credits

Course objective. Make students familiar with basic ideas and methods of computer science which will be the basis for other computer courses. Simple examples of programmes in local and web environment will be interesting for students and encouraging in their future usage of computers. Throughout lectures students will acquire knowledge of the basic concepts and their application. During exercises students will master basic techniques of programming (C and Java) on simple examples from standard and web programming.

Prerequisites. Not required.

Course contents.
1. Introduction. Short history of computer science. Computer architecture. Algorithms and programming, computers nets, databases, human-computer communication.
2. Programming. From data and algorithms to programmes. Types of data. Flowchart of programmes. Basic program control – program structures and loops. Compilers.
3. Markup Languages. Information on the Internet. XML (SGML) and HTML languages. Browsers. Interpreters. From editor to Javascript programme in browser.
4. Subroutines. Functions. Function arguments and parameters. Data transfer and data interchange. Simple examples in C and Javascript.
5. Users function and libraries. Programme libraries. Calling of functions. Construction of own Program libraries.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. During exercises students will become trained for solving concrete problems from the fields of biology, chemistry, physics and engineering by using ready-made software packages or by making their own programmes.
Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] C. Horstmann, Computing Concepts with Essentials (3rd Edition), John Wiley & Sons, Inc., New York, 2002
[2] Dale & Lewis, Computer Science Illuminated, Jones and Bartlett Publishers, http://csilluminated.jbpub.com/ Sudbury, 2002
Additional literature:
[3] A.S. Tanenbaum, Structured Computer Organization, 5th ed., Prentice-Hall, New Jersey, 1999
[4] D. Patterson, J. Hennessy, Computer Organization and Design: The Hardware / Software Interface, 2nd Edition, Morgan Kaufmann Publishers, San Francisco, 1997

Introduction to approximation theory M054 (2+2+0) - 4 ECTS credits

Course objective. The objective of this course is to make students familiar with the main ideas and methods of approximation theory. Special attention will be paid to Chebyshev’s approximations and least squares approximations. Where possible, the theory will be illustrated by practical examples from various fields of application. Students are expected to participate in the teaching process by doing independent seminar papers.

Prerequisites. Bachelor level degree in mathematics or engineering.

Course contents.
1Introduction. Motivation and examples. Convexity. Existence and uniqueness of the best approximation in normed vector spaces. Convex functions and local minima.
2. Chebyshev's approximation. Chebyshev solution of the nonconsistent system of linear equations. Characterisation of the solution. Algorithms: Polya, ascent algorithm, descent algorithm. Polynomial approximation. Weierstrass theorem. Uniqueness problem. Error of approximation. Remes algorithms.
3. Least squares approximation. Illustrative examples. Continuous least squares approximation. Systems of orthogonal polynomials. Fourier polynomial and series. Discrete least squares approximation.
4. Rational approximation. Existence. Characterisation of the best approximation. Uniqueness. Algorithm. Pade approximation.

Teaching methods and student assessment. Exercises are partially auditory and partially laboratory. Students will use PCs and an LCD projector with Mathematica or Matlab. The final assessment consists of both the written and the oral examination that can be taken after the completion of all lectures and exercises. During the course students can take 2-4 tests that completely cover course contents. Successfully passed tests replace the written examination. During their studies students are encouraged to prepare a seminar paper. Successful seminar papers influence the course final grade.

Literature:
Recommended literature:
[1] E.W. Cheney, Introduction to Approximation Theory, AMS, Providence, 1998
Additional literature: [2] J.R.Rice, The approximation of Function, Wesley, Reading,1969
[3] D.Kincaid, W.Cheney, Numerical Analysis, Brooks/Cole Publishing Company, New York, 1996
[4] J.Stoer, R.Bulirsch, Introduction to Numerical Analysis, 2^{nd} Ed.,Springer Verlag, New York, 1993
[5] R.Scitovski, Numerička matematika, Odjel za matematiku, Osijek, 2000

Vector spaces M051(2+2+0) - 6 ECTS credits

Course objective. The objective of the course is to give a more general view to the notions and results students encounter in linear algebra courses during the first two years of study. By a more abstract approach one should understand more deeply and more clearly the matter basic for many modern mathematical disciplines.

Prerequisites. Geometry of plane and space. Linear algebra I and II.

Course contents.
1. Finite dimensional spaces. Basis and dimension. Subspaces. Quotient spaces. Dual space.
2. Linear operators. The space L(V,W) and the algebra L(V). Matrix of a linear operator. Theorem on rank and defect. Dual operator.
3. Minimal polynomial and spectrum. Polynomial of a linear operator. Minimal polynomial. Spectrum. Characteristic polynomial. Hamilton–Cayley theorem.
4. Invariant subspaces. Projections. Invariant subspaces. Projections and their algebraic characterisation.
5. Nilpotent operators. Fitting decomposition. Nilindex. Nilpotent operator. Index of nilpotence. Nilpotent operators of maximal index. Elementary Jordan cell. Decomposition of a nilpotent operator.
6. Reduction of a linear operator. The greatest common divisor of polynomials. Relatively prime polynomials. Decomposition of the kernel of a polynomial of a linear operator. Jordan form of a matrix of a linear operator.
7. Unitary spaces. Inner product. Cauchy–Schwartz–Buniakowsky inequality. Orthonormal bases. Bessel's inequality. Gram–Schmidt theorem. Theorem on othogonal projection. Selfadjoint, skewadjoint, unitary and normal operators. Diagonalisation.
8. Functions of linear operators. Convergence in L(V). Definition of f(A) for entire function f. Matrix of f(A) in Jordan basis. Operator f(A) as a polynomial. Lagrange–Sylwester polynomial. General definition of a function of a linear operator. Properties of the mapping ff(A). Spectrum of f(A).

Teaching methods and student assessment. Attending lectures and exercises is compulsory. The examination consists of the written and the oral part which take place upon completion of lectures and exercises. During the semester students can take tests which replace the written part of the examination.

Literature:
Recommended literature:
[1] H.Kraljević, Vektorski prostori, Odjel za matematiku, Sveučilište u Osijeku, 2005
[2] S. Kurepa, Konačno dimenzionalni vektorski prostori i primjene, Liber, Zagreb, 1992
Additional literature:
[3] D.M. Bloom, Linear algebra and geometry, Cambridge Univ. Press, 1988
[4] S. Lang, Linear algebra, Springer Verlag, Berlin- Heiedelberg-New York, 2004
[5] P.R. Halmos, Finite dimensional vector spaces, Van Nostrand, New York, 1958

Introduction to probability and statistics M050 (2+2+0) - 5 ECTS credits

Course objective. To introduce and apply basic notions and results of probability and statistics.

Prerequisites. First-year courses in mathematics, Multivariate functions.

Course contents.
Descriptive statistics (types of data, tables and graphs of data, measures of central tendency, variation, and symmetry; two – dimensional data, scatter plots, LSE, simple regression).
Elements of probability theory (elementary events, examples of probability, definition of probability, properties of probability, finite probability space, conditional probability and independence, theorem of total probability, Bayes's rule).
Random variable (discrete random variable, mathematical expectation, other numerical characteristics and their meaning (Markov inequality, Chebyshev inequality), continuous random variable, distribution function).
Parametric families of random variables (Bernoulli, binomial (application of Moivre-Laplace theorems, Poisson approximation - application), Poisson, geometric, normal, uniform, exponential).
Random vectors (two – dimensional discrete random vector, covariance and correlation dependence and conditional distributions, independence, two – dimensional normal random vector, independence in normal case, hi-square distribution, student t-distribution).
Law of large numbers, central limit theorems.
Elements of statistical inference (population and random sample, statistical model, parameter estimation, confidence intervals and testing for numerical characteristics of one population, homogeneity and independence tests for discrete variables, tests about difference in means, tests in simple linear regression).

Teaching methods and student assessment. Students should attend lectures, do their homework and seminars. The final grade is a combination of grades obtained in seminars, homework and the final examination.

Literature:
Recommended literature:
[1] J. Pitman, Probability, Springer, 1993
[2] Ž. Pauše, Uvod u matematičku statistiku, Školska knjiga, Zagreb, 1993
[3] S. Lipschutz, J. Schiller, Introduction to probability and statistics, Shaum’s outline series, McGraw-Hill, 1998
Additional literature:
[4] F. Daly, D.J. Hand, M.C. Jones, A.D. Lunn, K.J. McConway, Elements of Statistics, Addison-Wesly, Wokingham, England, 1995
[5] N. Sarapa, Teorija vjerojatnosti, Školska knjiga, Zagreb
[6] G. McPherson, Applying and Interpreting Statistics, A comprehensive guide, Springer, 2001
[7] G.M. Clarke, D. Cooke, A Basic Course in Statistics, Arnold, London, 1992
[8] J.T. McClave, P.G. Benson, T. Sincich, Statistics for Business and Economics, Prentice Hall, New York, 2001
[9] G. K. Bhattacharyya, R.A. Johnson, Statistical Concepts and Methods, J. Wiley, 1977

Probability M052 (2+2+0) - 6 ECTS credits

Course objective. To introduce standard notions of probability theory in order to understand and apply them, especially through other courses based on probability (statistics, random processes, time series analysis, multivariate analysis, etc.).

Prerequisites. Bachelor level degree in mathematics.

Course contents.
Random variable (distribution function, expectation, moment generating function, functions of random variables, parametric families of density functions).
Random vector (distribution function, expectation, covariance and correlation, independence, functions of random vectors, linear transformation of random vector and moments).
Basic asymptotic (types of random variable convergence, relationships between convergence modes, laws of large numbers, central limit theorems, central limit theorems for dependent random variables, multivariate central limit results, asymptotic distributions of differentiable functions of asymptotically normal distributed random).

Teaching methods and student assessment. Students should attend lectures, do their homework and seminars. The final grade is a combination of grades obtained in seminars, homework and the final examination.

Literature:
Recommended literature:
[1] N. Sarapa, Teorija vjerojatnosti, Školska knjiga, Zagreb, 1987
Additional literature:
[2] R.C. Mittelhammer, Mathematical statistics for economics and business, Springer, 1996
[3] T. S. Ferguson, A Course in Large Sample Theory, Chapman & Hall, London, 1996

Web programming and applications I026 (2+1+1) - 4 ECTS credits

Course objective. Teach students basics of Web programming of client and server applications. Practice Javascript, Java, PHP/MySQL programming on dynamical contents of Apache and Java Web server.

Prerequisites. Introduction to computer science, Data structures and algorithms.

Course contents.
1. Introduction. World Wide Web. URL - Uniform Resource Locators. Addressing. Statical Web pages.
2. Programming on the client side. HTML programming. XHTML. Cascading style sheets (CSS). Extendible Markup Language (XML). Javascript. Events and object's modules. Dynamical contents.
3. Java programming. Classes and objects. Elements of object programming: procedure abstraction and encapsulation, data and method inheritance. Object programming elements: polymorphism, inner classes, overriding. Java applets: life cycle, events.
4. Programming on the server side. CGI. Apache and Java web servers. PHP programming: control structures, functions, forms. Cookies. XML parser. Programming with WEB Mathematica and Matlab Web server.
5. Data bases on the Web. SQL programming. Programming the MySQL database with PHP/SQL. Secure programming.

Teaching methods and student assessment. Students should attend lectures and exercises. Students learn important facts of statical and dynamical contents on the Web and programming of client-server communication. Through exercises students learn how to master Web programming by means of examples from Javascript, Java applets, PHP/MySQL solutions and Web server programming tools. Student’s knowledge is continuously assessed during the semester by means of tests and homework. The final examination consisting of a written and an oral part takes places upon completion of lectures and exercises.

Literature:
Recommended literature:
[1] R. W. Sebesta, Programming the World Wide Web, 2/E, Addison-Wesley, 2003
[2] M. Essert, WEB programiranje, Zavodska skripta, FSB Zagreb, 2001
Additional literature:
[3] T. Powell, Thomas, Web Design: The Complete Reference. Berkeley, CA, Osborne/McGraw-Hill, 2000
[4] K. Kalata, Internet Programming, Thompson Learning, 2001
[5] M.Hall, L. Brown; Core WEB programming, A Sun Microsystems Press/Prentice Hall PTR Book, 2001

Scientific computing I024 (2+2+0) - 6 ECTS credits

Course objective. Teach students how to use computers in science with applications in numerical analysis (linear and nonlinear equations, integration, interpolation, simulations and optimisations). Design, build programmes (C++ or Java) and analyse parallel and sequential algorithms with good numerical properties.

Prerequisites. Bachelor level degree in mathematics.

Course contents.
1. Introduction. Fundamentals of IEEE 754/854 standard of finite precision arithmetic. Precision problems. Forward and (Wilkinson) feedback error analysis. Special algorithms for precise calculations.
2. Linear algebra. Solving sparse systems. Direct and iterative methods. Overconditioning. Eigenvalues.
3. Computational geometry. Delaunay and Voronoi diagrams. Conformal mapping. Graph separators: spectral and geometric methods.
4. Simulations. Monte Carlo method. Markov processes.
5. Parallel programming. Parallel architectures, data and instructions (Split-C, CM Fortran). PVM programming. Parallel cluster.

Teaching methods and student assessment. Students are obliged to attend lectures and exercises. In lectures students study concepts of finite precision arithmetic, linear algebra systems, PDE approximation, graphics design and elementary methods of Hilbert space. In exercises students should design and build programmes sequential and parallel programmes in those fields. Students' knowledge is continuously assessed through tests and homework. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises.

Literature:
Recommended literature:
[1] T.F. Comena, C. van Loan, Handbook for Matrix Computations, SIAM, Philadelphia, 1988
[2] A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Mancheck, V. Sunderam, PVM: Parallel Virtual Machine. A Users' Guide and Tutorial for Networked Parallel Computing, The MIT Press, Boston, 1994
Additional literature:
[3] I. Foster, Designinig and Building Parallel Programs, ACM Press, New York, 1995
[4] J.R. Rice, Matrix Computations & Mathematical Software, McGraw-Hill, NewYork,1983
[5] Y. D. Lyuu, Financial Engineering and Computation: Principles, Mathematics, and Algorithms, Cambridge University Press, Cambridge, 2001

Professional Colloquium II Z008 (0+0+2) – 2 ECTS credits

Course objective. Professional Colloquium is held at the Department of Mathematics, University of Osijek. It is primarily intented for teachers of mathematics and computer science employed at primary and secondary schools, as well as for students and all others having interest in it. Professional colloquium initiates communication between teachers of mathematics and encourages experience exchange and contact with the students of final years. The idea for Professional Colloquium developed from the Scientific Mathematical Colloquium that has been continuously organized since 1993. The colloquium also hosts different professional workshops and lectures related to mathematics and computer science as well as to other fields in some way related to mathematics.

Teaching methods and student assessment. Student is obliged to actively participate in the activites of the Professional Colloquium of the Osijek Mathematical Society. Regular seminar attending is confirmed with lecturer’s signature- moderator of the Professional Colloquium.

Professional Colloquium I Z009 (0+0+2) - 3 ECTS credits

Course objective. To develop students’ presentational skills. Improve the level of communication between students and teachers of mathematics and computer science in primary and secondary schools in the region. Course Contents. Professional Colloquium is taught at the Department of Mathematics, University of Osijek. It is primarily intented for teachers of mathematics and computer science employed at primary and secondary schools, as well as for students and all others having interest in it. Professional colloquium initiates communication between teachers of mathematics and encourages experience exchange and contact with the students of mathematics. The colloquium also hosts different professional workshops and lectures related to mathematics and computer science as well as to other fields in some way related to mathematics.

Teaching methods and student assessment. Student is obliged to actively participate in the activites of the Professional Colloquium of the Osijek Mathematical Society. Regular seminar attending is confirmed with lecturer’s signature- moderator of the Professional Colloquium.

Introduction to integration theory M058 (2+2+0) – 4 ECTS credits

Course objective. The purspose of this course is to get a deeper and clearer insight into integration theory which is the basics for understanding many modern mathematical disciplines.

Prerequisites. Introduction to measure theory

Course contents.
1. Measurable functions. Topology at [-∞,∞]. The concept of measurablefunction. The properties of measurable functions. Simple functions. The “almost everywhere“ property.
2. Lebesgue integral. Nonnegative simple function integral. Nonnegative measurable function integral. Levi theorm on monotonous convergence. Fatou Lemma. Measurable function integral. Lebesgue theorem on dominated convergence. The Riemann-Lebesgue integral relation. Chebyshevlev, Cauchy, Hoelder and similar inequalities. Ways of function convergence: μ-almost everywhere convergence, Lp convergence, measure convergence.

Teaching methods and student assessment. Lectures and exercises are obligatory. The final examination consists of both a written and an oral part that can be taken after the completion of all lectures and exercises. During the semester students can take 2-3 tests that replace the written examination.

Literature:
Recommended literature:
[1] D. L. Cohn, Measure theory, Birkhäuser, 1980.
[2] D. Jukić, Uvod u teoriju jmjere i integracije, Odjel za matematiku, Osijek, 2008.
[3] S. Mardešić, Matematička analiza 2: Integral i mjera, Školska knjiga, 1977
[4] W.Rudin, Principles of Mathematical Analysis, Mc Graw-Hill, Book Company, 1964.
[5] R. L. Schilling, Measures, integrals and martingales,Cambridge University Press, New York, 2005.
[6] H. J. Wilcox, D. L. Myers, An Introduction to Lebesgue Integration and Fourier Series, Dover, New york, 1994.

Data grouping and applications M059 (2+1+1) – 4 ECTS credits

Course objective. To introduce students with basic facts and results prom the field of data clustering and its possible applications.

Prerequisites. Linear algebra II, Functions of Several Variables

Course contents.
1. Introduction and motivation. Problem statement and basic properties. Various application examples. Data clustering in R^1 and in R2.
2. Least Squares optimality criterion. Least Squares criterion and matrix trace. Data transformation. Reducing the minimum problem to the maximum problem.
3. Finding optimal LS-partition. k-means grouping (k-means algorithm). Inserting and dropping of the elements. Improved k-means algorithm. Substitution method.
4. Other methods. Agglomeration method
5. Monotnicity. Stability.
6. Generalized LS criterion.
7. Other geometry objects as group centres. System of linear equations.
8. Matrix approach and Ky Fan theorem application

Teaching methods and student assessment. Exercises are partially auditory, and partially done in a lab using Mathematica programme system. The exam consists of a written and oral part. During lectures students take 3-4 preliminary exams. Successfully completed preliminary exams can replace the written of the exam. Students are also given homework, and they can do a seminar, which influences the final grade.

Literature:
Recommended literature:
[1] R. Scitovski, Introduction to Cluster Analysis , lectures, Department of Mathematics, University of Osijek 2010
[2] J.Kogan, Introduction to Clustering Large and High-Dimensional Data, Cambridge University Press, 2007.
Additional Literature:
[3] H.Zha, X.He, C.Ding, H.Simon, M.Gu, Spectral Relaxation for k-means Clustering, Advances in Neural Information Systems, 2002.
[4] H. Späth, Cluster–Formation und- Analyse, R. Oldenburg Verlag, München, 1983.
[5] P. Bose, A. Maheshwari, P. Morin, Fast approximations for sum of distances, clustering and the Fermat–Weber problem, Computational Geometry 24(2003) 135–146
[6] G. Gan, CMa, J.Wu, Data clustering : theory, algorithms, and applications, SIAM, Philadelphia, 2007.
[7] B. S. Everitt, S. Landau, M. Leese, Cluster analysis, Wiley, London, 2001.
[8] L. Kaufman, P. J. Rousseeuw, Finding groups in data : an introduction to cluster analysis, Jonh Wiley & Sons, Hoboken, 2005.

Numerical Linear Algebra in Linear Systems Control M061 (2+1+0) – 3 ECTS credits

Course objective. The purpose of this course is to make students familiar with basic applications of stability and efficacy of some standard algorithms of numerical linear algebra in solving mathematical problems that appear in design and analysis of linear dynamic systems as well as their control.

Prerequisites. Vector spaces. Numerical linear algebra, Numeric mathematics, Ordinary differential equations, Selected capters of matrix theory

Course contents.
1. Linear dynamic systems. State-space representation. Solving continuous systems, system response (9 classes)
2. Controlability and observability, controlability distance.Controlability. Observability. Decomposition of system on controllable and observable part. Numerical tests of controlability nad observability. (9 classes)
3. Stability nad inertion. System stability. Lyapunov equation and controllable and observable gramians. Inertion theorems. (9 classes)
4. Numerical solving and the conditionality of Lyapunov and Sylvester equation. Existence and uniqueness of the solution to the Sylvester equation. Perturbation analysis and conditionality. Numerical methods for solving Sylvester and Lyapunov equation ( Bartels- Stewart, Hessenberg method) (18 classes)

Teaching methods and student assessment. Lectures, exercises and seminars are obligatory. The exam consists of written and oral part and it is taken after completion of lectures and exercises. Students can take 3 preliminary exams during the semester which, if done successfully, replace the written part of the final exam.

Literature:
Recommended literature:
[1] B. N. Datta, " Numerical Methods for Linear Control Systems Design and Analysis" , Elsevier Academic Press, 2003.
[2] A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, SIAM, Philadelphia, 2005.
[3] R. Scitovski, Numerička matematika, 2.. izdanje, Odjel za matematiku Sveučilišta u Osijeku, Osijek, 2004.
Additional literature:
[4] Z. Drmač, V. Hari, M. Marušić, M. Rogina, I. Slapničar, S. Singer, S. Singer, Numerička analiza, Predavanja i vježbe Zagreb, 2003. http://web.math.hr/~rogina/2001096/num_anal.pdf
[5] G. H. Golub, C. F. Van Loan, Matrix Computations, 3rd ed. The Johns Hopkins University Press, 1996, Baltimor.
[6] Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. SIAM, Philadelphia, 2003.
[7] Y. Saad, Numerical Methods for Large Eigenvalue Problems, Manchester University Press, 1992.

Reliability theory M057 (2+0+1) – 3 ECTS credits

Course objective. To work on the basics of reliability theory in mathematically formal way, but also with emphasis on application

Prerequisites. Basics of statistics, differential and integral calculus Note: It is expected that students of Electrical Engineering and Mechanical Engineering Faculty as well as Faculty of Food Technology will have interest in this course.

Course contents.
1. Introduction: Short historical overview. Areas of application.
2. Basic concepts of reliability theory. Reliability function. Failure distribution, hazard function, expected time of work without failure
3. Some distributions in reliability theory: Continuous distributions: exponential, normal, lognormal, Weibull, gamma and beta distribution. Discrete distributions: binomial, Poisson, geometrical and hypergeometrical distribution.
4. Determining the distribution based on empirical data: Graphical methods: histogram method and Weibull probability plot. Analytic methods: method of moments and maximum likelihood method.
5. Renewable systems maintenance policies: renewal theory. Renewal function and renewal density. Replacement of elements. Periodical replacement. Random replacement.
6. Optimum maintenance policies. Replacement policies. Inspection policies.
7. Redundant systems. Cold standby systems. Warm standby systems

Teaching methods and student assessment. Lectures are obligatory. Lectures provide basic concepts, mathematical aspects and problems in reliability theory. The second part of lectures is used for giving student seminars. Attendance at seminars is obligatory. The final exam consists of written and oral part, and it is taken after the completion of lectures. Students can hand in a seminar paper during a semester. A successful seminar paper influences final grade and can replace the oral part of the final exam.

Literature:
Recommended literature:
[1] R. Barlow, F. Proschan, Mathematical Theory of Reliability, SIAM, Philadelphia, 1996.
[2] S. V. Vukadinović, D. B. Teodorović, Elementi teorije pouzdanosti i teorije obnavljanja tehničkih sustava, Privredni pregled, Beograd, 1979.
[3] D. T. P. O'Connor, Practical Reliability Engineering, Heyden & Son, London, 1995. Additional literature:
[4] R.E. Barlow, Engineering Reliability, SIAM, Philadelphia, 1998.
[5] A. Birolini, Reliability Engineering. Theory and Practice, Springer Verlag, Berlin, 2007.
[6] B. Dodson, D. Nolan, Reliability Engineering Handbook, CRC Press, Boca Raton, 1999.
[7] J.F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley, New York, 1982.
[8] W. Nelson, Applied life data analysis, Wiley, New York, 1982.
[9] B. W. Silverman, Density estimation for Statistics and Data Analysis, Chapman & Hall/CRC, Boca Raton, 2000.
[10] P. A. Tobias, D. C. Trindade, Applied Reliability, Chapman & Hall/CRC, Boca Raton, 1995.
[11] E. Zio, An Introduction to the Basics of Reliability and Risk Analysis, World Scientific, New Jersey, 2007.