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.

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 ff(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.