Download Computer Science and Mathematics

Interdisciplinary Master’s study program
in
Computer Science and Mathematics
Study program cycle:
Second cycle study program.
Anticipated academic title:
Master Engineer in Computer Science and Mathematics.
In Slovenian: Magister inženir računalništva in matematike (masculine form) or Magistrica inženirka
računalništva in matematike (feminine form), for either gender abbreviated to mag. inž. rač. mat.
Duration:
2 full years (4 terms) based on 120 ECTS credits.
Basic goals:
The program is intended for Bachelors of first cycle study programs Computer science and mathematics,
Mathematics, Computer and information science as well as graduates of other first cycle programs. The study
program goals comprise the qualification for the development and usage of new information technologies, for
research in the fields of mathematics and theoretical computer science, and the capability of rapid acquisition
of new knowledge from the field of computer and information science and the related field of mathematics.
Generic competences developed by graduates of the study program:

the ability of abstract thinking and problem analysis,

the ability of devising effective solutions and of their critical evaluation,

the ability of application of knowledge in practice,

the ability of passing one’s knowledge, of professional communication and of written expression,

the ability of finding sources of information and critical assessment thereof,

the ability of individual professional work and (international) teamwork,

the development of professional responsibility and ethics
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Subject-specific competences developed by graduates of the study
program:

enhanced qualification in the field of theoretical computer science, logic, and discrete mathematics,
comprising both basic and advanced theoretical knowledge, practical knowledge and skills that are
essential to both computer science and mathematics,

the ability to translate practical problems into the language of mathematics and theoretical computer
science, and to qualitatively analyze the obtained mathematical problems,

the ability to conceive algorithms to solve a given problem, to implement those algorithms using
appropriate programming tools, to perform a detailed analysis of the obtained results, and to present
them,

understanding and the ability of applying computer and information science knowledge in other areas
of technology and other professionally relevant areas (economics, financial mathematics,
organizational science and others),

practical knowledge and skills in the usage of software, hardware, and information technology,

graduates of the study program are capable of individually performing demanding tasks in
development and organization within the area of their expertise, and to cooperate with experts of other
areas in order to perform complex tasks and solve complex problems
Employment possibilities
The need for application of computer technology is growing everywhere, and therefore graduates of the
Interdisciplinary Master’s study program in Computer science and mathematics can find employment in all
branches of business and the public sector. We expect our graduates to have a wide spectrum of working
activity, ranging from information and communication technologies to computer science and mathematical
support at management of complex systems the likes of financial, health care, educational, industrial, and
technological systems. The need for graduates of such capabilities is bound to get even greater in the future.
The study program’s graduates will be able to enroll into 3rd cycle study programs and start working in
scientific research and in development.
2
CURRICULUM
Abbreviations:
• L – lectures per week (in hours),
• P – problem sessions per week (in hours),
• S – seminar classes per week (in hours),
• ECTS – ECTS credits worth,
• TSW – estimated total student workload (in hours).
1st YEAR
Winter term
S
ECTS
0
5
Course
Mathematics specific elective
L
30
P
30
Mathematics specific elective
30
30
0
Mathematics specific elective
30
30
0
Computer science specific elective
45
30
Computer science specific elective
45
30
General elective
30
Algorithms
Computer systems
Summer term
S
ECTS
0
0
TSW
150
L
0
P
0
5
150
0
0
0
5
150
0
0
0
0
6
180
0
0
0
6
180
0
0
15
0
3
90
0
0
0
0
0
0
0
0
0
0
0
Mathematics specific elective
0
0
0
0
Mathematics specific elective
0
0
0
0
0
0
0
0
0
210
165
0
30
900
TSW
150
L
0
P
0
General elective
Term total
Total
TSW
0
ECTS
5
TSW
150
0
0
5
150
0
0
5
150
0
0
0
6
180
0
0
0
6
180
0
0
0
0
3
90
45
30
0
6
180
6
180
45
30
0
6
180
6
180
0
30
30
0
5
150
5
150
0
30
30
0
5
150
5
150
45
45
0
8
240
8
240
195
165
0
30
900
60
1800
TSW
0
ECTS
5
TSW
150
2nd YEAR
Winter term
S
ECTS
0
5
Summer term
S
ECTS
0
0
Total
Course
Mathematics specific elective
L
30
P
30
Mathematics specific elective
30
30
0
5
150
0
0
0
0
0
5
150
Computer science specific elective
45
30
0
6
180
0
0
0
0
0
6
180
Computer science specific elective
45
30
0
6
180
0
0
0
0
0
6
180
Master's thesis
0
0
0
8
240
0
0
0
0
0
8
240
Mathematics specific elective
0
0
0
0
0
30
30
0
5
150
5
150
Mathematics specific elective
0
0
0
0
0
30
30
0
5
150
5
150
Computer science specific elective
0
0
0
0
0
45
30
0
6
180
6
180
Computer science specific elective or
mathematics specific elective
0
0
0
0
0
30
30
0
5
150
5
150
Master's thesis
Term total
0
0
0
0
0
0
0
0
9
270
9
270
150
120
0
30
900
135
120
0
30
900
60
1800
3
Mathematics specific electives (Group A)
Course
Logic in computer science
Computer aided geometric design
oblikovanje geometry
Computational
Coding theory and cryptography
Probability methods in computer science
Total
L
30
30
30
30
30
P
30
30
30
30
30
S
0
0
0
0
0
ECTS
5
5
5
5
5
TSW
150
150
150
150
150
120∗
120∗
0
20∗
600∗
(*) Remark: Each student has to take 4 Mathematics specific electives from Group A.
Mathematics specific electives (Group B)
Course
Data analysis and visualization
Topics in computer mathematics
Topics in numerical mathematics
Topics in game theory
Mathematics with computers
Symbolic computation
Graph theory
Selected topics in discrete mathematics
Combinatorics 2
Optimization methods 2
Cryptography and computer security
Total
L
P
S
ECTS
TSW
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
5
5
5
5
5
5
5
5
5
5
5
150
150
150
150
150
150
150
150
150
150
150
150∗
150∗
0
0
0
0
0
0
0
0
0
0
0
0
25∗
750∗
(*) Remark: Each student has to take 5 Mathematics specific electives from Group B.
As mathematical courses of Group B the student can also choose up to 3 courses of
mathematical content in the second cycle Master’s study program in Mathematics at
UL FMF.
Computer science specific electives
Course
Artificial intelligence
Digital signal processing
Computability and computational complexity
Introduction to bioinformatics
Modern software development methods
Machine learning
Perception in cognitive systems
Soft computing and natural algorithms
Theory of programming languages
Interaction and information design
Contemporary approaches and architectures in IS development
Data mining
Total
L
P
S
ECTS
TSW
45
45
45
45
45
45
45
45
45
45
45
45
30
30
30
30
30
30
30
30
30
30
30
30
6
6
6
6
6
6
6
6
6
6
6
6
180
180
180
180
180
180
180
180
180
180
180
180
225∗
150∗
0
0
0
0
0
0
0
0
0
0
0
0
0
30∗
900∗
(*)Remark: Each student has to take 5 Computer science specific electives.
4
Admission requirements and admission limitation measures
Admission to the study program is open to the following:
1.
Graduates of the Academic (1st cycle) study programs in Computer Science and Mathematics
(Interdisciplinary); Mathematics; Financial Mathematics; Computer and Information Science.
2.
Graduates of the Professional study program in Computer and Information Science and the
Undergraduate professional study program in Computer and Information Science (accredited prior to
1 June 2004).
3.
Graduates of the Professional study program in Practical Mathematics and the Undergraduate
professional study program in Practical Mathematics (accredited prior to 1 June 2004)
4.
Graduates of the Academic (1st cycle) study programs, and Undergraduate university and
Undergraduate professional study programs (accredited prior to 1 June 2004) in technology or natural
sciences in which case the candidate is expected to have already acquired the basic competences in the
fields of mathematics and computer science. Prior to enrollment, the candidate must complete
additional courses that are essential for the proposed study program. These additional courses are
determined with respect to the candidate’s professional background and can amount to a total worth of
60 ECTS credits.
5.
Study programs equivalent to the above (classified under 6.1 according to the ISCED classification)
that are carried out at another higher education institution in Slovenia or abroad.
Additional study requirements
Applicants under 2 above have to pass the exams from the Interdisciplinary Academic (1st cycle) study
program in Computer Science and Mathematics: Analysis 3, Discrete structures 2, Linear algebra, and
Numerical methods.
Applicants under 3 above have to pass the exams from the Interdisciplinary Academic (1st cycle) study
program in Computer Science and Mathematics: Introduction to artificial intelligence, Operating systems,
Computer communications, Algorithms and data structures.
Applicants under 4 above have to prior to enrollment complete additional courses that are essential for the
proposed study program. These additional courses are determined with respect to the candidate’s professional
background and can amount to a total worth of 60 ECTS credits.
The candidate can complete the additional course during the 1st cycle study program in question, in a
preparatory program or by taking exams prior to enrollment in the proposed study program.
5
Selection criteria in the case of limited enrolment
In case of admission limitation, applicants are selected according to their merits in the respective first cycle (or
undergraduate) study programs (GPA of exams, problem sessions and seminars’ grades; the Senior seminar
project grade or Bachelor’s thesis grade if applicable) and according to the GPAs of the mathematical and
computer science exams of the respective 1st cycle study program. Of these, general merits are weighted to
50%, the GPA of the mathematical courses to 25%, and the GPA of the computer science courses to 25%.
Validation of competences, knowledge, and skills acquired prior to
admission to the study program
In the proposed study program, recognition of relevant knowledge, competence or abilities that candidates have
obtained through informal or experiential learning is possible in the form of a successfully completed course
unit. Normally, up to 6 ECTS credits can be awarded for knowledge, competence or abilities acquired outside
of a higher education institution. Formally acquired knowledge is recognized by awarding ECTS credits
corresponding to courses of the study program that are comparable in extent and content to the candidate’s
previously acquired knowledge.
For recognition of knowledge, course transcripts and other relevant documents must be presented.
Grading system
The methods for testing the competences, knowledge, and skills are described in the courses syllabi. The
basic knowledge testing rules are set in the Assessment and Grading Criteria and Exam Rules of the FRI
and the Exam guidelines of the FMF. Course examinations are either written or oral or both. They can
have the form of midterm exams, oral defense of the midterm exams, written exams, oral exams, seminar
or project work and oral defense of seminar and project work. Grading is based on the grading scale
determined in the Statutes of The University of Ljubljana. All forms of examinations are graded by grades
1-10, out of which 6-10 are passing grades, and 1-5 are failing grades.
Requirements for enrollment in the next study year
To enroll in the 2nd study year, students must complete all the requirements of the 1 st study year.
Re-enrollment requirements
To re-enroll in the 1st study year, a student needs to earn at least half of all possible credits of the 1st study
year (30 ECTS credits).
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Finishing requirements
To finish the program, students must:

Successfully complete all exams,

Prepare and defend the master's thesis.
Transition from other study programs
Graduates of the 2nd cycle study programs in Mathematics, Mathematics Education, Financial Mathematics,
and Computer and Information Science can be awarded up to 60 ECTS credits for courses they have already
completed within the respective study program.
Analogous conditions hold for transitions from comparable study programs in mathematics or computer and
information science at other higher education institutions or from comparable study programs in technology or
natural sciences (classified under 6.1 according to the ISCED classification) if the candidate meets the general
requirements for admission to a 2nd cycle study program. Prior to enrollment, the candidate must complete
additional courses that are essential for the proposed study program. These additional courses are determined
with respect to the candidate’s professional background and can amount to a total worth of 60 ECTS credits.
The candidate can complete the additional course during the 1st cycle study program in question, in a
preparatory program or by taking exams prior to enrollment in the proposed study program.
Transition with enrollment in the 2nd study year is possible if

the candidate meets the requirements for enrollment in the 2nd study year of the previous program and
has completed the required courses from the 1st study year of the proposed study program or,
alternatively,

the candidate’s previously completed and recognized courses meet the requirements for enrollment in
the 2nd study year of the proposed program.
Study program description:
The study program comprises two full academic years based on 120 ECTS credits. Of these, the
master's thesis accounts for 17 ECTS credits. All courses are single-term courses. Computer science courses
are typically with 45 hours of lectures and 30 hours of problem sessions altogether (with a weekly load of 3/2
hours of lectures/problem sessions) and 6 ECTS credits. Mathematical courses are typically with 30 hours of
lectures and 30 hours of problem sessions altogether (with a weekly load of 2/2 hours of lectures/problem
sessions) and are worth 5 ECTS credits. A student's choice of courses has to be approved by the department
study committee.
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Of 120 ECTS credits altogether

17 ECTS credits master's thesis

12 ECTS credits core courses

80 ECTS credits mathematical or computer science elective courses

11 ECTS credits general elective courses
There are core and elective courses:

Core coureses: computer science courses Algorithms and Computer systems

Elective courses:
o
5 computer science elective courses
o
4 mathematical elective courses (group A)
o
5 mathematical elective courses (group B)
o
specific elective course
o
2 general elective courses
Course descriptions
General electives
> Algorithms (6 ECTS)
The goal of this course is to gain the knowledge of the design and analysis of algorithms and data structures.
Responsible faculty: Prof. Dr. Marko Robnik Šikonja
> Computer systems (6 ECTS)
The goal of the course is to present basics of architecture and working of computer systems to students who
finished the first degree of the university study at other faculties. The emphasis is on the computer architecture,
while the second part consists of computer networks. Since for both one has to know some basics of electrical
engineering, electronics and Boolean algebra, the introductory chapters briefly cover also these subjects.
Responsible faculty: Prof. Dr. Branko Šter
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Specific mathematical electives (group A)
> Logic in computer science (5 ECTS)
The objective is to show students how logic and computer science are connected, as logic is an essential tool in
many areas of computer science. Students will obtain basic mathematical and logical knowledge, which they
will be able to use at solving computer-science tasks.
Responsible faculty: Prof. Dr. Andrej Bauer
> Computer aided geometric design (5 ECTS)
Computer aided geometric design (CAGD) is one of the most important interdiscplinary fields joining
mathematics and computer science. The objective of the course is to acquaint students with the basic
knowledge. Students will be able to solve and implement some basic problems in CAGD.
Responsible faculty: Prof. Dr. Jernej Kozak
> Computational geometry (5 ECTS)
Students build their knowledge of data structures and basic algorithms used for solving geometric and related
problems.
Responsible faculty: Prof. Dr. Sergio Cabello Justo
> Coding theory and cryptography (5 ECTS)
Students acquire competency to analyze communication channels with respect to security of information,
reliability of transmission and computational complexity.
Responsible faculty: Prof. Dr. Marko Petkovšek
> Probability methods in computer science (5 ECTS)
Student gets acquainted with the use of probability for algoritmic and related problems.
Responsible faculty: Prof. Dr. Sergio Cabello Justo
Specific mathematical electives (group B)
> Data analysis and visualization (5 ECTS)
The goal of the course is to introduce some modern methods for data analysis and visualization with their
theoretical background, and to enable the students to use these methods by themselves or also to develope their
own solutions.
Responsible faculty: Prof. Dr. Vladimir Batagelj
9
> Topics in computer mathematics (5 ECTS)
The students learn and understand basic concepts, problems, and tools in different areas of computer
mathematics.
Responsible faculty: Prof. Dr. Sergio Cabello Justo
> Topics in numerical mathematics (5 ECTS)
The student sees the details of one or more important areas of numerical mathematics, and learns about some
recent results in the subjects.
Responsible faculty: Prof. Dr. Jernej Kozak
> Topics in game theory (5 ECTS)
The student sees the details of one or more important areas of game theory, and learns about some recent
results in the subjects.
Responsible faculty: Prof. Dr. Sergio Cabello Justo
> Mathematics with computers (5 ECTS)
Modern computer technology has become an indispensible tool for solving mathematical problems. The
objective of the course is to acquaint the students with software and related methods of problem solving. The
students will be able to completently use computers on their own to solve mathematical problems.
Responsible faculty: Prof. Dr. Andrej Bauer
> Symbolic computation (5 ECTS)
Students acquire competency to use tools for automated solving of mathematical problems, important in
applications, such as the problem of representation of algebraic structures, the problem of simplification of
expressions, solving systems of algebraic equations, solving difference equations, and summation in closed
form.
Responsible faculty: Prof. Dr. Marko Petkovšek
> Graph theory (5 ECTS)
Students deepen and expand the knowledge of graph theory. They learn applicability of graphs and networks in
different fields of mathematics (combinatorics, linear algebra, group theory, partially ordered sets, ...) and
possibilities for their applications in other fields of science.
Responsible faculty: Prof. Dr. Martin Juvan
> Selected topics in discrete mathematics (5 ECTS)
Students shall gain a deeper understanding of problems in discrete mathematics and learn how to solve them on
their own.
Responsible faculty: Prof. Dr. Primož Potočnik
10
> Combinatorics 2 (5 ECTS)
Students shall gain a deeper understandig of combinatorial problems and learn how to solve them on their own.
Responsible faculty: Prof. Dr. Primož Potočnik
> Optimization methods 2 (5 ECTS)
The goal of the course is to introduce some modern optimization methods and to enable the students to use
these methods by themselves in solving practical problems.
Responsible faculty: Prof. Dr. Vladimir Batagelj
> Cryptography and computer security (5 ECTS)
Introduction to Cryptography and Computer Security.
Responsible faculty: Prof. Dr. Aleksandar Jurišić
Specific computer science electives
> Artificial intelligence (6 ECTS)
In-depth knowledge of methods and techniques of Artificial Intelligence (AI). Ability of solving complex
practical problems with AI methods. Competence in using methods and tools of AI in research, including
projects in other courses and in the final graduation project. Ability of conducting research in Artificial
Intelligence .
Responsible faculty: Prof. Dr. Ivan Bratko
> Digital signal processing (6 ECTS)
The objective is to present the processing of signals by digital techniques, including the application of
computers in this area. The theory which is the basis for understanding the processing methods is combined
with practical projects that are derived from the real world problems. Special attention is given to devices and
activities that use the digital signal processing methods.
Responsible faculty: Prof. Dr. Dušan Kodek
> Computability and computational complexity (6 ECTS)
Major part of the course is devoted to computability and computational complexity theory emphasizing on
application on various disciplines of computer science. In part the course covers the historical development of
the field as well as its recent achievements, again focusing on practical problem solving.
Responsible faculty: Prof. Dr. Borut Robič
11
> Introduction to bioinformatics (6 ECTS)
This is an introductory course to bioinformatics. During the course the students will become familiar with
computational methods and tools that can be used in bioinformatics, and with publically available data bases in
molecular biology. The course will start with introduction to molecular biology and genomics, which will
allow students of computer science to apply mathematical, statistical and computational techniques to problems
from evolution of living organisms, interactions of genes and biological processes, interactions between
genome and phenotypes and diseases, and similar.
Responsible faculty: Prof. Dr. Blaž Zupan
> Modern software development methods (6 ECTS)
In depth treatment and empirical evaluation of modern software development methods in comparison to
traditional approach. Students work on a project that serves as a case study for evaluation of modern
approaches in order to find their strengths and weaknesses.
Responsible faculty: Prof. Dr. Viljan Mahnič
> Machine learning (6 ECTS)
The goal is to present the basics and the basic principles of machine learning (ML) methods, the basic ML
algorithms and their usage in practice for knowledge discovery from data, data mining (DM) and for learning
classification and regression models. Students will practically apply the theoretical knowledge on real
problems from scientific and business environment. The students shall be able to decide for a given problem
which of the presented techniques should be used, and to develop a prototype solution.
Responsible faculty: Prof. Dr. Igor Kononenko
> Perception in cognitive systems (6 ECTS)
The objective of the course is to teach the students basic competences in the area of artificial perception in
cognitive systems, including selected computational theories of perception, computational models of
perceptual processes, and application of these models for designing active cognitive robotic systems.
Responsible faculty: Prof. Dr. Aleš Leonardis
> Soft computing and natural algorithms (6 ECTS)
The goal is to recognize an alternative ways of processing (exist in nature) and natural algorithms, that enable
solving the problems, where deterministic and/or stochastic procedures are not enough. Some learning
(supervised, unsupervised, reinforced) is necessary together with the different model of computing (neural
networks, evolutionary algorithms, fuzzy logic or simbolic computing).
Responsible faculty: Prof. Dr. Andrej Dobnikar
12
> Theory of programming languages (6 ECTS)
The objective of the course is to present modern, mathematical approach to theory of programming languages.
Students will attain the ability to analyze programming languages and the basic concepts related to them.
Responsible faculty: Prof. Dr. Andrej Bauer
> Interaction and information design (6 ECTS)
To teach the design and presentation of information with emphasis on interactivity based on user and data
centered multimedia software solutions.
Responsible faculty: Prof. Dr. Franc Solina
> Contemporary approaches and architectures in IS development (6 ECTS)
Main goal of this course is to teach students about contemporary and innovative approaches for developing
complex IS that require high level of integration, scalability, and flexibility. The course will specifically focus
on service oriented architectures (SOA) including event driven architectures. Through the course students will
learn about main concepts of SOA. After the course, students should be capable of understanding, how SOA is
used for developing complex IS.
Responsible faculty: Prof. Dr. Marko Bajec
> Data mining (6 ECTS)
Students will learn a number of core techniques for data mining. The course will include an introduction to
data mining as well as a detailed study of several selected methods. It will also focus on practical use of these
methods on real-life problems. The course will use a scripting data mining environment, where students will
learn how to use the existing data mining libraries and design and implement in code their own data mining
solutions.
Responsible faculty: Prof. Dr. Blaž Zupan
13