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
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.
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).
1
stYEAR
Winter term Summer term Total
Course L P S ECTS TSW L P S ECTS TSW ECTS TSW Mathematics specific elective 30 30 0 5 150 0 0 0 0 0 5 150 Mathematics specific elective 30 30 0 5 150 0 0 0 0 0 5 150 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
General elective 30 15 0 3 90 0 0 0 0 0 3 90
Algorithms 0 0 0 0 0 45 30 0 6 180 6 180
Computer systems 0 0 0 0 0 45 30 0 6 180 6 180
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
General elective 0 0 0 0 0 45 45 0 8 240 8 240
Term total 210 165 0 30 900 195 165 0 30 900 60 1800
2
ndYEAR
Winter term Summer term Total
Course L P S ECTS TSW L P S ECTS TSW ECTS TSW Mathematics specific elective 30 30 0 5 150 0 0 0 0 0 5 150 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 0 0 0 0 0 0 0 0 9 270 9 270
Mathematics specific electives (Group A)
Course L P S ECTS TSW
Logic in computer science 30 30 0 5 150 Computer aided geometric design
oblikovanje
30 30 0 5 150
Computational geometry 30 30 0 5 150
Coding theory and cryptography 30 30 0 5 150 Probability methods in computer science 30 30 0 5 150
Total 120∗ 120∗ 0 20∗ 600∗
(*) Remark: Each student has to take 4 Mathematics specific electives from Group A.
Mathematics specific electives (Group B)
Course L P S ECTS TSW
Data analysis and visualization 30 30 0 5 150 Topics in computer mathematics 30 30 0 5 150 Topics in numerical mathematics 30 30 0 5 150
Topics in game theory 30 30 0 5 150
Mathematics with computers 30 30 0 5 150
Symbolic computation 30 30 0 5 150
Graph theory 30 30 0 5 150
Selected topics in discrete mathematics 30 30 0 5 150
Combinatorics 2 30 30 0 5 150
Optimization methods 2 30 30 0 5 150
Cryptography and computer security 30 30 0 5 150
Total 150∗ 150∗ 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 L P S ECTS TSW
Artificial intelligence 45 30 0 6 180
Digital signal processing 45 30 0 6 180
Computability and computational complexity 45 30 0 6 180
Introduction to bioinformatics 45 30 0 6 180
Modern software development methods 45 30 0 6 180
Machine learning 45 30 0 6 180
Perception in cognitive systems 45 30 0 6 180
Soft computing and natural algorithms 45 30 0 6 180
Theory of programming languages 45 30 0 6 180
Interaction and information design 45 30 0 6 180
Contemporary approaches and architectures in IS development 45 30 0 6 180
Data mining 45 30 0 6 180
Total 225∗ 150∗ 0 30∗ 900∗
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.
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 1st 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).
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.
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
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
> 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
> 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
> 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
> 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
