This programme is designed for Bachelors in Mathematics (academic) wishing to take active part in planning, engineering and development in professional environment, or engage in scientific research in mathematics, theoretical computer science or theoretical mechanics.

# Mathematics, Second Cycle

**Please visit our Master's degree website for more information about the programme, department, and life in Ljubljana.**

This programme is designed for Bachelors in Mathematics (academic) wishing to take active part in planning, engineering and development in professional environments, or engage in scientific research in mathematics, theoretical computer science or theoretical mechanics.

Generic competences developed by the student:

abstraction, ability to analyze problems,

synthesiss, critical analysis of solutions,

ability to use theoretical concepts in pratice,

ability to use mathematical literature,

ability to present mathematics in writing and speaking,

ability to work autonomously or in a team,

lifelong self-education.

Subject specific competences developed by the student:

familiarity with classical and modern major results in pure and applied mathematics as well as closely related areas such as computer science and mechanics,

following and understanding hard mathematical proofs,

abstraction of practical problems,

adequate use of mathematical literature,

application of different mathematical methods in order to solve concrete problems,

computer programming using appropriate programming software,

Admission to the study programme is open to either: a) Graduates of the Academic study programme in Mathematics.

b) Graduates of another University undergraduate study programmes, provided that before enrolling, they pass additional exams. The additional exams (between 10 and 60 credits) are assigned by the department study committee.

c) Graduates of a professional undergraduate study programmes, provided that before enrolling, they pass additional exams. The additional exams (between 10 and 60 credits) are assigned by the department study committee.

d) Graduates of equivalent programmes from other universities.

Enrolment in Year 1 is granted upon admission. For enrolment in the second study year it is necessary to earn 50 ECTS credits from courses and exams in the current first study year.

For re-enrolment in the first study year, a student needs to earn at least half of all possible credits (30 ECTS credits). Re-enrolment is only possible once. A change of the study programme counts as re-enrolment.

It is possible to transfer from other study programmes. The appropriate year of study as well as other transfer requirements are determined on the basis of the programme the student is transferring from. The exact conditions for finishing the programme are determined by the department study committee.

To graduate, students need to complete all exams, pass the final exam, and submit and defend a thesis.

**KLASIUS-SRV**: Masters education (second Bologna cycle)/Master (second Bologna cycle)**ISCED**: Mathematics and statistics**KLASIUS-P**: Mathematics (broad programmes)**KLASIUS-P-16**: Mathematics**Frascati**: Natural Sciences**SOK level**: 8**EOK level**: 7**EOVK level**: Second cycle

### Curriculum

**P** = lecture and seminar hours per week

**V** = theoretical and laboratory exercise hours per week

**ECTS** = credit points

1. sem. | 2. sem. | ||
---|---|---|---|

Course | ECTS | P/V | P/V |

General electives | 6 | 3/2 | 0/0 |

General electives | 6 | 0/0 | 3/2 |

Electives from groups M1-M5, R1 and O | 24 | 0/0 | 12/8 |

Electives from groups M1-M5, R1 and O | 24 | 12/8 | 0/0 |

1. sem. | 2. sem. | ||
---|---|---|---|

Course | ECTS | P/V | P/V |

Master's thesis and exam | 25 | 0/0 | 0/0 |

Mathematical seminar | 3 | 1/0 | 1/0 |

General elective | 4 | 0/0 | 2/1 |

General electives | 16 | 7/6 | 0/0 |

Electives from groups M1-M5, R1 and O | 12 | 6/4 | 0/0 |

Electives M1 Analysis nad mechanics | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Analytical mechanics | 6 | 3/2 | 0/0 |

Dynamical systems | 6 | 3/2 | 0/0 |

Functional analysis | 6 | 3/2 | 0/0 |

Topics in analysis | 6 | 3/2 | 0/0 |

Complex analysis | 6 | 3/2 | 0/0 |

Mechanics of deformable bodies | 6 | 3/2 | 0/0 |

Fluid mechanics | 6 | 3/2 | 0/0 |

Continuum mechanics | 6 | 3/2 | 0/0 |

Partial differential equations | 6 | 3/2 | 0/0 |

Special functions | 6 | 3/2 | 0/0 |

Measure theory | 6 | 3/2 | 0/0 |

Operator theory | 6 | 3/2 | 0/0 |

Introduction to C* algebras | 6 | 3/2 | 0/0 |

Introduction to functional analysis | 6 | 3/2 | 0/0 |

Introduction to harmonic analysis | 6 | 3/2 | 0/0 |

Electives M2 Algebra and discrete mathematics | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Topics in algebra | 6 | 3/2 | 0/0 |

Topics in discrete mathematics 1 | 6 | 3/2 | 0/0 |

Topics in discrete mathematics 2 | 6 | 3/2 | 0/0 |

Cardinal arithmetic | 6 | 3/2 | 0/0 |

Combinatorics | 6 | 3/2 | 0/0 |

Commutative algebra | 6 | 3/2 | 0/0 |

Logic | 6 | 3/2 | 0/0 |

Nonassociative algebra | 6 | 3/2 | 0/0 |

Noncommutative algebra | 6 | 3/2 | 0/0 |

Graph theory | 6 | 3/2 | 0/0 |

Theory of semigroups and groups | 6 | 3/2 | 0/0 |

Number theory | 6 | 3/2 | 0/0 |

Applied discrete mathematics | 6 | 3/2 | 0/0 |

Ordered algebraic structures | 6 | 3/2 | 0/0 |

Electives M3 Geometry and topology | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Algebraic topology 1 | 6 | 3/2 | 0/0 |

Algebraic topology 2 | 6 | 3/2 | 0/0 |

Analysis on manifolds | 6 | 3/2 | 0/0 |

Differential geometry | 6 | 3/2 | 0/0 |

Convexity | 6 | 3/2 | 0/0 |

Lie groups | 6 | 3/2 | 0/0 |

Riemann surfaces | 6 | 3/2 | 0/0 |

Introduction to algebraic geometry | 6 | 3/2 | 0/0 |

Electives M4 Numerical mathematics | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Iterative numerical methods in linear algebra | 6 | 3/2 | 0/0 |

Topics in numerical mathematics | 6 | 3/2 | 0/0 |

Numerical approximation and interpolation | 6 | 3/2 | 0/0 |

Numerical integration and ordinary differential equations | 6 | 3/2 | 0/0 |

Numerical methods for linear control systems | 6 | 3/2 | 0/0 |

Numerical solving of partial differential equations | 6 | 3/2 | 0/0 |

Computer aided geometric design | 6 | 3/2 | 0/0 |

Electives M5 Probability, statistics and financial mathematic | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Actuarial mathematics | 6 | 3/2 | 0/0 |

Bayesian statistics | 6 | 3/2 | 0/0 |

Time series | 6 | 3/2 | 0/0 |

Econometrics | 6 | 3/2 | 0/0 |

Financial mathematics 2 | 6 | 3/2 | 0/0 |

Financial mathematics 3 | 6 | 3/2 | 0/0 |

Topics in financial mathematics 1 | 6 | 3/2 | 0/0 |

Topics in financial mathematics 2 | 6 | 3/2 | 0/0 |

Topics in game theory | 6 | 3/2 | 0/0 |

Modelling with stochastic processes | 6 | 3/2 | 0/0 |

Numerical methods for financial mathematics | 6 | 3/2 | 0/0 |

Optimization in finance | 6 | 3/2 | 0/0 |

Riesz spaces in mathematical economics | 6 | 3/2 | 0/0 |

Stochastic processes 2 | 6 | 3/2 | 0/0 |

Stochastic processes 3 | 6 | 3/2 | 0/0 |

Statistics 2 | 6 | 3/2 | 0/0 |

Probability 2 | 6 | 3/2 | 0/0 |

Electives R1 Computer science and mathematics | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Topics in optimization | 6 | 3/2 | 0/0 |

Topics in mathematical foundations of computer science | 6 | 3/2 | 0/0 |

Mathematics with computers | 6 | 3/2 | 0/0 |

Advanced Machine Learning | 6 | 3/2 | 0/0 |

Optimization 2 | 6 | 3/2 | 0/0 |

Data structures and algorithms 3 | 6 | 3/2 | 0/0 |

Computational complexity | 6 | 3/2 | 0/0 |

Computability theory | 6 | 3/2 | 0/0 |

Theory of programming languages | 6 | 3/2 | 0/0 |

Electives General | |||
---|---|---|---|

1. sem. | 2. sem. | ||

Course | ECTS | P/V | P/V |

Astronomy * | 7 | 2/1 | 2/1 |

Workplace experience 1 | 6 | 0/0 | 1/0 |

Workplace experience 2 | 6 | 0/0 | 1/0 |

Mathematical models in biology | 6 | 3/2 | 0/0 |

Mathematics in industry | 6 | 2/0 | 0/0 |

Modern physics | 6 | 3/2 | 0/0 |

Theoretical physics | 7 | 4/2 | 0/0 |