Graduates of this programme can take active part in planning and development in financial institutions and financial departments of large companies or engage in scientific research at economic research institutions.

# Financial Mathematics, Second cycle

This programme is designed for Bachelors in Financial Mathematics as well as graduates of other first cycle programs wishing to enhance their knowledge of probability and optimization and acquire new knowledge of economics and financial mathematics.

Admission to the study programme is open to either: a) Graduates of the Academic study programme in Financial 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 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 |

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

General elective | 5 | 0/0 | 3/2 |

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

Elective at Faculty of Economics | 7 | 3/2 | 0/0 |

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

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

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

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

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

Master's thesis | 18 | 0/0 | 0/0 |

General elective | 5 | 3/1 | 0/0 |

General elective or Workplace experience 2 | 6 | 0/0 | 1/0 |

Electives from groups M1-M5 and R1 | 18 | 9/6 | 0/0 |

Elective at Faculty of Economics | 7 | 2/1 | 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 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 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 |

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

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

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

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

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