The principal goal of the academic study programme in Financial Mathematics is to create experts capable of solving hard mathematical problems arising in the banking and insurance sector, in trading activities of stock exchanges and brokerage firms, and in management of pension and health funds.

# Financial mathematics, First Cycle

The principal goal of the academic study programme in Financial Mathematics is to create experts capable of solving hard mathematical problems arising in the banking and insurance sector, in trading activities of stock exchanges and brokerage firms, and in management of pension and health funds. Graduates of this study programme also acquire enough theoretical knowledge to be able to proceed with the Financial Mathematics programme in the second cycle.

Generic competencies developed by the student:

ability of abstract thinking and problem analysis,

ability of sorting out effective solutions and of their critical evaluation,

ability of application of knowledge at solving practical problems,

ability of using and following the professional literature,

ability to set forth both written and oral presentations of specialized topics,

ability to work both individually and as part of an (international) team,

ability of lifelong self-education.

Subject specific competences developed by the student:

basic knowledge of mathematics, basic knowledge of economics and finance, basis knowledge of informatics,

ability to solve non-deterministic problems with the help of probability theory and statistics,

ability to solve deterministic problems with the help of optimization methods and operations research,

ability of computation of approximate solutions with the help of numerical methods,

ability to use computers to solve problems and present results.

Admission to the study programme is open to either: a) Holders of the matura certificate (or an equivalent degree from a foreign institution).

b) Holders of the vocational matura certificate obtained in any of the four-year high school programmes (or an equivalent degree from a foreign institution). In this case, an additional examination in one of the general matura subjects different from those of the vocational matura is required. Either one of the vocational matura subjects or the additional one must be mathematics.

c) Holders of the final examination certificate obtained in any of the four-year high school programmes prior to 1 June 1995.

In case the number of applicants exceeds the maximum availability, the applicants are selected according to their final matura (or vocational matura) grade, their mathematics matura (or vocational matura) grade, their grade point average (GPA) in the last two years of high school, and their final mathematics grades in the last two years of high school. These are weighted in the following way.

Applicants under a)

• Matura certificate grade (30% of points),

• Matura mathematics exam grade (30% of points),

• GPA in the 3rd and 4th years of high school (20% of points),

• Final grade in mathematics in the 3rd and 4th years of high school (20% of points);

Applicants under b)

• Vocational matura grade (20% of points),

• Matura mathematics exam grade (40% of points),

• GPA in the 3rd and 4th years of high school (10% of points),

• Final grade in mathematics in the 3rd and 4th years of high school (30% of points);

Applicants under c)

• Final examination grade (30% of points),

• Mathematics final examination grade or mathematics grade in the 4th year of high school in case of

exemption from the final exam (30% of points),

• GPA in the 3rd and 4th years of high school (20% of points),

• Final mathematics grade in the 3rd and 4th years of high school (20% of points).

Enrolment in Year 1 is granted upon admission. For enrolment in the next study year it is necessary to earn 50 ECTS credits from courses and exams in the current study year. In addition to the credit quota, the completions of the following exams are obligatory:

For enrolment in Year 2: Analysis 1, Analysis 2, Algebra 1, Computer practical.

For enrolment in Year 3: all exams from Year 1, Probability 1, Probability and statistics, Analysis 3, Seminar.

For re-enrolment in Year 1, a student needs to earn:

at least half of all possible credits of the current study year (30 ECTS credits), and complete at least one of the exams in Analysis 1 and Algebra 1.

For re-enrolment in Year 2, a student needs to earn:

at least half of all possible credits of the current study year (30 ECTS credits), and

all credits from the previous study years.

Re-enrolment is only possible once. A change of the study programme counts as re-enrolment.

To graduate, students need to complete all exams.

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.

**KLASIUS-SRV**: Academic higher education (first Bologna cycle)/Academic higher education (first Bologna cycle)**ISCED**: Mathematics and statistics**KLASIUS-P**: Mathematics (broad programmes)**KLASIUS-P-16**: Mathematics**Frascati**: Natural Sciences**SOK level**: 7**EOK level**: 6**EOVK level**: First cycle

### Curriculum

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

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

**ECTS** = credit points

compulsory | |||
---|---|---|---|

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

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

Algebra 1 | 14 | 4/4 | 2/2 |

Analysis 1 | 7 | 4/4 | 0/0 |

Analysis 2 | 7 | 0/0 | 4/4 |

Discrete structures | 5 | 2/2 | 0/0 |

Microeconomics | 6 | 0/0 | 3/3 |

Optimization methods | 6 | 0/0 | 3/3 |

Introductory seminar | 4 | 2/2 | 0/1 |

Computer laboratory | 6 | 1/3 | 0/0 |

Introduction to programming | 5 | 0/0 | 2/3 |

compulsory | |||
---|---|---|---|

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

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

Analysis 3 | 9 | 4/4 | 0/0 |

Data analysis with program R | 5 | 2/2 | 0/0 |

Money and finance | 6 | 0/0 | 4/2 |

Financial mathematics 1 | 5 | 0/0 | 2/2 |

Macroeconomics | 6 | 4/2 | 0/0 |

Numerical methods 1 | 5 | 2/2 | 0/0 |

Numerical methods 2 | 5 | 0/0 | 2/2 |

Operational research | 5 | 0/0 | 2/2 |

Seminar | 3 | 0/0 | 2/0 |

Probability 1 | 5 | 2/2 | 0/0 |

Probability and statistics | 6 | 0/0 | 3/3 |

compulsory | |||
---|---|---|---|

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

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

Diploma seminar | 7 | 2/0 | 2/0 |

Financial lab | 6 | 4/2 | 0/0 |

Financial markets and institutions | 6 | 0/0 | 4/2 |

Elective courses | 10 | 5/4 | 0/0 |

Elective courses | 10 | 0/0 | 5/4 |

Stochastic processes 1 | 5 | 0/0 | 2/2 |

Statistics 1 | 5 | 0/0 | 2/2 |

Game theory | 6 | 3/3 | 0/0 |

Probability with measure | 5 | 2/2 | 0/0 |

In addition to the obligatory courses, each student opts for elective courses of total worth 20 ECTS credits. Of those, at least 5 ECTS credits must be earned by taking courses offered by the Department of Mathematics at UL FMF, and at least 5 ECTS credits by taking courses offered by the Department of Money and Finance at the Faculty of Economics (UL EF). The elective courses of the Faculty of Economics that are accredited at UL FMF is listed below, the list of offered courses that are accredited at UL EF is agreed annually. At most 3 ECTS credits can be earned by taking courses offered by other faculties (general elective courses).

Elective courses offered by the Faculty of Economics that are accredited at UL FMF | |||
---|---|---|---|

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

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

Econometrics 1 | 6 | 0/0 | 3/2 |

Monetary economics | 6 | 0/0 | 4/0 |

Industrial organization | 6 | 3/1 | 0/0 |

Foundations of financial and management accounting | 6 | 3/3 | 0/0 |

Mathematics electives | |||
---|---|---|---|

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

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

Affine and projective geometry | 5 | 0/0 | 2/2 |

Algebra 2 | 10 | 2/2 | 2/2 |

Algebra 3 | 5 | 0/0 | 2/2 |

Algebraic curves | 5 | 0/0 | 2/2 |

Analysis 3 (from Mathematics programme) | 6 | 3/3 | 0/0 |

Analysis 4 | 6 | 3/3 | 0/0 |

Discrete mathematics 1 | 5 | 0/0 | 2/2 |

Discrete mathematics 2 | 5 | 0/0 | 2/2 |

Topics in data analysis | 5 | 0/0 | 2/2 |

Mathematical modelling | 5 | 0/0 | 2/2 |

Fundamentals of databases | 5 | 0/0 | 2/2 |

Data structures and algorithms 1 | 5 | 2/2 | 0/0 |

Data structures and algorithms 2 | 5 | 0/0 | 2/2 |

Programming 1 | 5 | 2/2 | 0/0 |

Programming 2 | 5 | 0/0 | 2/2 |

Point-set topology | 5 | 2/2 | 0/0 |

Coding theory and cryptography | 5 | 0/0 | 2/2 |

Introduction to differential geometry | 5 | 2/2 | 0/0 |

Introduction to geometric topology | 5 | 0/0 | 2/2 |

Student's choice of electives must be approved by the department's study committee.