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Financial Mathematics (second cycle)

Study program cycle and type:

Second cycle study program.

Anticipated title:

In Slovenian: magister finan─Źne matematike, magistrica finan─Źne matematike, abbreviated to mag. fin. mat.

Duration:

2 full years (4 terms) based on 120 ECTS credits

Basic goals:

This program is designed for Bachelors in Financial Mathematics (academic) 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. Graduates of this program 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.

Subject specific competences developed by the student:

Employment possibilities:

Graduates of this program can find employment in major banks, insurance companies, stock brokerage companies, investment firms, pension companies, health benefits companies, public sector and public agencies, logistics sector (optimization), economic research institutes and universities.

Admission requirements

Admission to the study program is open to the following:

  1. Graduates of the Academic study program in Financial Mathematics.
  2. Graduates of the Academic study program in Mathematics or Mathematics Education.
  3. Graduates of the University undergraduate study programs in Applied mathematics, Pure Mathematics, Mathematics Education.
  4. Graduates of some accredited first cycle study program.

Applicants under 2, 3, or 4 above will have to pass additional exams in order to acquire the minimal competences required for admission to the Master's study program in Financial Mathematics. This can be done either prior to admission or prior to completion of the study program. The detailed conditions follow below.

Applicants under 2 or 3 above have to pass the exams from the financial-economic package (Macroeconomics, Microeconomics, Money and finance, Financial markets and institutions). Furthermore, in addition to the obligatory course Probability theory 2 these applicants also have to complete Random processes 1.

Applicants under 4 above have to pass the exams from the financial-economic package (Macroeconomics, Microeconomics, Money and finance, Financial markets and institutions). Additional requirements necessary to cover the minimal competences for admission are determined on a case-bycase basis by the department study committee.

The minimal competences can be validated or acquired in one of the following ways:

(a) The applicants who were previously enrolled in an accredited study program may submit the relevant transcripts in order to request validation of the completed courses.

(b) For applicants who have acquired the necessary competences by self-study, the department organizes one or more ad hoc examinations where the competences are tested. The examination(s) must be completed prior to admission.

(c) Applicants can acquire the requisite competences by attending lectures and problem sessions offered at the mathematics department of the FMF within the first-cycle program in Financial Mathematics; the competences are tested by exams at the end of the course(s).

The mathematics department offers the possibility of admission to the second-cycle study program prior to verification of the requisite competences. Applicants taking advantage of this offer acquire the missing competences by way of (c). They have to complete the corresponding examinations either prior to enrollment in the 2nd year or prior to completion of the study program, subject to decision of the department study committee.

Applicants under (b) above receive the list of minimal mathematical competences at the Student Office.

Admission limitation measures

Applicants are selected according to their GPA of exams, problem sessions and seminars' grades obtained at their respective first-cycle programs.

Enrollment requirements

To enroll in the second year, students must earn at least 50 ECTS credits from courses and exams in the first year.

Re-enrollment requirements

To re-enroll in the current study year, a student needs to earn at least half of all possible credits of the current study year (30 ECTS credits). Re-enrollment is only possible once in the course of the study program; any change in a study program as result of disability of enrollment in the second year is automatically counted as re-enrollment.

Finishing requirements

To finish the program, students must:

Transition from other study programs

Graduates of the second-cycle programs in Mathematics and Mathematics Education must meet the admission requirements. Granted that, they are exempted from retaking courses they have already completed within the respective programs. The exact requirements for enrollment in the second study year and completion of the program are determined by the department study committee.

Study program description

The study program comprises two full academic years based on 120 ECTS credits. Of these, the master's thesis accounts for 20 ECTS credits. All courses are single-term courses with 30 to 45 hours of lectures and 15 to 30 hours of problem sessions altogether (with a weekly load of 2/2 or 3/1 hours of lectures/problem sessions). Each course is worth 5 ECTS credits. A student's choice of courses has to be approved by the department study committee.

The courses are divided into the following groups:

M1 – Analysis and mechanics
M2 – Algebra and discrete mathematics
M3 – Geometry and topology
M4 – Numerical mathematics
M5 – Probability, statistics and financial mathematics
R1 – Computer mathematics

A minimum of 70 ECTS credits must be earned by completing exams from the following categories:

The master's thesis accounts for 20 ECTS credits.

Of the other requisite credits a maximum of 10 ECTS credits can be awarded for work experience or a scientific publication. To be awarded credits, work experience must comprise at least 150 working hours as well as an obligatory presentation preparation. Meeting this requirement, 1 ECTS credit is awarded for each 30 working hours.

Of the cognate courses offered by the Faculty of Economics, it is recommended that one of the following clusters of courses at the Department of Money and Finance be elected:

Macroeconomic cluster:

Entrepreneurial finance cluster:

Financial institutions and markets cluster:

Curriculum

The spreadsheet data are given for both the winter and the summer term.
Each term comprises 15 weeks of classes.

Abbreviations:
L = lectures per week (in hours),
P = problem sessions per week (in hours),
ECTS = ECTS credits worth,
TSW = estimated total student workload (in hours).

1st year

 Winter termSummer termTotal
CourseLPECTSTSWLPECTSTSWECTSTSW
Probability theory 2 3 1 5 150 0 0 0 0 5 150
Elective from group M5 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-4 and R1 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-4 and R1 2 2 5 150 0 0 0 0 5 150
Elective at Faculty of Economics 2 2 5 150 0 0 0 0 5 150
General elective 2 2 5 150 0 0 0 0 5 150
Elective from group M5 0 0 0 0 2 2 5 150 5 150
Elective from group M5 0 0 0 0 2 2 0 150 5 150
Basic elective from groups M1-4 and R1 0 0 0 0 2 2 5 150 5 150
Basic elective from groups M1-4 and R1 0 0 0 0 2 2 5 150 5 150
Elective at Faculty of Economics 0 0 0 0 2 2 5 150 5 150
General elective 0 0 0 0 2 2 5 150 5 150
Weekly total 13 11     12 12        
Term total 195 165 30 900 180 180 30 900 60 1800

2nd year

 Winter termSummer termTotal
CourseLPECTSTSWLPECTSTSWECTSTSW
Elective from group M5 2 2 5 150 0 0 0 0 5 150
Elective from group M5 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-4 and R1 2 2 5 150 0 0 0 0 5 150
Elective at Faculty of Economics 2 2 5 150 0 0 0 0 5 150
General elective 2 2 5 150 0 0 0 0 5 150
General elective 2 2 5 150 0 0 0 0 5 150
Work experience or project work 0 0 0 0 0 0 5 150 5 150
General elective or work experience or project work 0 0 0 0 0 0 5 150 5 150
Master's thesis 0 0 0 0 0 0 20 600 20 600
Weekly total 12 12     0 0        
Term total 180 180 30 900 0 0 30 900 60 1800

M1 Analysis and Mechanics

Course L P ECTS TSW
Measure theory 2 2 5 150
Introduction to functional analysis 2 2 5 150
Functional analysis 2 2 5 150
Introduction to C* - algebras 3 1 5 150
Operator theory 3 1 5 150
Introduction to harmonic analysis 3 1 5 150
Special functions 2 2 5 150
Partial differential equations 2 2 5 150
Complex analysis 2 2 5 150
Analytical mechanics 2 2 5 150
Continuum mechanics 2 2 5 150
Fluid mechanics 2 2 5 150
Mechanics of deformable bodies 2 2 5 150
Dynamical systems 2 2 5 150
Industrial mechanics 2 (seminar) 2 (practice) 5 150

M2 Algebra and Discrete Mathematics

Course L P ECTS TSW
Commutative algebra 3 1 5 150
Associative algebra 3 1 5 150
Non-associative algebra 3 1 5 150
Ordered algebraic structures 3 1 5 150
Group and semi-group theory 3 1 5 150
Number theory 3 1 5 150
Combinatorics 2 2 5 150
Graph theory 2 2 5 150
Cardinal arithmetic 3 1 5 150
Topics in discrete mathematics 2 2 5 150
Applied discrete mathematics 1 3 5 150
Logic 2 2 5 150

M3 Geometry and Topology

Course L P ECTS TSW
Analysis on manifolds 3 1 5 150
Introduction to algebraic geometry 3 1 5 150
Convexity 3 1 5 150
Algebraic topology 1 2 2 5 150
Algebraic topology 2 2 2 5 150
Differential geometry 3 1 5 150
Lie groups 3 1 5 150
Riemann surfaces 2 2 5 150

M4 Numerical Mathematics

Course L P ECTS TSW
Numerical integration and ordinary differential equations 2 2 5 150
Numerical solutions of partial differential equations 2 2 5 150
Iterative numerical methods in linear algebra 2 2 5 150
Computer aided (geometric) design 2 2 5 150
Numerical approximation and interpolation 2 2 5 150
Numerical methods for linear control systems 2 2 5 150

M5 Probability, Statistics and Financial Mathematics

Course L P ECTS TSW
Probability theory 2 3 1 5 150
Statistics 2 3 1 5 150
Financial mathematics 2 2 2 5 150
Introduction to random processes 2 2 5 150
Econometrics 3 1 5 150
Random processes 2 2 2 5 150
Actuarial mathematics 2 2 5 150
Modelling with random processes 2 2 5 150
Topics in game theory 2 2 5 150
Topics in financial mathematics 2 2 5 150
Optimization in finance 2 2 5 150
Time series 2 2 5 150
Riesz spaces in mathematical economics 2 2 5 150

R1 Computer Mathematics

Course L P ECTS TSW
Doing mathematics with a computer 1 3 5 150
Theory of computability 2 2 5 150
Computational complexity 2 2 5 150
Topics in computer mathematics 2 2 5 150
Topics in optimization 2 2 5 150
Optimization 2 2 2 5 150
Data structures and algorithms 3 2 2 5 150