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Mathematics (second cycle)

Study program cycle:

Second cycle study program.

Anticipated academic title:

In Slovenian: magister matematike, magistrica matematike, abbreviated to mag. mat.

Duration:

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

Basic goals:

This program 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.

Subject specific competences developed by the student:

Employment possibilities:

Graduates of this program can find employment in:

Admission requirements

Admission to the study program is open to the following:

  1. Graduates of the Academic study program in Mathematics or Mathematics Education.
  2. Graduates of the University undergraduate study programs in Applied mathematics, Pure Mathematics, Mathematics Education, Computer Science with Mathematics. In this case, applicants are exempted from taking some exams.
  3. Graduates of some accredited first cycle study program. (A technology or natural sciences program with a basic amount of mathematical analysis and linear algebra is recommended.) From the mathematical exams, a grade point average (GPA) of 8.0 or higher is recommended.

Additional requirements and exemptions:

Applicants under 2 are exempted from 60 to 90 ECTS credit requirements, and also from the final exam. The exact requirements and exemptions are determined by the department study committee for each applicant individually. Applicants have to file a formal written request and attach the relevant accredited transcripts. It is obligatory for graduates of the University undergraduate study program in Computer Science with Mathematics to complete the Point-set topology course.

For applicants under 3, the List of minimal mathematical competences required for admission to a second-cycle study program in mathematics (regardless of the program's specialization) is relevant. Beside these obligatory minimal requirements there are also additional requirements depending on the second-cycle program's specialization.

For Bachelors in Financial Mathematics, the course goals and competences of Algebra 2, Algebra 3, and Point-set topology are required. (In the List of minimal mathematical competences, the three courses belong to the Algebra package and the Theory of metric spaces and topology package).

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 of one or more courses offered at the mathematics department of the FMF; 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 study 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 program in Financial Mathematics must meet the admission requirements. Granted that, they are exempted from retaking courses they have already completed within the Financial Mathematics program. The exact requirements for enrollment in the second study year and completion of the program are determined by the department study committee.

Graduates of the second-cycle program in Mathematics Education are exempted from retaking courses they have already completed within the Mathematics Education program. 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 final "master's" exam and master's thesis account for 25 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

Other – Courses that do not belong to one of the above and courses that are offered by other departments (physics, chemistry, economics, education, linguistics, computer science, electrical engineering, etc.)

The requisite 120 ECTS are earned primarily by completion of exams, completion of the final (master's) exam, preparation and defense of a master's thesis, but possibly also by acquisition of work experience or publication of a scientific research paper.

A minimum of 75 ECTS credits must be earned by completing exams from the following categories:

The final exam and the master's thesis together account for 25 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.

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
Basic elective from groups M1-5 and R1 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-5 and R1 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-5 and R1 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-5 and R1 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-5 and R1 2 2 5 150 0 0 0 0 5 150
General elective 2 2 5 150 0 0 0 0 5 150
Basic elective from groups M1-5 and R1 0 0 0 0 2 2 5 150 5 150
Specific elective from groups M1-5 and R1 0 0 0 0 2 2 5 150 5 150
Specific elective from groups M1-5 and R1 0 0 0 0 2 2 5 150 5 150
Specific elective from groups M1-5 and R1 0 0 0 0 2 2 5 150 5 150
Specific elective from groups M1-5 and R1 0 0 0 0 2 2 5 150 5 150
General elective 0 0 0 0 2 2 5 150 5 150
Weekly total 12 12     12 12        
Term total 180 180 30 900 180 180 30 900 60 1800

2nd year

 Winter termSummer termTotal
CourseLPECTSTSWLPECTSTSWECTSTSW
Specific elective from groups M1-5 and R1 2 2 5 150 0 0 0 0 5 150
Specific elective from groups M1-5 and R1 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
General elective 2 2 5 150 0 0 0 0 5 150
General elective 2 2 5 150 0 0 0 0 5 150
General elective 0 0 0 0 2 2 5 150 5 150
Master's thesis and final exam 0 0 0 0 0 0 25 750 25 750
Weekly total 12 12     2 2        
Term total 180 180 30 900 30 30 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