# Specializations Mathematical Sciences

The programme has five specializations: Mathematics, Applied mathematics, Financial mathematics, Mathematical statistics, Statistical learning and AI.

Within each specialization there are a number of advanced courses to choose from. To some extent, lower-level courses required for the advanced courses may be taken as part of the programme. In addition, one may also take research-level courses, or courses in a related field.

The requirements for graduating with a master degree in either of the specializations above are specified below. It is the student’s own responsibility to choose and pass courses so that the requirements of one of the specializations are met at the end of the studies.

**Before you start the studies you should contact the programme coordinator Hjalmar Rosengren to set up an individual study plan.**

For all specializations, the following requirements apply:

- The degree must include courses covering 120 higher educational credits (corresponding to 2 years full-time studies).
- Out of these credits, at most 30 may be from bachelor-level courses, the rest must be master or research level courses.
- The degree must include a thesis of 30 higher educational credits, within the area of specialisation. Half of the study time over the whole of the second year is normally spent on the thesis.
- The course Perspectives in mathematics is mandatory for all specializations.
- Further requirements are listed for each specialization.

For more options see the complete lists of courses in Mathematics and Mathematical Statistics.

## Requirements for the specialization Mathematics

In addition to the general requirements, at least two of the courses

- MMA110 Integration Theory
- MMA120 Functional Analysis
- MMA130 Theory of Distributions
- MMA210 Advanced Differential Calculus
- MMA421 Ordinary Differential Equations and Dynamical Systems (given last time spring 2018)
- MMA430 Partial Differential Equations II
- Spectral Theory and Operator Algebras
- Multivariable Complex Analysis (new course spring 2020)

and at least two of the courses

- MMA100 Topology
- Representation Theory
- Analytic Number Theory
- Algebraic Number Theory (new course spring 2020)
- MMA310 Galois Theory
- MMA320 Introduction to Algebraic Geometry
- MMA330 Commutative Algebra

Note that even if some of the information about the courses is in Swedish, the courses will be taught in English when required.

The specialization requirements must be fulfilled before the student can be registered for MMA910 Thesis in Mathematics for the two-year Masters Program in Mathematical Sciences.

## Requirements for the specialization Applied Mathematics

In addition to the general requirements, at least four of the courses

- MMA400 Applied Functional Analysis
- MMA410 Fourier and Wavelet Analysis
- MMA430 Partial Differential Equations II
- MMA500 Project Course in Partial Differential Equations
- MMA511 Large-scale Optimization
- MMA520 Project Course in Mathematical Modelling
- MMA600 Numerical Linear Algebra
- MMA620 High Performance Computing
- MMA630 Computational methods for stochastic differential equations

Note that even if some of the information about the courses is in Swedish, the courses will be taught in English when required.

Master’s thesis in Applied Mathematics (MMA920) is normally done at half speed during the second year.

## Requirements for the specialization Financial Mathematics

This specialization is a cooperation with the School of Business, Economics, and Law (Handelshögskolan) at the University of Gothenburg.

In addition to the general requirements, you need the compulsory courses

- MMG810 Options and Mathematics
- GM0701 Advanced Microeconomic Theory
- HNF635(NEG300) Portfolio Investment

at least three of the courses

- MMA110 Integration Theory
- MMA711 Financial Derivatives and Partial Differential Equations
- MMA630 Computational methods for stochastic differential equations
- MSA101 Computational Methods for Bayesian Statistics
- MSA220 Statistical Learning for Big Data
- MSA350 Stochastic calculus
- MSA400 Financial risk
- MSA410 Financial time series

and at least two of these courses given at the School of Business, Economics and Law:

- GM1002 Financial Institutions and Markets
- GM1015 Advanced Corporate Finance
- GM1014 Applied Portfolio Management (NOTE: This course may be difficult to follow for students without additional background in economics)

Courses with codes GMxxxx or HNFxxx are given at Handelshögskolan. Other courses, (MMA/MSA) are given at the Department of Mathematical Sciences.

### Courses in business and economics

Courses with course codes GMxxxx are given at Handelshögskolans Graduate School. To sign up for these courses contact programme coordinator Hjalmar Rosengren.

Courses with course codes HNFxxx are given as part of Handelshögskolans Bachelor degree in Economics. For more information about these courses, and to sign up, contact Katarina Renström.

As a master student in mathematical sciences, you may also attend other courses in the Master of Science in Finance at Handelshögskolan. See their web pages for information about such courses.

The three compulsory courses and one of the specialization courses listed above and given at the Department of Mathematical Sciences are required before the student can be registered for either MMA930 Thesis in Mathematics for the two-year Master Program in Mathematical Sciences, specialisation Finance Mathematics, or MSA930 Thesis in Mathematical Statistics for the two-year Master Program in Mathematical Sciences, specialisation Finance Mathematics. The course is normally done at half speed during the second year.

## Requirements for the specialization Mathematical Statistics

Knowledge corresponding to the courses

- MSG110 Sannolikhetsteori
- MSG200 Statistical Inference
- MSG400 Stochastic Data Processing and Simulation
- MSG500 Linear Statistical Models

is required. Students should normally have this knowledge when starting the program. However, it is possible to include in the masters degree up to 30 higher education credits of bachelor level courses as needed. Further, in addition to the general requirements, the course

and one of the courses

- MSA101 Computational Methods for Bayesian Statistics
- MSA220 Statistical Learning for Big Data
- MSF100 Statistical inference principles (given every second year)

is required.

Including the required courses above, courses covering at least 30 higher education credits must be selected from our department’s advanced-level courses in mathematical statistics before the student can be registered for MSA910 Thesis in mathematical Statistics for the two-year Masters Program in Mathematical Sciences.

## Requirements for the specialization Statistical Learning and AI

In addition to the course MVA200 Perspectives on mathematics, which is compulsory for the whole programme, you need eight specialization courses. The following three courses are compulsory:

- MSA101 Computational methods for Bayesian statistics
- MSA220 Statistical learning for big data
**** - MMG621 Nonlinear optimization

In addition, you need at least two of the courses:

- MSA520 Project course in statistical modelling
- MSA150 Foundations of probability theory
- MSF100 Statistical inference principles
- MSA251 Experimental design and sampling
- MSA301 Spatial statistics and image analysis
- MSA410 Financial time series
- MSF200 Stochastic processes

and at least three of the courses:

- FIM720 Neural networks
- FIM750 Simulation of complex systems
- DIT742 Computational methods in bioinformatics
- DIT602 Algorithms
- DIT621 Databases
- DIT405 Introduction to data science and AI (given for the first time 20/21)
- DIT866 Applied machine learning
- DIT728 Design of AI systems (given for the first time 20/21)
- DIT245 Machine learning for natural language processing (give for the first time 20/21)
- DIT381 Algorithms for machine learning and inference

You need to write a master’s thesis in mathematical statistics (30 hec), with specialization Statistical learning and AI (MSA940). In order to start the thesis you should have finished the three compulsory courses and one of the courses from the second list above (starting with MM or MS). The master’s thesis is normally written as a half-time course during the second year.

The specialization is inter-disciplinary, and you will mainly choose from the specialization courses above. You can find other courses to choose from in our lists of courses in mathematics and mathematical statistics.

Depending on your background you may need to include some courses at bachelor level (for instance, in mathematical statistics). At most 30 hec bachelor level courses may be included in your degree.