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

**Before you start the studies you will be contacted by 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 specialization. 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.

## 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
- MMA211 Advanced Differential Calculus
- MMA430 Partial Differential Equations II
- MMA140 Spectral Theory and Operator Algebras
- MMA150 Complex Analysis in Several Variables

and at least two of the courses

- MMA100 Topology
- MMA201 Representation Theory
- MMA340 Analytic Number Theory
- MMA350 Algebraic Number Theory
- MMA310 Galois Theory
- MMA320 Introduction to Algebraic Geometry
- MMA330 Commutative Algebra

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. The course is normally done at half speed during the second year.

Below, you can see when the various required courses are given.

**Early autumn (HT1)**

Integration Theory

Representation Theory (1)

Commutative Algebra (2)

**Late autumn (HT2)**

Functional Analysis

Galois Theory (1)

Introduction to Algebraic Geometry (2)

**Early spring (VT1)**

Topology

Advanced Differential Calculus (1)

Theory of Distributions (2)

Algebraic Number Theory (1)

Analytic Number Theory (2)

**Late spring (VT2)**

Partial Differential Equations II

Complex Analysis in Several Variables

Spectral Theory and Operator Algebras

(1) The course is given in academic years starting with a year with an odd number, e.g., 21/22.

(2) The course is given in academic years starting with a year with an even number, e.g., 22/23.

## Requirements for the specialization Applied Mathematics

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

- MMA400 Applied Functional Analysis
- MMA430 Partial Differential Equations II
- 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

The specialization requirements above must be fulfilled before the student can be registered for MMA920 Thesis in Mathematics for the two-year Master Program in Mathematical Sciences, specialization Applied Mathematics.

Below you can see when the various required courses are given.

**Early autumn (HT1)**

Applied Functional Analysis

Numerical Linear Analysis

High Performance Computing

**Late autumn (HT2)**

Large-scale Optimization

Project course in Mathematical Modelling

**Early spring (VT1)**

Computational Methods for Stochastic Differential Equations

**Late spring (VT2)**

Partial Differential Equations II

## 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
- GM0751 Advanced Microeconomic Theory
- NEK308 Portfolio Investment

at least four of the courses

- MMA110 Integration Theory
- MMA711 Financial Derivatives and Partial Differential Equations
- MMA630 Computational Methods for Stochastic Differential Equations
- MSA102 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:

- GM1032 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 course codes GMxxxx or NEKxxx are given at the School of Business, Economics and Law. To sign up for these courses contact programme coordinator Hjalmar Rosengren. Other courses (MMA/MSA) are given at the Department of Mathematical Sciences. As a master student in mathematical sciences, you may also attend other courses in the Master of Science in Finance at the School of Business, Economics and Law. See their web pages for information about such courses.

This specialization leads to a master's degree either in Mathematics or in Mathematical Statistics. To get a degree in Mathematics, you should finish the three compulsory courses and one of the specialization courses beginning with MMA before registering at MMA930 Thesis in Mathematics for the two-year Master Program in Mathematical Sciences, specialization Finance Mathematics. For a degree in Mathematical Statistics, you need to finish the three compulsory courses and one of the specialization courses beginning with MSA before registering at MSA930 Thesis in Mathematical Statistics for the two-year Master Program in Mathematical Sciences, specialization Finance Mathematics.

Below, you can see when the required courses and some other relevant courses are given.

**Early autumn (HT1)**

Stochastic Calculus

Computational Methods for Bayesian Statistics

Advanced Microeconomic Theory

Portfolio Investments (**)

Advanced Corporate Finance (*)

Integration Theory

**Late autumn (HT2)**

Options and Mathematics

Financial Institutions and Markets (**)

Other courses:

Project Course in Mathematical Modelling

Project Course in Statistical Modelling

**Early spring (VT1)**

Financial Derivatives and PDE

Computational Methods for Stochastic Differential Equations

Other courses:

Statistical Inference Principles (1)

**Late spring (VT2)**

Statistical Learning for Big Data

Financial Risk

Financial Time Series

Applied Portfolio Management (**)

Other courses:

Partial Differential Equations II

(1) The course is given in academic years starting with a year with an odd number, e.g., 21/22.

(2) The course is given in academic years starting with a year with an even number, e.g., 22/23.

Most of the courses at Handelshögskolan goes at full speed and (*) means that they run in the first half of the study period and (**) that they run in the second half.

## Requirements for the specialization Mathematical Statistics

Knowledge corresponding to the courses

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

is required. Students should normally have this knowledge when starting the programme. 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 prerequisites and general requirements, at least 30 higher education credits must be selected from our department’s advanced-level courses in mathematical statistics, among them

and at least one of the courses

- MSA102 Computational Methods for Bayesian Statistics
- MSA220 Statistical Learning for Big Data
- MSF100 Statistical Inference Principles (given every second year)

is required.

The specialization requirements above must be fulfilled before the student can be registered for above MSA910 Thesis in Mathematical Statistics for the two-year Masters Program in Mathematical Sciences.

Here is schedule for when the required courses and some other relevant courses are given.

**Early autumn (HT1)**

Computational Methods for Bayesian Statistics

Stochastic Calculus

Integration Theory

**Late autumn (HT2)**

Foundations of Probability Theory

Project Course in Statistical Modelling

**Early spring (VT1)**

Statistical Inference Principles (1)

Experimental Design and Sampling (2)

Data Science for Biomedicine

Advanced topics in probability

**Late spring (VT2)**

Spatial Statistics and Image Analysis

Financial Time Series

Financial Risk

Statistical Learning for Big Data

Stochastic Processes (1)

(1) The course is given in academic years starting with a year with an odd number, e.g., 21/22.

(2) The course is given in academic years starting with a year with an even number, e.g., 22/23.

## Requirements for the specialization Statistical Learning and AI

You need eight specialization courses. The following three courses are compulsory:

- MSA102 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
- MSA680 Data Science for Biomedicine
- 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
- DIT743 Computational Methods in Bioinformatics
- DIT093 Algorithms
- DIT621 Databases
- DIT407 Introduction to Data Science and AI
- DIT867 Applied Machine Learning
- DIT728 Design of AI Systems
- DIT245 Machine Learning for Natural Language Processing
- DIT382 Algorithms for Machine Learning and Inference
- DIT471 Advanced Topics in Machine Learning
- DIT930 Advanced Databases

The three compulsory courses and one of the specialization courses listed above given at the Department of Mathematical Sciences (starting with MM or MS) must be finished before the student can be registered for MSA940 Thesis in Mathematical Statistics for the two-year Masters Program in Mathematical Sciences, specialization Statistical learning and AI (MSA940).

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.

Here is schedule for when the required courses and some other relevant courses are given.

**Early autumn (HT2)**

Computational Methods for Bayesian Statistics

Nonlinear Optimization

Neural Networks

Algorithms

Other courses:

Stochastic Calculus

Integration Theory

**Late autumn (HT2)**

Project Course in Statistical Modelling

Foundations of Probability

Simulation of Complex Systems

Introduction to Data Science and AI

Computational Methods in Bioinformatics

Machine Learning for NLP

Databases

**Early spring (VT1)**

Statistical Inference Principles (1)

Experimental Design and Sampling (2)

Applied Machine Learning

Design of AI Systems

Algorithms

Introduction to Data Science and AI

Databases

Algorithms for Machine Learning

Data Science for Biomedicine

Other courses:

Data Structures and Algorithms

**Late spring (VT2)**

Financial Time Series

Spatial Statistics and Image Analysis

Statistical Learning for Big Data

Stochastic Processes (1)

Applied Machine Learning

Introduction to Data Science and AI

Advanced Topics in Machine Learning

Advanced Databases

Other courses:

Data Structures

(1) The course is given academic years starting with an odd number, e.g. 2021/2022.

(2) The course is given academic years starting with an even number, e.g. 2022/2023.