University of Gothenburg
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  3. Specializations Mathematical Sciences

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

and at least two of the courses

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

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

at least four of the courses

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

  • GM1032 Financial Institutions and Markets
  • GM1014 Applied Portfolio Management (NOTE: This course may be difficult to follow for students without additional background in economics)
  • GM1042 Credit risk modelling
  • GM1038 Financial econometrics
  • GM1048 Quantitative finance

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 are given.

Early autumn (HT1)
Stochastic Calculus
Computational Methods for Bayesian Statistics
Advanced Microeconomic Theory
Portfolio Investments (**)
Integration Theory
Quantitative finance (**)

Late autumn (HT2)
Options and Mathematics
Financial Institutions and Markets (**)
Credit risk modelling (*)

Early spring (VT1)
Financial Derivatives and PDE
Computational Methods for Stochastic Differential Equations
Financial Risk
Financial econometrics (**)

Late spring (VT2)
Statistical Learning for Big Data
Financial Time Series
Applied Portfolio Management (**)

(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

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 following courses is required.

The course MMA110 Integration theory can be included in these 30 credit points. 

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 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
Financial Risk

Late spring (VT2)
Spatial Statistics and Image Analysis
Financial Time Series
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:

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

and at least three of the courses: 

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 are given.

Early autumn (HT1)
Computational Methods for Bayesian Statistics
Nonlinear Optimization
Neural Networks
Algorithms
Deep machine learning
Advanced Topics in Machine Learning

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
Data structures and algorithms

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

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 Databases


(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.

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