Mathematics: Representation Theory

In this course, you will investigate how finite groups can be represented through linear algebra over the complex numbers. You will learn the fundamental ideas of representation theory and character theory, and see how these concepts provide powerful methods for tackling deep mathematical problems.

Topics covered include

• Group representations: linear and equivalent representations, regular representations, induced and restricted representations, irreducible representations, Maschke’s Theorem, dual representations, tensor products.
• Character theory: Characters of representations, induced and irreducible characters, orthogonality relations, integrality, character tables, Mackey formula, Frobenius reciprocity.
• Applications: Burnside’s Theorem, Frobenius’ Theorem, Frobenius divisibility.

The course is alternative-compulsory within the Master’s programme in Mathematics at Lund University. It is also available as a standalone course. 

The course combines lectures and seminars, giving you both structured learning and space for discussion. You will work with abstract concepts and concrete examples and develop your ability to explain mathematical ideas clearly, both in writing and speech.

Assessment includes a written exam followed by an oral exam. You must pass the written part to take the oral exam. If needed, a resit is offered shortly after. The final grade is based on both exams, with the written part weighted three times more than the oral. 

Representation theory is a central tool in many areas of mathematics, including algebra, number theory, and physics. After completing this course, you will be prepared for certain other advanced studies in algebra and related fields. The skills you develop—logical reasoning, abstract thinking, and problem-solving—are also valuable in research, data science, and technology-driven industries.

Entry requirements

For admission to the course, English 6/B is required as well as at least 90 credits in pure mathematics including knowledge equivalent to the courses MATM31 Algebraic Structures, 7.5 credits and MATP33 Group and Ring Theory, 7.5 credits.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.