Mathematics: Group- and Ring Theory

This course offers a deeper exploration of group theory and ring theory, two core areas of modern algebra. You will examine how abstract structures reveal patterns, transformations, and the behaviour of mathematical systems. The course builds on the material from Algebraic Structures and prepares you for advanced studies in algebraic geometry, number theory, and related fields.

Topics covered

• Groups: Permutation groups. Burnside's lemma with application to Pólya arithmetic. Sylow's theorems. Symmetric and alternating groups. The structure of finitely generated Abelian groups.
• Rings: Noetherian and Artinian rings and modules. Artin-Wedderburn's theorem. Finitely generated modules over a principal ideal domain with application to the Jordan's normal form of matrices.
• Linear algebra: Multilinear mappings. Tensor products.

The course is an alternative-compulsory course within the Master’s programme in at Lund University. It may be suitable for interested students at Bachelor’s level. The course is also available as a stand-alone course. 

Teaching consists of lectures and seminars where you engage actively with theory and examples. You will practise reasoning mathematically, solving problems, and clearly communicating algebraic ideas. The course concludes with a written exam followed by an oral exam; both are required to pass. A resit is offered shortly after the first exam, and the oral exam is only available to students who have passed the written part.

This course provides an excellent foundation for further study in algebraic disciplines such as algebraic geometry and number theory. It is particularly valuable if you are considering a researchoriented career or want to strengthen your theoretical background in mathematics. The skills you develop — abstract reasoning, problemsolving, and precise mathematical communication — are equally relevant in academia, data science, cryptography, and other areas where advanced mathematics is applied.

Entry requirements

For admission to the course, English 6 / B is required as well as at least 90 credits in pure mathematics including the course MATC31 Algebraic structures, 7.5 credits or equivalent.

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.