Mathematics: Galois Theory

In this course, you will develop a deeper understanding of field extensions and explore the fundamental connection between polynomial equations and group theory. The course introduces the algebraic framework that explains when equations can be solved and uncover why some problems have no solution by radicals.

Topics covered include

• Field extensions: splitting fields, normal and separable extensions, field automorphisms, normal closures.
• Galois groups: Galois extensions, the Galois Correspondence, the Fundamental Theorem of Galois Theory.
• Polynomial equations: solvability by radicals, the unsolvability of quintic equations, symmetric polynomials, cyclotomic extensions.

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 is based on lectures and seminars where you engage actively with the material. You will work on problems that require integrating ideas from different parts of the course and develop your ability to explain mathematical reasoning clearly, both in writing and speech, using precise terminology.

Assessment consists of a written exam followed by an oral exam. Only students who have passed the written exam may take the oral exam. A resit of the written exam is offered shortly after the regular examination.

Grading is based on both exams, with the written exam weighted three times more than the oral. To earn a “Pass with distinction,” you need at least 75% of the total possible points.

Galois theory is a key component of modern algebra and underpins many areas of mathematics. Completing this course prepares you for advanced studies in algebra, number theory, and related fields. The course strengthens skills such as logical reasoning, abstract thinking, and problemsolving—competencies valued in academic research as well as in fields that rely on rigorous mathematical methods.

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 MATM31 Algebraic Structures, 7.5 credits or equivalent. The course MATP33 Group and Ring Theory, 7.5 credits is recommended but it is not required.

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.