Course syllabus

Algebra and Representation Theory, 7.5 credits

Course code: MA105A Credits: 7.5
Main field of study: Mathematics Progression: A1N
    Last revised: 11/09/2020
Education cycle: Second cycle Approved by: Head of school
Established: 02/12/2019 Reading list approved: 11/09/2020
Valid from: Spring semester 2021 Revision: 1

Aims and objectives

General aims for second cycle education

Second-cycle courses and study programmes shall involve the acquisition of specialist knowledge, competence and skills in relation to first-cycle courses and study programmes, and in addition to the requirements for first-cycle courses and study programmes shall

  • further develop the ability of students to integrate and make autonomous use of their knowledge
  • develop the students' ability to deal with complex phenomena, issues and situations, and
  • develop the students' potential for professional activities that demand considerable autonomy, or for research and development work.

(Higher Education Act, Chapter 1, Section 9)

Course objectives

Knowledge and Understanding
After completed studies the student shall be able to account for

  • how the representation theories of different algebraic structures are included in that for associative algebras.

Competence and Skills
After completed studies the student shall be able to

  • formulate important results and theorems in representation theory,
  • exemplify and interpret important concepts from representation theory in concrete situations, and
  • in simple cases, use standard methods to decompose fully reducible representations in irreducible constituents.

Main content of the course

Definition, structure- and representation theory for different algebraic structures: finite groups, associative algebras, Lie groups, finite dimensional Lie algebras. Tensor products of representations.

Teaching methods

Tutoring using internet-based communication platforms.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Examination methods

Examination, 7.5 credits (Code: A001)
Examination through written and oral presentation of assignments.


For students with a documented disability, the university may approve applications for adapted or other forms of examinations.

For further information, see the university's local examination regulations (in Swedish).

Grades

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).

In accordance with university regulations regarding grading systems for first and second-cycle courses (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades shall be used: Fail (U), Pass (G) or Pass with Distinction (VG). For courses that are included in an international Master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the grading scale of A-F shall be used. The vice-chancellor, or a person appointed by the vice-chancellor, may decide on exceptions from this provision for a specific course, if there are special grounds.

Grades used on course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Examination
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

For further information, see the university's local examination regulations (in Swedish).

Specific entry requirements

Abstract Algebra, 7.5 credits, Combinatorics, 6 credits and Linear Algebra II, 7.5 credits.

For further information, see the university's admission regulations (in Swedish).

Transfer of credits for previous studies

Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.

For further information, see the university's local credit transfer regulations (in Swedish).

Other provisions

All or part of the course may be given in English.

Reading list and other teaching materials

Required reading

Fulton, William och Harris, Joe (2013)
Representation Theory - A First Course. Vol. 129, Graduate Texts in Mathematics
Springer Verlag

Additional course material is contributed by the Department of Mathematics.