MAMO2500 Symmetry and Algebraic Structures Course description

The course involves abstract algebra, covering groups, rings, fields, modules and representations. This allows us to translate our understanding of numbers and linear algebra into a more general framework, which for instance is used in cryptography. Symmetry also plays an important role in the course, with key aspects of it being highlighted and the understanding further developed.

Language of instruction: Norwegian

The course builds upon

• MAMO2300 - Linear algebra and introduction to group theory.

None

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence.

Knowledge

The student can:

• state and explain structure theorems for groups
• explain what actions and orbits are
• understand basic concepts related to representations, equivalence, and irreducibility
• explain rings and field extensions and their relation to polynomials
• describe modules as generalizations of vector spaces and recognize how group representations can be viewed as modules over the group algebra

Skills

The student can:

• determine whether groups are isomorphic
• characterize actions using quotient space
• decompose representations into simpler components
• decompose polynomial rings and carry out concrete computations over finite fields

General competence

The student can:

• exploit symmetry in the natural world to solve concrete problems
• decompose important, general algebraic structures in the same way one decomposes integers into primes

Lectures and exercise sessions. The main component will be plenary lectures. In the exercise sessions, we work on problems that are solved individually and in groups, which are then discussed and, when appropriate, presented. The aim is to keep students actively engaged throughout the semester.

None

Individual written exam of 3 hours under supervision.

The exam result can be appealed.

In the event of resit or rescheduled exams, another exam form may also be used. If oral exams are used, the result cannot be appealed.

All written and printed aids are allowed. Handheld calculator that cannot be used for wireless communication or to perform symbolic calculations. If the calculator has the capability for internal memory storage, the memory must be cleared before the exam. Random checks may be carried out.

Grade scale A-F

One internal examiner. External examiners are used regularly.