MAMO2300 Linear algebra and introduction to group theory Course description

The course covers linear algebra and elementary group theory. Emphasis is placed more on structure than on concrete manipulation of matrices, which allows for a deeper understanding and generalizations. Groups are the mathematical foundation for symmetry, used to solve concrete problems.

The course builds on

• DAPE1300 - Discrete Mathematics
• DAFE1000 - Mathematics 1000

The course can advantageously be taken simultaneously with DAPE2000 - Mathematics 2000 with Statistics. Linear algebra and matrices appear in both courses, but the approach and focus are different.

No requirements over and above the admission requirements.

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:

• know the definition of a vector space and examples thereof, as well as handle concepts such as subspaces, bases, and dimension.
• understand the relationship between matrices and linear transformations and relate it to geometric operations such as rotation and reflection.
• know the basics of inner product spaces, such as orthogonal bases and projections.
• perform Jordan decomposition with applications to systems of differential equations.
• handle tensor products and quotient vector spaces.
• provide examples of elementary groups and homomorphisms.

Skills

The student can:

• set up bases and calculate with matrices and determinants, determine eigenvalues, and decompose matrices related to generalized eigenvector spaces.
• perform concrete calculations with tensor products via bases and relate such products to multilinear mappings.
• use exterior algebra as a tool.
• relate groups via homomorphisms and understand the actions of matrix groups on vector spaces.

General competence

The student can:

• introduce linear structures in various situations to solve concrete problems
• bring structure into concrete problems by abstracting them and placing them into a more ordered form that allows the use of mathematical tools

Lectures and exercises. The main part will be lectures in plenary. In the exercise sessions, we look at tasks that are solved individually and in groups, and which are discussed or possibly presented. The aim is to engage the students 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.