MAMO2300 Linear Algebra and Introduction to Group theory Course description

The course covers linear algebra and gives an introduction to elementary group theory. Emphasis is placed more on structure than on concrete manipulation of matrices, which allows for a deeper understanding and generalizations.

Language of instruction: Norwegian and English

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:

• knows the definition of a vector space and examples thereof, and concepts such as subspaces, bases, and dimension
• understands the relationship between matrices and linear transformations and can relate it to geometric operations
• knows the basics of inner product spaces, such as orthogonal bases and projections
• knows the spectral theorem for normal matrices and the existence of the Jordan decomposition
• can relate groups via homomorphisms and understand the actions of matrix groups on vector spaces, such as rotation and reflection
• can formulate results on quadratic forms

Skills

The student can:

• set up bases and use Gram-Schmidt orthogonalization
• calculate the rank of a matrix and use the rank result
• perform calculations with matrices and determinants, and determine eigenvalues and eigenvectors
• perform calculations with tensor products via bases
• calculate and use the singular value decomposition of a matrix

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.