NB! This is an elective course and may be cancelled if fewer than 10 students are enrolled by January 20th for the spring semester.
This course gives an introduction to matrix groups and their applications. Matrices as linear transformations of vector spaces over the real numbers, complex numbers and quaternions will be introduced. The associated general linear, special linear and orthogonal groups will be defined in each case, with lots of examples and applications to symmetry groups. The topology of a matrix group will be described. The structure of matrix groups as manifolds will also be covered, and the important notion of a Lie algebra associated with a matrix group will be developed.
Learning outcome
After completing the course, the student should have knowledge of how to use matrices to describe general linear, special linear and orthogonal groups over the real numbers, complex numbers and quaternions. They should also be familiar with the most common examples in low dimension. The student should also know how to think of matrix groups as topological spaces, and indeed as manifolds. Moreover, the student should also be able to derive the Lie algebra of a matrix group and compute its Lie bracket.
Forkunnskapskrav
Ingen
Anbefalte forkunnskaper
Mathematical Methods 1 (MAT100), Linear Algebra (MAT110), Discrete Mathematics (MAT120), Real and Complex Calculus (MAT210), Abstract Algebra (MAT250), Vector Analysis (MAT300), Differential Equations (MAT320), Manifolds (MAT510)
Exchange programme at Faculty of Science and Technology
Emneevaluering
There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.
The course description is retrieved from FS (Felles studentsystem). Version 1
