SF2723 Topics in Mathematics III, 7,5 hp
Matrix Groups
Course Web Page
News
- 10/12
- Homework XII has been graded now.
- 3/12
- Homework XI is now graded. As I said in the lecture today, next lecture will be a problem session, where we discuss interesting problems that has arised in the homework during the course. Please let me know which problems you are mostly interested in discussing.
The oral exams will take place on December 17 and December 18 between 8.30 and 12.00. Let me know which day you prefer so that I can set a schedule.
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Contents
Course description
There are several different sets of matrices occurring naturally in different area of mathematics that all have the property that they are closed under multiplication and taking inverses. Some of these are called the classical groups and you have certainly already met them in some form, even if you don't know them by name. They are the general linear group, GLn, the special linear group, Sln, the orthogonal group, On, the special orthogonal group, SOn and the symplectic group, Spn.
During this course, we will go through several important concepts from the 19th and 20th century mathematics which will help us in understanding what the classical groups are like. We will use algebraic, topological, differential geometric and algebraic geometric methods. The idea is that the matrix groups, which themselves have important roles in mathematics and physics, till serve as tools for understanding the abstract concepts needed in order to study them.
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