Special Mathematics Lecture (Groups and their representations)

Goals of the Course

Group theory plays an important role in many fields, as for example in quantum mechanics or in particle physics. During this one semester course, we shall introduce the main concepts of groups, their representations, and present some classical groups. Lie groups and Lie algebras will also be discussed.

Objectives of the Course

Get enough knowledge about groups for perceiving their importance in several theories and for recognizing them in numerous applications.

Course Contents or Plan

This course should cover the following topics:

1. Groups
2. Linear representations
3. Lie groups and Lie algebras
4. Semi-simple theory
5. Examples

Course Prerequisites and Related Courses

Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II. Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.

Course Evaluation Method and Criteria

The final grade will be based on the active participation during the lectures and on some written reports. Students will be encouraged to work on applications related to their major during the semester. Students need to notify the course withdrawal to the instructor when they have no intention of finishing the course during the semester.

Study Load (Self-directed Learning Outside Course Hours)

Students are expected to read their notes, and to be familiar with the content of the previous lectures before each new lecture.

Notice for students

It is expected that the students will show a certain maturity in studying independently and in choosing some exercises and problems to solve. Study sessions will be organized on a weekly basis. This course is an optional subject which does not count towards the number of credits required for graduation in any program at Nagoya University.

Textbook

Lecture Notes

Additional information

Reference Website

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