Advanced Mathematical Physics
Vahid Karimipour
Sharif University of Technology
Description and Prerequisites
This is a short course, in which we start with the basic concepts of point set topology, and continue to homotopy and homology theories, and then manifolds, Riemannian Geometry, fiber bundles and complex manifolds. It is suitable for students in high energy physics and condensed matter physics and in fact every subject in theoretical physics. A basic knowledge of mathemtical physics and group theory is necessary for this course.
Textbook: Geometry, Topology and Physics, by Mikio Nakahara
Contents
These lecture notes are not complete and are being developed as I teach the course from time to time.
- Introduction to metric and topological spaces
- Homotopy groups
- Homology groups
- Manifolds
- Lie groups
- Cohomology theory
- Reimannian geometry
- Fiber bundles
- Connections in fibre bundles
Weekly Schedule: Saturdays and Mondays, Spring Semester, 2024; 5:00-7:00 pm, Room 412.
Grading Systems
An important portion of your grade is based upon your homeworks which you deliver presentation of special topics at the end of the course. You are supposed to work on your homework and your presentations on a collaborative basis. Each group of 2 or 3 students, will deliver one homework set and oen lecture at the end of the semester.
| Score from 20 | Date | |
|---|---|---|
| Homework | 6 | |
| Midterm exam | 6 | |
| Final exam | 8 |