Description of the course

This is a onesemester course on advanced mathematical physics
(WinterSpring semester of 139192) taught be me in Sharif University
of Technology. It is open to all Phd students from departments of
physics and mathematics. (MS and BS students are supposed to consult me
before they enroll for this class.) At the end of the course, the
student is supposed to be able to master the essentials of modern
mathematics used in various fields of research in physics, including
high energy physics, condensed matter theory, mathematical physics and
quantum information theory. I
should stress that while these concepts and techniques are becoming
widespread in some fields of theoretical physics, you may or may not
need this level and kind of mathematical methods depending on your
specifid subject of research.
Prerequisites

Knowledge of essential mathematics, linear algebra, and group theory
and some geometry is useful but not necessary. Our emphasis in the
class will be on problem solving so the students are required to stuy a
great deal on their own.
Textbook

Geometry, Topology and Physics, by Mikio Nakahara, Institute of Physics
Publishin (IOP), Bristol and Philadelphia.
Contents:
 Basic notions of topology, homotopy groups, homology groups, differential geometry and manifolds, Riemmanian geometry, differential forms, cohomology groups, complex manifolds, fibre bundles....
 Set no. 1:
 Set no. 2:
 Set no. 3:
 Set no. 4:
Homeworks: