Reference Material

The basic reference for the course is Part I of the textbook: 

• Lectures On Advanced Mathematical Methods for Physicists by Sunil Mukhi and N. Mukunda. 

The lectures will follow the plan and style of the book quite closely.

Some exercises are provided in this book. Dr Sachin Jain and Dr Renjan John have kindly agreed to help out by providing exercises (with solutions) that will be posted on this page. 

Other textbooks aimed at physicists are:

• Topology and Geometry for Physicists" by Charles Nash and Siddhartha Sen,
• "Geometry, Topology and Physics" by Mikio Nakahara.

They are at a slightly higher level than this course.

A very useful textbook aimed at mathematicians is:

• "Lecture Notes on Elementary Topology and Geometry" by Itzhak Singer and John Thorpe. 

I used this textbook extensively when preparing my own book. It contains proofs of all the main results that will be introduced in the present course. Proofs are of course essential to mathematicians, but for physicists who want a conceptual/practical grasp of the subject, they will often be skipped in the course.