87970 - ADVANCED MATHEMATICAL METHODS FOR PHYSICS

Course Unit Page

Academic Year 2020/2021

Learning outcomes

At the end of the course the student will learn some of the mathematical tools necessary for the study of modern theoretical physics. In particular, he/she will acquire advanced analytical and geometrical methods that have a wide range of theoretical applications.

Course contents

1. Manifolds, vectors, tensors, forms.

2. Tensor calculus.

3. Lie derivatives.

4. Differential forms and their applications.

5. Lie groups and their Lie algebras.

6. Metric and affine connection. Riemannian geometry.

 

Readings/Bibliography

My lectures notes.

Teaching methods

Lectures on the blackboard.

Assessment methods

Oral exams, which include also the solution of exercises. The list of exercises is presented to the students in advance and all the exercises were resolved during the lectures and are described in the lecture notes. The student should show the understanding of the main notions of the course and the capacity to do calculations, proofs and reasonings. After the solutions of the problem two other topics of the course are discussed.

Teaching tools

Lectures.

Office hours

See the website of Alexandr Kamenchtchik