00709 - Mathematical Methods Of Physics

Learning outcomes

At the end of the course the student acquires the mathematical notions and methods necessary for the understanding of the modern physics. First, the student studies the theory of holomorphic functions and is able to calculate the contour integrals in the complex plane. Then the student learns element of the topology, linear and normed spaces. Then the student studies the Hilbert spaces and their operators, which permits to use the mathematical formalism of quantum mechanics.

Course contents

1. Theory of the holomorphic functions.

2. Topological spaces.

3. Linear spaces and normed spaces.

4. Hilbert spaces.

5. Operators in the Hilbert spaces.

Readings/Bibliography

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. The final mark for the exam is given by taking into account the capacity to make calculations, to make logical reasoning, the knowledge of definitions of the notions introduced during the course, the industriousness shown during the course, the capacity to think about the things which are close to the topics discussed in detail during the lectures. 

Teaching tools

Lectures.

Office hours

See the website of Alexandr Kamenchtchik