00709 - Mathematical Methods Of Physics (A-L)

Learning outcomes

At the end of the course the student acquires the mathematical notions and the methodologies necessary for the study of the comprehension of the modern physics. I the first part of the course, the student acquires the familiarity with the holomorphic functions and is able to calculate the contour integrals in the complex plane.In the second part of the course the student studies the formalism of the infinite-dimensional vector spaces, in particular, the Hilbert spaces and is able to use this formalism for the study of quantum mechanics.

Course contents

1. Theory of functions of the complex variable.

2. Topological spaces.

3. Linear spaces and normed spac ces.

4. Hilbert spaces.

5. Operators in the Hilbert spaces.

Readings/Bibliography

Lecture notes.

Teaching methods

Lectures at a blackboard.

Assessment methods

Oral exams, which include an immediate solution of an exercise. The list of exercises is known to the students in advance.  All the exercises were solved during the lectures and are described in the lecture notes. The student should show capacities of calculations and of logic reasoning. The remaining part of the exam includes the discussion of two theoretical topics belonging to different chapters of the course. The final mark is given by taking into account the ability of calculations, of the reasoning, of the knowledge of the definitions of the notions introduced in the course, the diligence and the ability to understand things which were not explained directly during the lectures but which are very close to the content of the lectures.

Teaching tools

Lectures.

Office hours

See the website of Alexandr Kamenchtchik