*Conducted in terms:*2022/23Z, 2023/24Z

*ISCED code:*0533

*ECTS credits:*6

*Language:*English

*Organized by:*Faculty of Physics, Astronomy and Informatics

# Advanced mathematical methods 0800-PA-AMATH

Lectures and classes

I. Complex analysis

1) Cauchy-Riemann conditions,

2) Cauchy theorem,

3) Infinite complex series

4) residua and its applications,

5) contour integration,

II. Tensor calculus

1) tensor algebra,

2) exterior algebra

3) manifolds and tangent vectors,

4) tensor fields

5) tensor analysis: covariant derivative, parallel transport,

Lie derivative, Killing vectors, differential forms

6) Riemannian manifolds

III. Elements of group theory

1) introduction to discrete and continuous group,

2) basics of representation theory, Schur lemma, orthogonality conditions

3) basics of Lie group and Lie algebra theory.

## Total student workload

## Learning outcomes - knowledge

## Learning outcomes - skills

## Learning outcomes - social competencies

## Teaching methods

## Expository teaching methods

## Exploratory teaching methods

## Type of course

## Prerequisites

## Course coordinators

## Assessment criteria

Assessment methods:

- written examination - W1-W3, U1-U3

- written test - W1-W3, U1-U3

fail- less than 50%

satisfactory- 50-60%

satisfactory plus- 60-70%

good - 70-80%

good plus- 80-90%

very good- more than 90%

## Additional information

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: