*Conducted in term:*2022Z

*Erasmus code:*11.1

*ECTS credits:*5

*Language:*Polish

*Organized by:*Faculty of Physics

*Related to study programmes:*

# Algebra with geometry I 1100-1AF10

The purpose of the course is to explain notions that appear in mathematics and physics throughout the entire period of studies. These abstract notions will be illustrated with various examples to make them maximally comprehensible and to demonstrate their usefulness in physics.

1. Complex numbers, number fields.

2. Third degree algebraic equations.

3. Basic properties of polybomials, the greatest common divisor.

4. The notion of a group, permutation groups, permutation sign and the decomposition of permutation into cycles.

5. Vector spaces, linear independence, basis, subspaces, sums and intersections of subspaces.

6. Linear maps, kernel, image, the matrix of a linear map.

7. Determinant.

## Main fields of studies for MISMaP

## Mode

## Prerequisites (description)

## Course coordinators

## Learning outcomes

After having completed the course students should:

a) be familiar with the notion of complex numbers and calculations involving complex numbers;

b) understand the notions of a vector space, linear independance, a basis;

c) understand the notion of a linear map and a matrix;

d) be able to solve systems of linear equations;

e) be able to compute determinants and find the inverese matrix.

## Assessment criteria

Midterms and written exam -- computational part;

oral exam -- theoretical part.

## Practical placement

none

## Bibliography

1. S. Zakrzewski, Algebra i geometria, Warsaw University publication.

2. P. Urbański, Algebra liniowa i geometria, Warsaw University publication.

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

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