Algebra with geometry I

physics

Finished high school.

Classroom

The purpose of the course is to explain basic notions of algebra such as complex numbers, polynomials, groups, vectors and matrices.

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.

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

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

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.

Midterms and written exam -- computational part;

oral exam -- theoretical part.

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