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
Course coordinators
Mode
Prerequisites (description)
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.