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.
Main fields of studies for MISMaP
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.
1. S. Zakrzewski, Algebra i geometria, Warsaw University publication.
2. P. Urbański, Algebra liniowa i geometria, Warsaw University publication.
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: