Syllabus
Actual topics will be established mainly on the basis of questions of students and on the monitoring of their needs. The set of all possible topics is determined by contents of bachelor exam:
1. Relations, mappings and their basic properties.
2. Construction and properties of number domains.
3. Groups and their homomorphisms.
4. Ring, integral domain, division ring and their basic properties.
5. Vector space, base, dimension, linear mapping. Vector space equipped with dot product, cross product.
6. Matrices and their properties, application for solution of systems of linear equations.
7. Determinants and their properties, Cramer's rule.
8. Basic concepts of divisibility in integral domains.
9. Differential calculus of functions of one real variable - limit, continuity, derivative, Taylor's theorem, behaviour of a function.
10. Elementary functions and their definition.
11. Primitive function. Integration by parts and substitution.
12. Riemann integral and its applications, improper integrals.
13. Sequences of real numbers, limits.
14. Infinite series and their sums. Basic theorems concerning absolute and nonabsolute convergence, criteria of convergence.
15. Differential equations, basic methods of their solution.
16. Affine and Euclidean space.
17. Groups of geometric projections.
Annotation
This seminar is intended for third-year students of teaching mathematics. The subject is based on needs of students who went through appreciable part of their bachelor's degree study.
Its content is determined by that what students consider problematic. On the basis of their questions we will go over the first and second year passages from mathematical analysis, linear algebra, geometry and algebra.
In this way student manages to a considerable extent its own education and student is encouraged to creative approach to mathematics.