English

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prof. RNDr. Josef Šlapal, CSc.

Institute of Mathematics

Students are expected to know the following subjects taught within the bachelor's study programme: Mathermatical Analysis I-III, Functional Analysis, both Linear and General Algebra, and Methods of Discrete Mathematics. Concerning the the master's study programme, knowledge of Graph Theory is required.

The course is completed with an exam. Students' knowledge will be assessed based on a writen test and oral exam.

Since the attendance at lectures is not compulsory, it will not be checked, and compensation of possible absence will not be required.

The aim of the course is to show the students possibility of a unified perspective on seemingly different mathematical subjects and constructions.

Students will acquire the ability of viewing different mathematical structures and constructions from a unique, categorical point of view. This will help them to realize new relationships and links between different branches of mathematics. The students will also be able to apply their knowledge of the theory of mathematical structures, e.g. in computer science.

Programme N-MAI-A: Mathematical Engineering, Master's, compulsory

Programme N-MAI-P: Mathematical Engineering, Master's, compulsory

Programme N-AIM-A: Applied and Interdisciplinary Mathematics, Master's, compulsory

26 hours, optionally

prof. RNDr. Josef Šlapal, CSc.

1. Sets and classes
2. Mathematical structures
3. Isomorphisms
4. Fibres
5. Subobjects
6. Quotient objects
7. Free objects
8. Initial structures
9. Final structures
10.Cartesian product
11.Cartesian completeness
12.Functors
13.Reflection and coreflection