Course detail
Mathematical Structures
FSI-SSR-AAcad. year: 2024/2025
The course will familiarise students with basic concepts and results of the theory of mathematical structures. A number of examples of concrete structures which students know from previously passed mathematical subjects will be used to demonstrate the exposition.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
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.
Aims
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.
Study aids
Prerequisites and corequisites
Basic literature
Jiří Adámek, Theory of Mathematical Structures, D. Reidel Publ. Company, Dordrecht, 1983. (EN)
Steve Awodey: Category Theory, Oxford University Press Inc. 2006. (EN)
Recommended reading
Jiří Adámek, Matematické struktury a kategorie, SNTL Praha, 1982 (CS)
Classification of course in study plans
- Programme N-AIM-A Master's 2 year of study, summer semester, compulsory
- Programme N-MAI-A Master's 2 year of study, summer semester, compulsory
- Programme N-MAI-P Master's 2 year of study, summer semester, compulsory
- Programme C-AKR-P Lifelong learning
specialization CLS , 1 year of study, summer semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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