Mathematical Structures (FSI-SSR-A)

Academic year 2018/2019
Supervisor: prof. RNDr. Josef Šlapal, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: English
Aims of the course unit:
The aim of the course is to show the students possibility of a unified perspective on seemingly different mathematical subjects.
Learning outcomes and competences:
Students will acquire the ability of viewing different mathematical structures 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.
Prerequisites:
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.
Course contents:
The course will familiarise students with basic concepts and results of the theory of mathematical structures. A number of examples of concrete structures will be used to demonstrate the exposition.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
The graded-course unit credit is awarded on condition of having passed a written test assessing the knowledge of the theory presented..
Controlled participation in lessons:
Since the attendance at lectures is not compulsory, it will not be checked, and compensation of possible absence will not be required.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
Course curriculum:
    Lecture 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
Literature - fundamental:
2. Jiří Adámek, Theory of Mathematical Structures, D. Reidel Publ. Company, Dordrecht, 1983.
4. A.Adámek, H.Herrlich. G.E.Strecker: Abstract and Concrete Categories, John Willey & Sons, New York, 1990
Literature - recommended:
1. Jiří Adámek, Matematické struktury a kategorie, SNTL Praha, 1982
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
M2A-P full-time study M-MAI Mathematical Engineering -- GCr 4 Compulsory 2 2 S
M2A-A full-time study M-MAI Mathematical Engineering -- GCr 4 Compulsory 2 2 S