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Course detail

Mathematical Structures

Course unit code: FSI-SSR-A
Academic year: 2016/2017
Type of course unit: compulsory
Level of course unit: Master's (2nd cycle)
Year of study: 2
Semester: summer
Number of ECTS credits:
Learning outcomes of the course unit:
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.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Prerequisites:
Students are expected to know the mathematics taught within the bachelor's study programme and the graph theory taught in the master's study programme.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
Recommended or required reading:
Jiří Adámek, Matematické struktury a kategorie, SNTL Praha, 1982
Jiří Adámek, Matematické struktury a kategorie, SNTL Praha, 1982
Jiří Adámek, Theory of Mathematical Structures, D. Reidel Publ. Company, Dordrecht, 1983.
Jiří Adámek, Theory of Mathematical Structures, D. Reidel Publ. Company, Dordrecht, 1983.
A.Adámek, H.Herrlich. G.E.Strecker: Abstract and Concrete Categories, John Willey & Sons, New York, 1990
Planned learning activities and teaching methods:
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.
Language of instruction:
English
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
The aim of the course is to show the students possibility of a unified perspective on seemingly different mathematical subjects.
Specification of controlled education, way of implementation and compensation for absences:
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: 26 hours, optionally
Teacher / Lecturer: prof. RNDr. Josef Šlapal, CSc.
Syllabus: 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

The study programmes with the given course