Course detail
Mathematical Structures
FSI-SSR-A Acad. year: 2021/2022 Summer semester
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
English
Number of ECTS credits
4
Supervisor
Department
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.
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.
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 assessing the knowledge of the theory presented..
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.
The study programmes with the given course
Programme N-MAI-A: Mathematical Engineering, Master's, compulsory
Programme M2A-P: Applied Sciences in Engineering, Master's
branch M-MAI: Mathematical Engineering, compulsory
Programme M2A-A: Applied Sciences in Engineering, Master's
branch M-MAI: Mathematical Engineering, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
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