MA0011 Algebra 3

Faculty of Education
Spring 2022
Extent and Intensity
0/2/0. 3 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Helena Durnová, Ph.D. (seminar tutor)
RNDr. Břetislav Fajmon, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Beránek, CSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
MA0011/01: Tue 12:00–13:50 učebna 11, B. Fajmon
MA0011/02: Tue 14:00–15:50 učebna 24, B. Fajmon
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is aimed at deepening algebraic knowledge of concepts introduced in subjects Discrete mathematics, algebra 1, algebra 2. The emphasis is put on lattice theory and Boolean algebras.
Learning outcomes
1. Polynomials, operations with polynomials, ring of polynomials, value and root of a polynomial. 2. Greatest common divisor and least common multiple. 3. Factoring polynomials, determining the root of a polynomial, relationship between the roots and coefficients of a polynomial. 4. Algebraic equations and their solution. Elementary theorem of algebra. 5. Polynomials in more variables, symmetric polynomials and applications. 6. Models of Boole algebra, logical circuits. 7. Complex numbers and their introduction and applications in school mathematics and in technological practice.
Syllabus
  • 1. Binary relations, equivalence relations, ordering, mapping. Modular and distributive lattices. 2. Algebraic structures with one or two operations. Boolean algebra. 3. Set relations, set operations. Boolean algebras on power sets. 4. Vector spaces, linear mapping between vector spaces. Matrices, determinants and systems of linear equations related to vector spaces. 5. Fundamental theorem of algebra, axioms and constructions of number systems. 6. Combinatorial identities, discrete probabilities.
Literature
    recommended literature
  • KOPKA, Jan. Svazy a booleovy algebry. Ústí nad Labem, 1991, 243 s. ISBN 80-7044-025-2. info
Teaching methods
Seminar with active participation of the students.
Assessment methods
Oral exam on basic concepts introduced in class.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2019, Autumn 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2022, recent)
  • Permalink: https://is.muni.cz/course/ped/spring2022/MA0011