MA0011 Algebra 3

Faculty of Education
Spring 2021
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)
RNDr. Karel Lepka, Dr. (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 10:00–11:50 D44 učebna, K. Lepka
MA0011/02: Mon 16:00–17:50 D44 učebna, K. Lepka
Prerequisites
Any of the courses FOundations of Mathematics, Algebra 1.
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
Abstract
The course provides basic knowledge about polynomials and about solving algebraic equations, it further aims at actively mastering theoretical constructions of number domains and their basic properties. An inseparable part of this course is the theory of lattices and Boole 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. Fundamental theorem of algebra.
Key topics
1. Complex numbers, operations. 2. Taking the power and the root of a complex number. 3. Polynomials, rational roots of polynomials with integer coefficients. 4. Fundamental theorem of algebra. 5. Peano axioms, axioms of sets Z, Q. 6. Construction of R,C.
Study resources and literature
    recommended literature
  • BERÁNEK, Jaroslav. Vybrané kapitoly z algebry (Chosen Chapters from Algebra). první. Brno: Masarykova Univerzita, 2012, 71 pp. ISBN 978-80-210-5765-4. info
  • HORÁK, Pavel. Polynomy. 1. vyd. Brno: Rektorát UJEP, 1978, 127 s. info
Approaches, practices, and methods used in teaching
Seminar with active participation of the students.
Method of verifying learning outcomes and course completion requirements
Oral exam.
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 2022, Spring 2023, Spring 2024, Spring 2025, Spring 2026, Spring 2027.
  • Enrolment Statistics (Spring 2021, recent)
  • Permalink: https://is.muni.cz/course/ped/spring2021/MA0011