MA0011 Algebra 3

Faculty of Education
Spring 2020
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 8:00–9:50 učebna 34, B. Fajmon
Prerequisites
Successful completion of 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
Course objectives
The course provides basic knowledge about polynomials, complex numbers and about solving algebraic equations, it further aims at actively mastering theoretical constructions of number domains and their basic properties.
Learning outcomes
1. Factoring polynomials, determining the root of a polynomial, relationship between the roots and coefficients of a polynomial. 2. Algebraic equations and their solution. Elementary theorem of algebra. 3. Numerical methods of finding roots of polynomials. 4. Complex numbers and their introduction and applications in school mathematics and in technological practice.
Syllabus
  • Syllabus 1. Algebraic equations and their solution. Elementary theorem of algebra. 2. Numerical methods of solution of algebraic equations. 3. Natural numbers. Peano axioms. Integers and their constructions as a subtraction group of additive semigroup of natural numbers. 4. Rational numbers and their construction as a division field of the integral domain of integers. Real numbers and their construction as a normal envelope of an ordered set of rational numbers. Irrational numbers, algebraic and transcendental numbers. 5. Complex numbers and their introduction and applications in school mathematics and in technological practice. 6. Solution of binomial equations, the Moivre theorem.
Literature
  • BERAN, Ladislav. Grupy a svazy. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1974, 358 s. info
Teaching methods
Seminar with active participation of the students.
Assessment methods
Oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2019, Autumn 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2020, recent)
  • Permalink: https://is.muni.cz/course/ped/spring2020/MA0011