MA0011 Algebra 3

Faculty of Education
Autumn 2019
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
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 1 student(s).
Current registration and enrolment status: enrolled: 0/1, only registered: 0/1, only registered with preference (fields directly associated with the programme): 0/1
fields of study / plans the course is directly associated with
Course objectives
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. 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
  • Syllabus 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. Lattices: distributive and modular lattices, Boole algebra. 7. Models of Boole algebra, logical circuits. 8. Natural numbers. Peano axioms. Systems with another base than 10. 9. Integers and their constructions as a subtraction group of additive semigroup of natural numbers. 10, Rational numbers and their construction as a division field of the integral domain of integers. 11. Real numbers and their construction as a normal envelope of an ordered set of rational numbers. Irrational numbers, algebraic and transcendental numbers. 12. Complex numbers and their introduction and applications in school mathematics and in technological practice.
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
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Autumn 2019, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2019/MA0011