Course: Algebra

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Course title Algebra
Course code UMB/567
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the winter semester.
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Zalabová Lenka, doc. Mgr. Ph.D.
Course content
We study algebraic structures with one and two binary operations. We give basic definitions and properties and we study important cases of these structures. Summary: Algebraic structures with one operation - grupoids, semigropus, groups. Subgroups, homomorphisms, isomorphisms. Group of permutations. Symmetry groups. Cyclic and dihedral groups. Congruence relation and groups of congruence classes. Divisibility of integers. Euklid agorithm. Bezout equality and consequences. Primes. Linear congruence equations. Euller theorem. Applications in crypthography. Algebraic structures with two operations - rings, domains, fields. Rings/fields of numbers. Rings/fields of congruence classes. Polynomials, roots of polynomials, irreducibility. Complex polynomias, fundamental theorem of algebra. Rational and real polynomials. Eisenstein criterion.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
  • Class attendance - 56 hours per semester
  • Preparation for classes - 56 hours per semester
  • Preparation for exam - 56 hours per semester
Learning outcomes
The goal of the course is the introduction into elementary algebraic structures.
The student will acquire the basic knowledge of abstract algebra and number theory.
Prerequisites
The knowledge of mathematics on the level of secondary school and the theory of matrices and their properties.

Assessment methods and criteria
Combined exam, Seminar work

Active participation in the course, project focusedon mathematic olympiad and applied algebra (including programming), passing both written and oral part of the exam (50%).
Recommended literature
  • J. Blažek, E. Calda, M. Koman, B. Kussová, Algebra a teoretická aritmetika 1, SPN Praha, 1983..
  • J. Blažek, M. Koman, B. Vojtášková, Algebra a teoretická aritmetika 2, SPN Praha, 1985..
  • J. Procházka a kolektiv, Polynomy, Jihočeská univerzita, České Budějovice, 1985..
  • J. Rosický: Algebra, Masarykova univerzita, Brno, 2007..
  • P. Tlustý: Obecná algebra pro učitele, Jihočeská univerzita, České Budějovice, 2006..
  • Skripta ke kurzu UMB567 Algebra.
  • Lenka Zalabová. Skripta ke kurzu UMB567 Algebra.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Applied Mathematics (2010) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 2 Recommended year of study:2, Recommended semester: Winter