Algebraic Structures (KMD/E-AG2)

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  • 6 credits
  • Lecturer: Ing. Tomáš Barot, Ph.D.
  • Lessons (Lectures + Exercises + Seminars): 1 + 0 + 1 [hours/week]
  • Semester: Winter / Summer
  • Language of instruction: English
  • Language of consultation: English
  • Level of qualification (Bc., Mgr.): Bc., Mgr.
  • Method of completion: Examination

Synopsis / description / annotation:

The course deals with concepts and their properties introduced within the course Linear algebra in more details. It extends the concept of grupoids and groups together with their properties. It also defines a concept of a group homomorphism, congruences, factor groups, finite groups, Lagrange's theorem, cyclic groups, rings and theirs properties, a ring homomorphism, congruences, factor rings, Galois fields, ordered rings, a splitting field, the ring of integers, the field of rational numbers.

Requirements on student:

An active participation in the full-time form of the education, an active approach to solving tasks, the successful passing of the written test of the final exam.

Content:

  1. Grupoids, semigroups, monoids.
  2. Basic properties of groups.
  3. Group decomposition.
  4. Cyclic groups.
  5. Overview of finite groups.
  6. Rings – basic properties, homomorphisms, decompositions.
  7. Integral domains, fields.
  8. A splitting field.

Time requirements:

  • Being present in classes - 26 h.
  • Self-tutoring - 30 h.
  • Consultation of work with the teacher/tutor (incl. electronic) - 5 h.
  • Preparation for an exam - 30 h.

Prerequisites:

The secondary school knowledge of mathematics is assumed.

Course results:

After finishing the course, in which an understanding of topics of the algebraic structures is offered, students will have knowledge about the advanced aspects of these parts of mathematics. Student will have abilities to solve problems using a software support for mathematics.

Assessment methods:

  • Written examination
  • Continuous analysis of student’s achievements

Teaching methods:

  • Computer-based tutoring
  • Dialogic (discussion, dialogue, brainstorming)
  • Individual tutoring

Literature:

  • Lang, S. Undergraduate Algebra. Springer, 2005. ISBN 0-387-22025-9.

Updated: 03. 10. 2022