MUC34 Algebra applications seminar

Faculty of Science
Autumn 2025
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable of Seminar Groups
MUC34/01: Mon 10:00–11:50 M5,01013, R. Kučera
Course Enrolment Limitations
The course is offered to students of any study field.
Abstract
The aim of this seminar is to support future teachers of mathematics by giving them some concrete algebraic examples to explain the usefulness of mathematics to their pupils/students.
Learning outcomes
After this subject a student will be able to explain some practical algebraic applications to his pupils/students.
Key topics
  • After explaining the necessary algebraic background we shall discuss some of the following topics:
  • Encryption: RSA.
  • Coding: self-correcting codes.
  • Compass and ruler construction: impossibility of squaring of a circle, trisection of an angle, doubling of a cube.
  • Linear models.
  • Iteration processes: Perron and Frobenius theory for primitive matrices.
  • Graph theory: there are only 5 convex regular polyhedra (the Platon ones).
  • Combinatorics: Burnside's lemma.
  • Infomation concerning the book series "Škola mladých matematiků".
Study resources and literature
Approaches, practices, and methods used in teaching
Lectures followed by discussions.
Method of verifying learning outcomes and course completion requirements
Final written test of the revised algebraic background.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2019, autumn 2021, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2025/MUC34