MUC03 Fundamentals of Mathematics

Faculty of Science
autumn 2021
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Jan Vondra, Ph.D. (lecturer)
RNDr. Iva Dřímalová, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jan Vondra, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
MUC03/01: Thu 10:00–11:50 M4,01024, I. Dřímalová
MUC03/02: Wed 14:00–15:50 M5,01013, I. Dřímalová
MUC03/03: Thu 14:00–15:50 M6,01011, I. Dřímalová
MUC03/04: Wed 12:00–13:50 M5,01013, I. Dřímalová
Prerequisites
! M1120 Discrete Mathematics && !NOW( M1120 Discrete Mathematics )
Knowledge of high school mathematics.
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 aim of this cource is to lay the foundations of mathematics. The course deals with basic concepts and their good understanding and use.
Learning outcomes
Upon successful completion of this course the student should be able to: understand and explain the selected basic mathematical concepts; understand and explain the selected basic mathematical techniques; understand and explain the connection between the basic mathematical concepts.
Syllabus
  • 1. Basic logical notions
  • 2. Basic set-theoretical notions
  • 3. Basic number sets
  • 4. Basic properties of integers
  • 5. Mappings
  • 6. Relations
  • 7. Ordered sets
  • 8. Equivalences and partitions
  • 9. Basic algebraic structures with one operation
  • 10. Basic algebraic structures with two operations
  • 11.Homomorfhisms of algebraic structures.
Literature
    required literature
  • Horák, Pavel. Základy matematiky. Učební text. https://www.math.muni.cz/~vondra/vyuka/p2020/zm/zm_skripta_2013.pdf
  • Horák, Pavel. Základy matematiky. Učební text ke cvičení. https://www.math.muni.cz/~vondra/vyuka/p2020/zm/zm_sbirka_2013.pdf
    not specified
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • CHILDS, Lindsay. A concrete introduction to higher algebra. 2nd ed. New York: Springer, 1995, xv, 522. ISBN 0387989994. info
Teaching methods
Lectures: theoretical explanations with practical applications. Exercises: practical solving problems focused on basic concepts and theorems, individual problem solving by students.
Assessment methods
Teaching: lectures, consultative exercises. Exam: written and oral.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (autumn 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2021/MUC03