MA0001 Fundamentals of Mathematics

Faculty of Education
Autumn 2024
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
RNDr. Břetislav Fajmon, Ph.D. (lecturer)
RNDr. Karel Lepka, Dr. (seminar tutor)
Mgr. Lukáš Másilko (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Beránek, CSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable
Mon 14:00–15:50 učebna 30
  • Timetable of Seminar Groups:
MA0001/01: Tue 16:00–17:50 učebna 6, B. Fajmon
MA0001/02: Wed 12:00–13:50 učebna 32, B. Fajmon
MA0001/03: Thu 12:00–13:50 učebna 35, B. Fajmon
MA0001/04: Tue 12:00–13:50 učebna 10, B. Fajmon
Prerequisites
The subject is aimed at acquiring knowledge of fundamental concepts necessary for the study of the follow-up mathematical disciplines. Students will review and deepen their grasp of some parts of discrete mathematics taught at secondary level.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of the course the SS will know the following concepts: propositions, logical connectors, predicate formulas, tautologies, contradictions, truth value, predicate form, quantifiers, direct and indirect proof, proof by contradiction, proof of (non-)existence and uniqueness, mathematical induction, set relations and operations, number sets, congruence of integers, lower/upper bound, maximum, minimum, supremum as the least upper bound, infimum as the greatest lower bound, binary relation, mapping, injection, surjection, bijection, ordered sets, Hasse diagram, the lowest element, minimal element, equivalence relation, partition, real function of one real variable, graph of a function, elementary functions.
Learning outcomes
After the completion of the course the students will be acquainted with: a) fundamental mathematical notions, especially logical statement, set, cartesian product, relation, operation, mapping; b) fundamental methods of mathematical reasoning, especially: proof of an implication, proof of an equivalence of statements, proof of set equality, proof by mathematical induction, proof using logical contradiction; c) basic notation of mathematical symbols in mathematical literature
Syllabus
  • 1. Fundamentals of propositional calculus. Propositions, logical connectors, propositional formula, tautology, contradiction, truth value.
  • 2. Fundamentals of predicate logic. Predicate form, quatifiers, direct and indirect proof.
  • 3. Proof by contradiction, proof of (non-)existence and uniqueness. Mathematical induction.
  • 4. Fundamental set theory. Set relations and operations, their properties.
  • 5. Sets of numbers. Elementary approach to numbers. Fundamental properties of numbers. Conguence of integers. Lower/upper bound, maximum, minimum, supremum as the least upper bound, infimum as the greatest lower bound.
  • 6. Binary relations and their properties.
  • 7. Mappings and their properties. Injection, surjection, bijection.
  • 8. Ordered sets, Hasse diagram. The lowest element, minimal element, etc.
  • 9. Equivalence relations and their properties.
  • 10. Partitions and equivalence relations.
  • 11. Fundamental information on real functions of one real variable. Graphs of functions.
  • 12. Elementary functions, their graphs and basic properties.
Literature
    recommended literature
  • BUŠEK, Ivan and Emil CALDA. Matematika pro gymnázia : základní poznatky. 3., upr. vyd. Praha: Prometheus, 2001, 178 s. ISBN 9788071961468. info
  • ODVÁRKO, Oldřich. Matematika pro gymnázia : goniometrie. 2. vyd. Praha: Prometheus, 1995, 127 s. ISBN 8071960004. info
  • ODVÁRKO, Oldřich. Matematika pro gymnázia : funkce. 2. vyd., v Prometheu 1. Praha: Prometheus, 1994, 160 s. ISBN 8085849097. info
Teaching methods
Teaching methods chosen will reflect the contents of the subject and the level of students as newcomers to the university.
Assessment methods
Tests in the course of the study, oral final exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The duties of a students studying in English will be given by the teacher.
The course is also listed under the following terms Autumn 2017, Autumn 2018, Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2024/MA0001