IMAp12 The Mathematics 2

Faculty of Education
Spring 2023
Extent and Intensity
0/1/0. 2 credit(s). Type of Completion: z (credit).
Taught in person.
Teacher(s)
doc. RNDr. Jaroslav Beránek, CSc. (seminar tutor)
Mgr. Jitka Panáčová, Ph.D. (seminar tutor)
Guaranteed by
Mgr. Jitka Panáčová, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
IMAp12/01: each even Wednesday 13:00–14:50 učebna 37, J. Panáčová
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
Mathematical logic. Set theory - applications (Sets and their visualizations, operations with sets). Propositional forms and formulae, definitions of basic notions, deducible rules of propositional and predicate calculus, proofs of theorems. Binary relations, their visualizations and properties ordering, equivalence, mapping. Study and utilizing of the concepts in school mathematics.
Learning outcomes
At the end of the course students should be able to understand and explain the fundaments of Mathematical Branches, Fundaments of logic and set theory. > Propositions, propositional formulae. > Sets and their visualizations. > Operations with sets. > Propositional forms. > Definitions of basic notions. > Deducible rules of propositional and predicate calculus. > Proofs of theorems. > Binary relations, their visualizations and properties. > Equivalence relations, set partitions. > Ordered sets. > Composition of relations. > Study and utilizing of the concepts in school mathematics. Mappings between sets, equivalent sets, finite and infinite sets.
Syllabus
  • Solving of selected problems of propositional calculus, set theory especially verbal problems. Rules of derivation of propositional and predicate calculus - examples of correct and erroneous reasoning. Proofs of mathematical theorems, examples of basic principles of proofs of specific simple mathematical theorems. Study of specific binary relations with respect to school mathematics.
Literature
    required literature
  • PANÁČOVÁ, Jitka and Jaroslav BERÁNEK. Základy elementární matematiky s didaktikou pro učitelství 1. stupně ZŠ (Fundamentals of elementary mathematics with didactics for primary school teaching). 1st ed. Brno: Masarykova univerzita. 167 pp. ISBN 978-80-210-9863-3. 2020. info
  • DRÁBEK, Jaroslav and Václav VIKTORA. Základy elementární aritmetiky : pro učitelství 1. stupně ZŠ. 1. vyd. Praha: Státní pedagogické nakladatelství. 223 s. 1985. URL info
    recommended literature
  • VIKTORA, Václav. Matematika I pro studium učitelství v 1. až 4. ročníku ZŠ. čtvrté. Brno: Univerzita Jana Evangelisty Purkyně v Brně. 222 s. 1983. info
    not specified
  • HORÁK, Pavel. Základy matematiky: Učební text. 2007. URL info
Teaching methods
Seminar. Solving of problems.
Assessment methods
Seminar Credit: Active participation in the seminar and homework
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/spring2023/IMAp12