IMA02 Fundamentals of Algebra and Arithmetics 1

Faculty of Education
Spring 2025
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
doc. RNDr. Jaroslav Beránek, CSc. (seminar tutor)
Mgr. Jitka Panáčová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jaroslav Beránek, CSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
IMA02/KombiSem01: Fri 21. 2. 16:00–18:50 učebna 36, Fri 14. 3. 14:00–16:50 učebna 30, Fri 28. 3. 14:00–15:50 učebna 36, J. Panáčová
IMA02/PrezSem01: Thu 7:00–8:50 učebna 6, J. Panáčová
IMA02/PrezSem02: Wed 7:00–8:50 učebna 42, J. Panáčová
IMA02/PrezSem03: Thu 16:00–17:50 učebna 41, J. Beránek
IMA02/PrezSem04: Mon 15:00–16:50 učebna 41, J. Beránek
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. Mappings between sets, equivalent sets, finite and infinite sets.
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, 2020, 167 pp. ISBN 978-80-210-9863-3. info
  • DRÁBEK, Jaroslav and Václav VIKTORA. Základy elementární aritmetiky : pro učitelství 1. stupně ZŠ. 1. vyd. Praha: Státní pedagogické nakladatelství, 1985, 223 s. 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, 1983, 222 s. info
    not specified
  • HORÁK, Pavel. Základy matematiky: Učební text. 2007. URL info
Teaching methods
Seminar. Solving of problems.
Assessment methods
Credit: 2 written tests during the semester.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Information on completion of the course: Obsah tohoto předmětu bude součástí požadavků u zkoušky z předmětu Aritmetika 1 ve 3. semestru studia.
The course is taught annually.
Information on the extent and intensity of the course: 8 konzultací (KS).
Listed among pre-requisites of other courses
Teacher's information
The Department of Mathematics recommends students the optional course IMA12. Recommended literature: PANÁČOVÁ, Jitka a Jaroslav BERÁNEK. Základy elementární matematiky s didaktikou pro učitelství 1. stupně ZŠ. 1. vyd. Brno: Masarykova univerzita, 2020. 167 s. ISBN 978-80-210-9863-3. DRÁBEK, Jaroslav a Václav VIKTORA. Základy elementární aritmetiky : pro učitelství 1. stupně ZŠ. 1. vyd. Praha: Státní pedagogické nakladatelství, 1985. 223 s. The content of this course will be part of the requirements for the exam in the course IMA03, which is included in the 3rd semester of study.
The course is also listed under the following terms Spring 2024.
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