MA2RC_UVOD Introduction to Mathematics

Faculty of Education
Autumn 2022
Extent and Intensity
0/0/1.3. 4 credit(s). Type of Completion: k (colloquium).
Teacher(s)
Mgr. Helena Durnová, 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
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.
Teaching methods
Lectures and individual study.
Assessment methods
Written test and oral feedback
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: in blocks.
Information on the extent and intensity of the course: 16 hodin.
The course is also listed under the following terms Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2019, autumn 2020, Autumn 2023.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2022/MA2RC_UVOD