M8502 Selected topics of school mathematics

Faculty of Science
Autumn 2008
Extent and Intensity
2/0/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: k (colloquium).
Teacher(s)
doc. RNDr. Jaromír Šimša, CSc. (lecturer)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M5,01013
Prerequisites (in Czech)
M4502 Mathematical Analysis 3
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
A series of lectures on deeper questions and topics from the areas of mathematics that are included in the high-school mathematics programe. After passing the course, students should be able to understand presented topics, to teach them in secondary schools especially when preparing talented, mathematically gifted pupils.
Syllabus
  • Types of mathematical proofs and their examples in different areas of mathematics.
  • Principle of mathematical induction.
  • Pigeonhole principle.
  • Classic algebraic inequalities and their applications.
  • Introduction to the theory of functional equations.
Literature
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory. 1st ed. New York: Springer-Verlag, 2000, 355 pp. Canadian Mathematical Society Books in Math., 1. ISBN 0-387-98942-0. info
  • HERMAN, Jiří, Radan KUČERA and Jaromír ŠIMŠA. Metody řešení matematických úloh. Vyd. 1. Brno: Rektorát Masarykovy univerzity, 1991, 425 s. ISBN 8021002794. info
  • THIELE, Rüdiger. Matematické důkazy. Translated by Alois Kufner - Štefan Schwabik. 2. nezm. vyd. Praha: SNTL - Nakladatelství technické literatury, 1986, 160 s. info
  • VÝBORNÝ, Rudolf. Matematická indukce. 1. vyd. Praha: Mladá fronta, 1963, 61 s. URL info
Assessment methods
Lecture 2 hours a week. Colloquium in a written form.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.
  • Enrolment Statistics (Autumn 2008, recent)
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