M8502 Selected topics of school mathematics

Faculty of Science
Autumn 2015
Extent and Intensity
2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 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
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M4502 Mathematical Analysis 4
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
At the end of the course student should be more deeply acquitanted with questions and topics from the areas of mathematics that are included in the high-school mathematics programme. 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
Teaching methods
Lectures supported by individual reading and moderated group discussions.
Assessment methods
Colloquium in a form of a written test composed of two parts. The first one contains 10 "theoretical" questions, while the second one contains 3 examples algorithmic character. 50% of points in each of two parts is needed to pass.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
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 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.
  • Enrolment Statistics (Autumn 2015, recent)
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