Course: Mathematical Proofs and their Structure

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Course title Mathematical Proofs and their Structure
Course code KMA/MDS
Organizational form of instruction Seminar
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 2
Language of instruction Czech, English
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Tomeček Jan, doc. RNDr. Ph.D.
Course content
- about mathematics, theorems and proofs - propositional logic - predicate logic - axiom systems and formal proof - types of proofs: direct proof, proof by contradiction, proof by mathematical induction - various proof techniques and patterns (proof of existence, uniqueness, ...)

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Homework for Teaching - 20 hours per semester
  • Attendace - 26 hours per semester
  • Semestral Work - 20 hours per semester
Learning outcomes
Understand basic principles of a mathematical proof. Obtain ability to read proofs efectively and make them on one's own.
Comprehension Understand the notion of matematical proof.
Prerequisites
Grammar school mathematics

Assessment methods and criteria
Seminar Work

Seminar work
Recommended literature
  • Bělohlávek R., Vychodil V. (2004). Diskrétní matematika pro informatiky II. UP Olomouc.
  • Bělohlávek R., Vychodil V. (2004). Diskrétní matematika pro informatiky I. UP Olomouc.
  • Garnier, R., & Taylor, J. (1996). 100% mathematical proof. Chichester: John Wiley and Sons.
  • Thiele, R., Schwabik, Š., & Kufner, A. (1986). Matematické důkazy. Praha: Státní nakladatelství technické literatury.
  • Velleman. (2006). How to prove it. Canbridge University Press.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Mathematics and Applications (1) Mathematics courses 1 Winter