Course: Logic and Axiomatic Systems

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Course title Logic and Axiomatic Systems
Course code KMA/M302
Organizational form of instruction Lecture
Level of course Master
Year of study 2
Semester Winter
Number of ECTS credits 3
Language of instruction Czech, English
Status of course Compulsory
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Kuřil Martin, RNDr. Ph.D.
Course content
unspecified

Learning activities and teaching methods
unspecified
Learning outcomes
The first part of the course is devoted to the construction of the classical sentential calculus. At the same time the fundamental notions of logic are demonstrated (axiom, deduction rule, formal proof, formal theorem) and some fundamental assertions are proved (deduction theorem, completeness theorem). It follows an information about further variants of sentential calculus (three-valued sentential logic, modal sentential logic, intuitionistic sentential logic). The second part of the course is devoted to the work with some concrete formal systems (formal arithmetic, group theory, Euclidean and non-Euclidean geometries, ...).

Prerequisites
Teaching in English is meant only for erasmus and foreign students. In the case of a small number of students is teaching in a form of individual consultations.

Assessment methods and criteria
unspecified
Recommended literature
  • Balcar, B., Štěpánek, P. Teorie množin. Praha, 1986.
  • Blažek, J., Calda, E., Koman, M., Kussová, B. Algebra a teoretická aritmetika I. Praha, 1983.
  • Kleene, S. C. Mathematical Logic. New York, London, Sydney, 1967.
  • Kopka J. Logika (učební text pro gymnázia).
  • Kopka, J. Matematická logika I.. Praha, 1973.
  • Kopka, J. Přirozená čísla, Přir. F. UJEP, Ústí nad Labem, 2006.
  • Švejdar, V. Logika: neúplnost, složitost a nutnost. Praha, 2002.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Teaching of mathematics for Secondary schools (A14) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter