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Logic and Set Theory - NUMP016

Title:	Logika a teorie množin
Guaranteed by:	Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2019
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Jana Glivická doc. Mgr. Petr Gregor, Ph.D.
Classification:	Informatics > Theoretical Computer Science
Is incompatible with:	NMUM818, NMUM505, NMUE023, NLTM017
Is interchangeable with:	NMUM818, NMUM505, NMUE023

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KTI (19.05.2004)

Basic course for prospective teachers of math at secondary level. Rules for deduction in propositional and first order calculi. Main concepts of set theory and some basic structures (e.g. natural numbers) are studied.

Aim of the course - Czech

Last update: T_KTI (23.05.2008)

Naučit základy logiky a teorie množin

Course completion requirements -

Last update: doc. Mgr. Petr Gregor, Ph.D. (11.06.2019)

The course is completed by an exam.

Literature - Czech

Last update: T_KTI (19.05.2004)

Štěpánek,P.: Matematická logika (skriptum), SPN 1982

Balcar,B., Štěpánek,P.: Teorie množin, Academia, Praha 1986

Čuda K.: Základy logického kalkulu

Čuda K.: Základy teorie množin

Requirements to the exam - Czech

Last update: RNDr. Martin Rmoutil, Ph.D. (13.10.2017)

Předmět bude zakončen písemnou zkouškou, při které se od studentů budou požadovat definice, věty a důkazy z přednášky; přesný seznam požadavků bude studentům průběžně upřesňován na přednáškách a bude k dispozici na webu vyučujícího.

V případě nerozhodného výsledku u písemné zkoušky může v některých případech dojít též na ústní část zkoušky. Typicky bude student žádán, aby upřesnil nebo dovysvětlil nejasné body z písemky; může však dojít i na další úlohy.

Syllabus -

Last update: T_KTI (19.05.2004)

Propositional calculus: propositional variables, logical connectives,

truth tables, propositional formulae, truth value of a formula with a

given evaluation, inference techniques (modus ponens, deduction, proof

by contradiction, etc.) Duality (also de Morgan's rules), Disjunctive

and Conjunctive normal forms.

First-Order Logic: language of 1st order logic, terms, formulae. 1st

order mathematical structures, examples. Formulae true for a

structure. Bound and free variable occurrences, the extent of a

quantifier, open and closed formulae, term substitution. Inference

techniques for formulae with quantifiers. Prenex normal form.

Axiomatic approach to mathematics, classical and modern approaches.

Brief note on consistence, independence, and completeness in various

axiomatic systems.

Set Theory and its importance for mathematics. Intuitive description

of the universum of sets as used in today's mathematics. Definable

classes. Russel's paradox.

Boolean calculus and other calculative properties of set operations

and relations.

Zermelo-Fraenkel axioms.

Equipollent sets, cardinality, Cantor-Bernstein Theorem, Cantor Theorem.

Model of natural numbers in set theory. Finite sets, countably infinte sets.

Integer, rational and real numbers.

Well ordered sets, cardinal and ordinal numbers (operations, ordering).

Axiom of Choice and its equivalents.