SubjectsSubjects(version: 845)
Course, academic year 2018/2019
   Login via CAS
Logic and Set Theory (CŽV) - NMUM818
Title in English: Logika a teorie množin (CŽV)
Guaranteed by: Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty: Faculty of Mathematics and Physics
Actual: from 2015 to 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Is provided by: NUMP016
Guarantor: Mgr. Jana Glivická
Mgr. Petr Gregor, Ph.D.
Class: Učitelství matematiky
Classification: Informatics > Theoretical Computer Science
Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NUMP016
Interchangeability : NUMP016
Is incompatible with: NMUM505
Is interchangeable with: NMUM505
Annotation -
Last update: JUDr. Dana Macharová (10.10.2012)
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: JUDr. Dana Macharová (10.10.2012)

Naučit základy logiky a teorie množin

Course completion requirements -
Last update: Mgr. Petr Gregor, Ph.D. (11.06.2019)

The course is completed by an exam.

Literature - Czech
Last update: JUDr. Dana Macharová (10.10.2012)
  • 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: Mgr. Petr Gregor, Ph.D. (13.10.2017)

Předmět bude zakončen písemnou zkouškou, při které se od studentů budou 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: JUDr. Dana Macharová (10.10.2012)

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.

 
Charles University | Information system of Charles University | http://www.cuni.cz/UKEN-329.html