FI:MA006 Set Theory - Course Information

MA006 Set Theory

Extent and Intensity

2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).

Teacher(s)

prof. RNDr. Jiří Rosický, DrSc. (lecturer)

Guaranteed by

prof. RNDr. Jiří Rosický, DrSc.
Departments – Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc.

Prerequisites

! M006 Set Theory
Prerequisites M005 Foundations of mathematics

Course Enrolment Limitations

The course is only offered to the students of the study fields the course is directly associated with.

fields of study / plans the course is directly associated with

• Applied Informatics (programme FI, N-AP)
• Informatics (programme FI, M-IN)
• Informatics (programme FI, N-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, M-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, M-SS)
• Upper Secondary School Teacher Training in Informatics (programme FI, N-SS)

Course objectives (in Czech)

Navazuje na úvodní kurzy základů matematiky. Je probírána teorie svazů a aritmetika kardinálních a ordinálních čísel.

Syllabus

• Complete lattices: distributive lattice, directed set, complete posets, compact elements, algebraic lattice
• Cardinal numbers: cardinal number, ordering of cardinal numbers, Cantor--Bernstein theorem, operations with cardinal numbers
• Well-ordered sets: well-ordered set, transfinite induction, operations with well-ordered sets
• Ordinal numbers: ordinal number, ordering of ordinal numbers, ordinal arithmetic, countable ordinal numbers
• Axiom of choice: axiom of choice, well-ordering principle, maximality principle

Literature

• Rosický, Jiří, Teorie množin, učební text, 1996, Masarykova univrazita v Brně
• KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL. Logika, algebry a grafy. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1989, 434 s. info
• BALCAR, Bohuslav and Petr ŠTĚPÁNEK. Teorie množin. 1. vyd. Praha: Academia, 1986, 412 s. info
• FUCHS, Eduard. Teorie množin. Vyd. 1. Brno: Rektorát UJEP, 1974, 176 s. info

Language of instruction

Czech

Further Comments

The course is taught annually.
The course is taught: every week.

• Enrolment Statistics (Spring 2003, recent)
  
• Permalink: https://is.muni.cz/course/fi/spring2003/MA006