FI:IB000 Induction and Recursion - Course Information
IB000 Induction and Recursion
Faculty of InformaticsAutumn 2005
- Extent and Intensity
- 2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
- Teacher(s)
- prof. RNDr. Antonín Kučera, Ph.D. (lecturer)
RNDr. Vojtěch Forejt, Ph.D., LL.B. (Hons) (seminar tutor)
prof. RNDr. Petr Hliněný, Ph.D. (seminar tutor)
Mgr. Jan Holeček (seminar tutor)
Mgr. Jitka Kudrnáčová (seminar tutor)
Mgr. Zdeněk Řehák (seminar tutor)
RNDr. Jana Tůmová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Antonín Kučera, Ph.D. - Timetable
- Wed 14:00–15:50 D1, Wed 14:00–15:50 D3, Wed 14:00–15:50 D2
- Prerequisites (in Czech)
- ! I000 Induction and Recursion
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- there are 12 fields of study the course is directly associated with, display
- Course objectives
- This course is focused on understanding basic mathematical concepts necessary for describing program semantics and formalization of the relationship between intuitive program constructs and their mathematical meaning. This is essential for building up a set of basic concepts needed for other courses which fit theoretical essentials of the dicipline.
- Syllabus
- The course focuses on understanding basic mathematics as a tool for formal modeling and analysis of computer programs. Basic set theory. Relations between sets and their properties. Propositional logic and first-order logic. Inductively defined sets and functions, structural induction. Syntax nad semantics of a simple declarative programming language. Proving program corectness.
- Basic set theory. Cantor theorem. The halting problem and its undecidability.
- Relations between sets and their basic properties. Functions as relations. Operations over relations, relational databases.
- Equivalences and quotients. Orders and preorders. Transitive (and other) closures.
- Propositional logic, its syntax and semantics. NP-complete problems. First-order logic.
- Inductively defined sets and functions. Structural induction.
- A simple declarative language and its operational semantics. Proving program corectness by induction.
- Literature
- WAND, Mitchell. Induction, recursion, and programming. New York: North Holland, 1980, 202 s. ISBN 0444003223. info
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Listed among pre-requisites of other courses
- Enrolment Statistics (Autumn 2005, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2005/IB000