IB000 Induction and Recursion

Faculty of Informatics
Autumn 2004
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Antonín Kučera, Ph.D. (lecturer)
doc. RNDr. Tomáš Brázdil, Ph.D. (seminar tutor)
RNDr. Mgr. Silvie Luisa Brázdilová, Ph.D. (seminar tutor)
Mgr. Jan Holeček (seminar tutor)
Mgr. Tomáš Kratochvíla (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
Tue 10:00–11:50 D2, Tue 10:00–11:50 D3, Tue 10:00–11:50 D1
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
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2005, Spring 2006, Autumn 2006, Autumn 2007, Spring 2008, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2004, recent)
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