IB000 Induction and Recursion

Faculty of Informatics
Autumn 2008
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Petr Hliněný, Ph.D. (lecturer)
RNDr. Václav Brožek, Ph.D. (seminar tutor)
RNDr. Ondrej Moriš (seminar tutor)
Mgr. Zdeněk Řehák (seminar tutor)
Mgr. et Mgr. Martin Derka, M.Sc. (seminar tutor)
RNDr. Robert Ganian, Ph.D. (assistant)
Mgr. Lukáš Másilko (seminar tutor)
Ing. Mgr. Dávid Dereník (seminar tutor)
Ing. Mgr. Lucie Vernerová (seminar tutor)
Mgr. Petra Ovesná, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Timetable
Wed 12:00–13:50 D3, Wed 12:00–13:50 D2, Wed 12:00–13:50 D1
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 20 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 and formalisms needed for other theoretical courses in informatics. Most importantly, a successful student shall be able to formulate mathematically precise statements, understand them, and carry out their proofs.
Syllabus
  • The course focuses on understanding basic mathematics as a tool for formal modeling and analysis of algorithms and computer programs:
  • Basic formalism - proof and algorithm.
  • Proof techniques, induction.
  • Sets, relations, and functions.
  • Binary relations, equivalence.
  • Orderings and closures.
  • Properties of functions, composition.
  • Brief introduction to logic.
  • Proving algorithmic properties.
  • Simple declarative language.
  • Proof techniques for algorithms.
  • Infinite sets and halting problem.
  • Computational complexity in brief.
Literature
  • Petr Hliněný, Úvod do informatiky, http://www.fi.muni.cz/~hlineny/Vyuka/UINF/UInf-text07.pdf.
  • WAND, Mitchell. Induction, recursion, and programming. New York: North Holland, 1980, 202 s. ISBN 0444003223. info
Assessment methods
This subject has regular weekly lectures, but no tutorial classes - the students are expected to do homework and discuss it with tutors online via IS MU.
To pass the course, the students have to understand the presented theory and be able to apply it. The grade is composed of several term tests (out of which a minimal score is required), and subsequent computer and written exams.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.fi.muni.cz/~hlineny/Vyuka/UINF.html
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Spring 2006, Autumn 2006, Autumn 2007, Spring 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 2008, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2008/IB000