IB000 Induction and Recursion

Faculty of Informatics
Autumn 2010
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. Petr Hliněný, Ph.D. (lecturer)
RNDr. Ondrej Moriš (assistant)
Mgr. Miroslav Klimoš (seminar tutor)
RNDr. Štěpán Kozák (seminar tutor)
Mgr. Dušan Švancara (seminar tutor)
Mgr. Monika Kolouchová (seminar tutor)
Mgr. et Mgr. Martin Derka, M.Sc. (seminar tutor)
Mgr. Vojtěch Havel (seminar tutor)
Mgr. Petra Ovesná, Ph.D. (seminar tutor)
Mgr. Lukáš Másilko (seminar tutor)
doc. Mgr. Jan Obdržálek, PhD. (assistant)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science - Faculty of Informatics
Timetable
Mon 8:00–9:50 D2, Mon 8:00–9:50 D1, Mon 8:00–9:50 D3
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 computer science. At the end of this course the students should: know the basic notions of discrete mathematics and of propositional logic; understand the logical structure of mathematical statements and mathematical proofs; be able to precisely formulate their claims, algorithms, and relevant proofs; and apply acquired knowledge in other CS courses as well as in practice later on.
Syllabus
  • The course focuses on understanding basic mathematical tools for formal modeling and analysis of algorithms and other informatical notions:
  • Basic formalisms - proof and algorithm.
  • Proof techniques, induction.
  • Sets, relations, and functions.
  • Binary relations, equivalence.
  • Partial orderings and closures.
  • Properties of functions, composition.
  • Brief introduction to logic.
  • Proving algorithmic properties.
  • Simple declarative language.
  • Proof techniques for algorithms.
  • Infinite sets and the halting problem.
  • Computational complexity in brief.
Literature
    required literature
  • HLINĚNÝ, Petr. Úvod do informatiky. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
    not specified
  • WAND, Mitchell. Induction, recursion, and programming. New York: North Holland, 1980. 202 s. ISBN 0444003223. info
Teaching methods
This subject has regular weekly lectures, but no tutorial classes - the students are expected to practice at home using online questionaries, and discuss their homework with tutors online via IS MU. All the study materials and study agenda are presented through the online IS syllabus.
Assessment methods
Students' evaluation in this course consists of (the sum of) three parts which have rougly equal weights: through term evaluation (minimal score is required), "computer" written exam, and voluntary classical written exam.
The semester evaluation is computed as the sum of a certain number of best out of all term tests, plus possible bonus points for solving voluntary assignments. All the details can be found in IS syllabus and on the web page. Then the "computer" exam follows, and its sum with the semester evaluation determines student's success in the course. Optional written exam at the end gives students the opportunity to get higher grades.
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://is.muni.cz/el/1433/podzim2010/IB000/index.qwarp
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 2008, Autumn 2009, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.
  • Enrolment Statistics (Autumn 2010, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2010/IB000