IB112 Math Foundations

Faculty of Informatics
Spring 2010
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Strejček, Ph.D. (lecturer)
doc. RNDr. Petr Novotný, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Timetable
Wed 10:00–11:50 B411
  • Timetable of Seminar Groups:
IB112/01: Tue 14:00–15:50 C525, P. Novotný
Prerequisites (in Czech)
! MB000 Calculus I && ! MB001 Calculus II && ! MB003 Linear Algebra and Geometry I && ! MB005 Foundations of mathematics && ! MB008 Algebra I && ! MB101 Mathematics I
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
Course objectives
At the end of the course students should be able to: understand the content of theoretical informatic courses;
Syllabus
  • Naive set theory: set, list of elements, basic operations on set, Cartesian product.
  • Number sets: natural numbers, integers, rational and real numbers, arithmetic operations, sequences and series.
  • Relations and function: relations over sets, functions as relations, composition of functions or relations.
  • Equivalence and orderings: properties of relations, equivalence, decomposition, partition, partial order, Hasse diagram.
  • Linear equations I: definition of matrices, systems of linear equations, basic algorithms solving systems of linear equations.
  • Linear equations II: other algorithms solving systems of linear equations, rank, determinant, inverse matrix.
  • Combinatorics: enumerative combinatorics, combinations, permutations, factorial.
  • Combinatorial probability: throws of the dice, shuffling cards, finite probabilistic space.
  • Descriptive statistics: statistical population, mean, median, dispersion, correlation.
  • Graphs I: graph, subgraph, isomorphism, vertex degree, connected components, flow networks.
  • Graphs II: distances in a graph, shortest paths problem, acyclic graphs, trees and their properties.
  • Propositional logic: definition of propositional formulae, validity and satisfability, normal forms.
Literature
  • KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL. Logika, algebry a grafy. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1989, 434 s. info
  • ŠTĚPÁNEK, Petr. Matematická logika. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 281 s. info
Teaching methods
lectures and class exercises
Assessment methods
written exam
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2018, Spring 2019.
  • Enrolment Statistics (Spring 2010, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2010/IB112