SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Combinatorics - NMUM208
Title in English: Kombinatorika
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Antonín Slavík, Ph.D.
Class: M Bc. MZV
M Bc. MZV > Povinné
M Bc. MZV > 2. ročník
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NMUM814, NUMP008
Interchangeability : NMUM814, NUMP008
Annotation -
Last update: T_KDM (24.04.2017)
An introductory course in classical combinatorics.
Course completion requirements - Czech
Last update: doc. RNDr. Antonín Slavík, Ph.D. (07.06.2019)

Písemná zkouška

Literature -
Last update: T_KDM (29.04.2013)
  • R. B. J. T. Allenby, A. Slomson: How To Count. An Introduction to Combinatorics, CRC Press, 2011.
  • J. M. Harris, J. L. Hirst, M. J. Mossinghoff: Combinatorics and Graph Theory, Springer, 2008.
  • J. Matoušek, J. Nešetřil: Invitation to Discrete Mathematics, Oxford University Press, 2008.
  • N. Ya. Vilenkin: Combinatorics, Academic Press, 1971.
  • R. L. Graham, D. E. Knuth, O. Patashnik: Concrete Mathematics, Addison-Wesley, 1994.

Requirements to the exam - Czech
Last update: doc. RNDr. Antonín Slavík, Ph.D. (07.06.2019)

Zkouška sestává ze čtyř příkladů z témat, která korespondují s obsahem přednášky.

Syllabus -
Last update: T_KDM (24.04.2017)
  • High school combinatorics.
  • Inclusion-exclusion principle, derangements.
  • Rook polynomials and permutations with forbidden positions.
  • The twelvefold way (distributing objects into boxes).
  • Recurrent problems and their solution, Fibonacci numbers and their properties.
  • Generating functions and their use in solving recurrences.
  • Catalan numbers.
  • Combinatorial applications of polynomials and infinite series.
  • Combinatorial identities.

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