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Course, academic year 2023/2024
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Combinatorics - NMTM208
Title: Kombinatorika
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Antonín Slavík, Ph.D.
Incompatibility : NMUM208
Interchangeability : NMUM208
Is incompatible with: NMUM208
Is interchangeable with: NMUM208
Annotation -
An introductory course in classical combinatorics.
Last update: Staněk Jakub, RNDr., Ph.D. (14.06.2019)
Literature -
  • 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.

Last update: Slavík Antonín, doc. RNDr., Ph.D. (12.06.2019)
Requirements to the exam - Czech

Písemná zkouška sestává z úloh souvisejících s obsahem přednášky.

Last update: Slavík Antonín, doc. RNDr., Ph.D. (22.02.2024)
Syllabus -
  • Basics of 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.
  • Catalan numbers.
  • Generating functions and their use in solving recurrences.
  • Combinatorial applications of polynomials and infinite series.
  • Combinatorial identities.

Last update: Slavík Antonín, doc. RNDr., Ph.D. (22.02.2024)
 
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