Course details

Algebra, Combinatorics and Graphs

QM3 Acad. year 2003/2004 Winter semester

Current academic year

Universal algebras. Vatieties. Categories of classes of algebras. Special binary systems more general than groups. Chapters from group theory, rings and skew-fields. Finite fields and polynomials over fields. Lattices and theory of varieties. Representative selected parts of Combinatorial analysis and Graph theory: Counting, recurrence relations, exclusion-inclusion, transversals of systems of sets, traveling in multigraphs, planarity and colourings, sequences of degrees of vertices and of couples of halfdegrees of vertices, isomorphism problem, selected matrix methods.

Details ...

Guarantor

Havel Václav, prof. RNDr., DrSc.

Language of instruction

Czech

Completion

Examination

Time span

  • 39 hrs lectures

Department

Department of Mathematics (UMAT)

Subject specific learning outcomes and competences

Enlarging of the knowledges in General Algebra,Combinatorial Analysis and Graph Theory and thus to be better equipped for the study of special disciplines of Computer Science.

Learning objectives

To recall and make deeper the lower level knowledges from algebra and discrete mathematics. To obtain ability of applying of algebraic reasoning in informatics.

Study literature

  • Učební texty přednášejícího (rozmnožené).
  • Bang-Jensen Gutin, Digraphs, London-Berlin-Heidelberg, 2000, inv.č. 5141.
  • Buchmann, Introduction to Cryptography, New York-Berlin-Heidelberg, 2000, inv.č. 5316.
  • J.Matoušek-J.Nešetřil:Kapitoly z diskrétní matematiky, nakl. Karolinum, Praha, 2003
  • J.A.Bondy-U.S.R.Murty:Graph Theory with Applications,North-Holland,New York-Amsterdam-Oxford, 1986
  • Michal Winczer,Teória grafov,Univerzita Komenského Bratislava, 2003; viz   http://user.edi.fmph.uniba.sk/winczer/diskretna.html
  • Radan Kučera:Základy univerzální algebry,MU Brno, 2003; viz http://www.math.muni.cz/~kucera/

Fundamental literature

  • Skornjakov, Elementy obščej algebry, Moskva, 1983.
  • McKenzie-McNulty-Taylor, Algebras, lattices, varieties I, Monterey, California, 1987.
  • Mitchell, Theory of categories, New York, 1965.
  • Rosen, Discrete mathematics and its applications, New York, 1965.
  • Balakrishnan-Ranganathan, A textbook of graph theory, New York-Berlin-Heidelberg, 2000.
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