Course

Enumerative combinatorics

Course under construction · 14 of 32 concepts published; more are added as they are reviewed.

Advanced counting techniques are learned: generating functions, partitions, Stirling, Bell and Catalan numbers, symmetry via Burnside and Pólya, posets and extremal methods. They are used to solve enumeration problems and bound combinatorial objects in discrete mathematics, number theory, algebra and probability; it is advisable to have taken Discrete mathematics, Elementary number theory, Modern algebra I, Probability and statistics.

Recommended before this course: Discrete mathematics · Elementary number theory · Modern algebra I · Probability and statistics (5 concepts come from those courses and are tagged)

19concepts
6topics
190exercises
≈ 10 hof study approx.

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Course path

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Sources

  • Kenneth H. Rosen, Discrete Mathematics and Its Applications, 8th edition, McGraw-Hill, 2019.
  • Susanna S. Epp, Discrete Mathematics with Applications, 5th edition, Cengage, 2019.
  • Ralph P. Grimaldi, Discrete and Combinatorial Mathematics: An Applied Introduction, 5th edition, Pearson, 2003.
  • Richard P. Stanley, Enumerative Combinatorics, Volume 1, 2nd edition, Cambridge University Press, 2012.
  • Herbert S. Wilf, generatingfunctionology, 3rd edition, A K Peters, 2006.
  • David S. Dummit, Richard M. Foote, Abstract Algebra, 3rd edition, Wiley, 2004.
  • Joseph A. Gallian, Contemporary Abstract Algebra, 9th edition, Cengage, 2017.
  • I. N. Herstein, Abstract Algebra, 3rd edition, Wiley, 1996.
  • John B. Fraleigh, A First Course in Abstract Algebra, 7th edition, Pearson, 2002.