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Course Description

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).

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Course Syllabus
  • Mod-01 Lec-01 Pigeon hole principle - (Part 1)
  • Mod-01 Lec-02 Pigeon hole principle - (Part 2)
  • Mod-01 Lec-03 Pigeon hole principle - (Part 3)
  • Mod-01 Lec-04 Pigeon hole principle - (Part 4)
  • Mod-02 Lec-05 Elementary concepts and basic counting principles
  • Mod-02 Lec-06 Elementary concepts; Binomial theorem; Bijective proofs - Part (1)
  • Mod-02 Lec-07 Bijective proofs -- Part (2)
  • Mod-02 Lec-08 Bijective proofs - Part (3); Properties of binomial coefficients;
  • Mod-02 Lec-09 Combinatorial identities - Part (2); Permutations of multisets -- Part (1)
  • Mod-02 Lec-10 Permutations of multisets -- Part (2)
  • Mod-02 Lec-11 Multinomial Theorem, Combinations of Multisets -- Part (1)
  • Mod-02 Lec-12 Combinations of Multisets - Part (2)
  • Mod-02 Lec-13 Combinations of Multisets -- Part (3), Bounds for binomial coefficients
  • Mod-02 Lec-14 Sterling's Formula, Generalization of Binomial coefficients - Part (1)
  • Mod-02 Lec-15 Generalization of Binomial coefficients - Part (2)
  • Mod-02 Lec-16 Generalization of Binomial coefficients - Part (3); Double counting - Part (1)
  • Mod-03 Lec-17 Double counting - Part (2)
  • Mod-03 Lec-18 Hall's Theorem for regular bipartite graphs; Inclusion exclusion principle - Part (1)
  • Mod-03 Lec-19 Inclusion exclusion principle - Part (2)
  • Mod-03 Lec-20 Inclusion exclusion principle - Part (3)
  • Mod-03 Lec-21 Inclusion exclusion principle - Part (4)
  • Mod-03 Lec-22 Inclusion exclusion principle - Part (5)
  • Mod-04 Lec-23 Recurrence Relations - Part (1)
  • Mod-04 Lec-24 Recurrence Relations - Part (2)
  • Mod-04 Lec-25 Recurrence Relations - Part (3)
  • Mod-04 Lec-26 Recurrence Relations - Part (4)
  • Mod-04 Lec-27 Recurrence Relations - Part (5)
  • Mod-04 Lec-28 Generating functions - Part (1)
  • Mod-04 Lec-29 Generating functions - Part (2)
  • Mod-04 Lec-30 Solving recurrence relations using generating functions - Part (1)
  • Mod-04 Lec-31 Solving recurrence relations using generating functions - Part (2)
  • Mod-04 Lec-32 Exponential generating functions - Part (1)
  • Mod-04 Lec-33 Exponential generating functions - Part (2), Partition Number - Part (1)
  • Mod-05 Lec-34 Partition Number - Part (2)
  • Mod-05 Lec-35 Partition Number - Part (3)
  • Mod-05 Lec-36 Partition Number - Part (4); Catalan Numbers - Part (1)
  • Mod-05 Lec-37 Catalans Numbers - Part (2)
  • Mod-05 Lec-38 Catalan Numbers - Part (3), Sterling numbers of the 2nd kind
  • Mod-05 Lec-39 Difference Sequences
  • Mod-05 Lec-40 Sterling Numbers
  • Mod-05 Lec-41 Summary
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