Combinatorics

Lecture 1: Introduction [slides][Lecture]

Lecture 2: Two Basic Counting Principles [slides][Lecture]

Lecture 3: Simple Arrangements and Selections  [slides][Lecture]

Lecture 4: Arrangements and Selections with Repetition  [slides][Lecture]

Lecture 5: Distributions  [slides][Lecture]

Lecture 6: Binomial Identities [slides][Lecture]

Problem Sheet 1 [slides]

Lecture 7: Introduction to Generating Functions [slides][Lecture]

Lecture 8: Calculating Coefficients of Generating Functions [slides][Lecture]

Lecture 9: Partitions [slides][Lecture]

Lecture 10: Exponential Generating Functions [slides][Lecture]

Lecture 11: A Summation Method [slides][Lecture]

Problem Sheet 2 [slides]

Lecture 12: Introduction to Recurrence Relations [slides][Lecture]

Lecture 13: Recurrence Relations with two Variables [slides][Lecture]

Lecture 14: Solving Homogeneous Recurrence Relations [slides][Lecture]

Lecture 15: Solving non-Homogeneous Recurrence Relations [slides][Lecture]

Lecture 16: Solving Recurrence Relations  Using Generating Functions [slides][Lecture]

Lecture 17: Inclusion Exclusion Using Venn Diagrams [slides][Lecture]

Lecture 18: Inclusion Exclusion Formula [slides][Lecture]

Lecture 19: Dearrangements [slides][Lecture]

Problem Sheet 3 [slides]

Lecture 20: Rook Polynomial Part-I [slides][Lecture]

Lecture 21: Rook Polynomial Part-II [slides][Lecture]

Lecture 22: Rook Polynomial Part-III [slides][Lecture]

Lecture 23: Equivalence and Symmetry Groups [slides][Lecture]

Lecture 24: Burnside's Lemma [slides][Lecture]

Lecture 25: The Cycle Index [slides][Lecture]

Lecture 26: The Polya's Formula [slides][Lecture]

Lecture 27: Number of non-isomorphic graphs [slides][Lecture]

Lecture 28: Pigeonhole Principle [slides][Lecture]

Lecture 29: Ramsey Numbers [slides][Lecture]

Lecture 30: Catalan Numbers [slides][Lecture]

Lecture 31: Stirling Numbers of Second Kind [slides]

Lecture 32: Stirling Numbers of First Kind [slides]