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]