NOC:Combinatorics

Lecture 1 - Pigeonhole Principle

Lecture 2 - Dirichlet theorem and Erdos-Szekeres Theorem

Lecture 3 - Ramey theorem as generalisation of PHP

Lecture 4 - An infinite flock of Pigeons

Lecture 5 - Basic Counting - the sum and product rules

Lecture 6 - Examples of basic counting

Lecture 7 - Examples: Product and Division rules

Lecture 8 - Binomial theorem and bijective counting

Lecture 9 - Counting lattice paths

Lecture 10 - Multinomial theorem

Lecture 11 - Applying Multinomial theorem

Lecture 12 - Integer compositions

Lecture 13 - Set partitions and Stirling numbers

Lecture 14 - Stirling and Hemachandra recursions

Lecture 15 - Integer partitions

Lecture 16 - Young's diagram and Integer partitions

Lecture 17 - Principle of Inclusion and Exclusion

Lecture 18 - Applications of PIE

Lecture 19 - The twelvefold way

Lecture 20 - Inclusion exclusion: Linear algebra view

Lecture 21 - Partial Orders

Lecture 22 - Mobius Inversion Formula

Lecture 23 - Product theorem and applications of Mobius Inversion

Lecture 24 - Formal power series, ordinary generating functions

Lecture 25 - Application of Ordinary generating functions

Lecture 26 - Product of Generating functions

Lecture 27 - Composition of generating functions

Lecture 28 - Exponential Generating Function

Lecture 29 - Composition of EGF

Lecture 30 - Euler pentagonal number theorem

Lecture 31 - Graphs - introduction

Lecture 32 - Paths Walks, Cycles

Lecture 33 - Digraphs and functional digraphs

Lecture 34 - Componenets, Connectivity, Bipartite graphs

Lecture 35 - Acyclic graphs

Lecture 36 - Graph colouring

Lecture 37 - Mycielski graphs

Lecture 38 - Product of graphs

Lecture 39 - Menger's theorem

Lecture 40 - System of Distinct representatives

Lecture 41 - Planar graphs

Lecture 42 - Euler identity

Lecture 43 - Map colouring problem - History

Lecture 44 - The Discharging Method - Part 1

Lecture 45 - The Discharging Method - Part 2

Lecture 46 - Introduction to Group actions

Lecture 47 - Colouring and symmetries - examples

Lecture 48 - Bursides lemma

Lecture 49 - Proof of Bursides lemma

Lecture 50 - Polya's theorem

Lecture 51 - Species of structures- definitions and examples

Lecture 52 - Associated seris and Product of species

Lecture 53 - Species: Substitution and Derivative

Lecture 54 - Species: Pointing and countilg labelled trees

Lecture 55 - Review and Further directions

Lecture 56 - More on further topics

Lecture 57 - Linear Algebra method: Ultra short introduction

Lecture 58 - Probabiistic Method: Ultra short introduction