Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Narayanan N
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 58
NPTEL Course Size : 4.2 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
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