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Indian Institute of Technology Madras

Combinatorics

Indian Institute of Technology Madras and NPTEL via Swayam

Overview

We start with the finite and infinite avatars ofthe Pigeonhole Principle, Basic counting tools and the twelvefold way followed bycompositionsand partitions ofintegers and Stirlingnumbers.We then look atInclusion exclusion and Mobius inversion followed by generatingfunctions.We thenlook atPolya'stheorem,graphs andconclude witha short introduction to species of structures.INTENDED AUDIENCE :UG studentsPRE-REQUISITES : Basic Mathematical Maturity expected from a Mathematics student at the level of 10+2. Familiarity with group theory will be addedadvantage (not necessary).INDUSTRY SUPPORT : TCS, Infosys, Microsoft Research, Any companies developing discrete mathematics related areas or algorithms.

Syllabus

Week 1 : Pigeonhole Principle

Week 2 :BasicandBijectivecounting.

Week 3 : Compositions and Partitions.

Week 4 : Advanced Counting.

Week 5 : Inclusion Exclusion, Mobius Inversion.

Week 6 : Generating Functions

Week 7 : Graph theory,introduction, trees, connectivity.

Week 8 : Menger, Hall, Konig - equivalence and System of Distinct Representatives.

Week 9 : Planar graphs.

Week 10: Groups and Polya theory.

Week 11: Species of structures.

Week 12: An overview, scope and further directions.

Taught by

Prof. Narayanan N

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