Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Indian Institute of Technology Madras


Indian Institute of Technology Madras and NPTEL via Swayam


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.


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

Related Courses


Start your review of Combinatorics

Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free