Combinatorics
Offered By: Indian Institute of Technology Madras via Swayam
Course Description
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
Tags
Related Courses
Combinatorial Mathematics | 组合数学Tsinghua University via edX Problem Solving Techniques
YouTube Discrete Math II - Combinatorics
Kimberly Brehm via YouTube Discrete Mathematical Structures
NIOS via YouTube A Brief Tour of Proof Complexity - Lower Bounds and Open Problems - Toniann Pitassi
Institute for Advanced Study via YouTube