ABOUT THE COURSE:The aim of this course is to learn discrete mathematics. It is the study of mathematical structures which are discrete (elements take finite values as opposed to continuous structures). It is very difficult to find a branch in computer science & engineering which does not use discrete mathematics.We will be covering five main topics-- proofs, combinatorics, graphs, number theory, and algebra. The emphasis will be to learn different concepts and techniques used to prove theorems in computer science. The course will be full of puzzles and CS examplesINTENDED AUDIENCE: Computer Science & Engineering, Mathematics, Electronics, Physics, & similar disciplinesPREREQUISITES: A very good grasp of Class-XII level Mathematics.INDUSTRY SUPPORT: Discrete Optimization, Cryptography/ Cyber Security, Coding theory, Computer Algebra, Symbolic Computing Software, , Learning Software
Overview
Syllabus
Week 1: Formalizing Proofs and Proof Paradigms.Week 2:Counting. Generating Functions.Week 3:Basic Combinatorics.Week 4:Posets, Chains and Anti-chains.Week 5:Basic Graph theory.Week 6:Tours, Cycles, Cliques, Covers.Week 7:Coloring, Matching, Planarity.Week 8:Basic Number theory.Week 9:Density of Primes. Cryptography.Week 10:Finite Fields. Codes.Week 11:Basic Group theory.Week 12:Orbit Counting. Normal Subgroups.
Taught by
Prof. Nitin Saxena
