Discrete Mathematical Structures

Propositions, Conditional Propositions, Logical Connectivity, Propositional calculus, Universal and Existential Quantifiers, Normal forms, methods of proofs, Mathematical Induction

Sets, Combination of sets, Finite and Infinite sets, Un-countably infinite sets, Principle of inclusion and exclusion, multisets.

Algebraic Systems, Groups, Semi Groups, Monoid, Subgroups, Permutation Groups, Codes and Group codes, Isomorphism and Automorphisms, Homomorphism and Normal Subgroups, Ring, Integral Domain, Field, Ring Homomorphism, Polynomial Rings and Cyclic Code

Properties of Binary Relations, Closure of relations, Warshall’s algorithm, Equivalence, Relations and partitions, Partial ordering relations and lattices, Chains and Anti chains.

Functions, Composition of functions, Invertible functions, Pigeonhole Principle

Recurrence Relation, Linear Recurrence Relations With constant Coefficients, Homogeneous Solutions, Total solutions, solutions by the method of generating functions

Basic terminology, multi graphs and weighted graphs, paths and circuits, shortest path in weighted graph, Hamiltonian and Euler paths and circuits, factors of a graph, planar graph and Travelling salesman problem, Graph Coloring Problem

Trees, rooted trees, path length in rooted trees, prefix codes, binary search trees, spanning trees and cut set, minimal spanning trees, Kruskal’s and Prim’s algorithms for minimal spanning tree, The Max flow –Min cut theorem (transport network).

Permutations and Combinations: rule of sum and product, Permutations, Combinations,  Discrete Probability, Conditional Probability, Bayes’ Theorem, Information and Mutual Information