Propositions, Conditional Propositions, Logical Connectivity, Propositional calculus, Universal and Existential Quantifiers, Normal forms, methods of proofs, Mathematical Induction
Proposition, Primitive Statement, Compund Propositions, Negations, Conjunction, Disjunction, Inplication, Biconditional, Truth Table, and other topics.
Sets, Combination of sets, Finite and Infinite sets, Un-countably infinite sets, Principle of inclusion and exclusion, multisets.
Sets, Set Notations, Subset / Proper Subset, Universal Set, Set Operations: Complement, Set Operations: Union, Set Operations: Intersection, Disjoint Sets, Properties: Set Operations, and other topics.
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
Inverse of an Element, Group, Abelian Group, Order of a Group, Order of An element, Cyclic Group, Product Group, Properties of a Group, Sub-Group, Cosets, Properties of a Coset, and other topics.
Properties of Binary Relations, Closure of relations, Warshall’s algorithm, Equivalence, Relations and partitions, Partial ordering relations and lattices, Chains and Anti chains.
Cartesian Product, Theorems, Relations, Domain, Range, Complement of a relation, Converse of a relation, Composite Relation, and other topics.
Functions, Composition of functions, Invertible functions, Pigeonhole Principle
Functions, Types of relations (1:1 etc.), Domain, codomain, Range, Identity Function, Identical Function, Surjective / Onto Function, Injective Function, Composite Function, and other topics.
Recurrence Relation, Linear Recurrence Relations With constant Coefficients, Homogeneous Solutions, Total solutions, solutions by the method of generating functions
Sequence, Series, Generating Functions, Standard Gen. Functions, Examples, Recurrence Relation, Order and Degree of a Rec. Relation, Homogeneos Rec. Relation, and other topics.
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
Graph, Terminal Vertex, Loop, Isolated Vertex, Parallel Edges, Simple Graph, Adjacent Vertices, Incident Edge, Weighted Graph, Degree of a Vertex, Pendant Vertex, Handshaking Lemma, Examples, and other topics.
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).
Tree, Terminal / Internal Node, Rooted Tree, Level of a node, Height / Depth, Father / Son, Brothers, Ancestor / Descendant, M-ary Tree, Complete m-ary tree, Example, and other topics.
Permutations and Combinations: rule of sum and product, Permutations, Combinations, Discrete Probability, Conditional Probability, Bayes’ Theorem, Information and Mutual Information
Rule of Sum, Rule of product, Combination, Arrangements, Permutation, Examples, and other topics.