Video Lessons - 5

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 4

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 7

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 5

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 2

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 3

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 7

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 6

Revision Notes - 1

Revision Notes - 1

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.

Video Lessons - 2

Revision Notes - 1

Revision Notes - 1

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.

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