# Discrete Mathematical Structures

Video Lessons & Revision Notes

### 1. Logic and Propositions

Video Lessons - 5
Revision Notes - 1

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

All Lessons and Notes
##### Propositions, Connectives and Introduction to Truth Tables
41 mins Video Lesson

Proposition, Primitive Statement, Compund Propositions, Negations, Conjunction, Disjunction, Inplication, Biconditional, Truth Table, and other topics.

### 2. Set Theory

Video Lessons - 4
Revision Notes - 1

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

All Lessons and Notes
##### Sets - Basic Concepts, Set Operations (Complement, Union and Intersection)
47 mins Video Lesson

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.

### 3. Algebraic Structures - Groups and Rings

Video Lessons - 7
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

All Lessons and Notes
##### Inverse, Groups, Abelian Group, Cyclic Group and Cosets
53 mins Video Lesson

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.

### 4. Relations, Poset and Lattice

Video Lessons - 5
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.

All Lessons and Notes
##### Relations - Basic Concepts, Complement, Converse, Composite Relation
47 mins Video Lesson

Cartesian Product, Theorems, Relations, Domain, Range, Complement of a relation, Converse of a relation, Composite Relation, and other topics.

### 5. Functions

Video Lessons - 2
Revision Notes - 1

Functions, Composition of functions, Invertible functions, Pigeonhole Principle

All Lessons and Notes
##### Functions - Basic Concepts, Injective, Surjective Functions
46 mins Video Lesson

Functions, Types of relations (1:1 etc.), Domain, codomain, Range, Identity Function, Identical Function, Surjective / Onto Function, Injective Function, Composite Function, and other topics.

### 6. Recurrence Relations and Generating Functions

Video Lessons - 3
Revision Notes - 1

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

All Lessons and Notes
##### Sequence, Series, Generating Functions, Recurrence Relations
41 mins Video Lesson

Sequence, Series, Generating Functions, Standard Gen. Functions, Examples, Recurrence Relation, Order and Degree of a Rec. Relation, Homogeneos Rec. Relation, and other topics.

### 7. Graphs

Video Lessons - 7
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

All Lessons and Notes
##### Graph - Basic Concepts and Handshaking Lemma
40 mins Video Lesson

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.

### 8. Trees

Video Lessons - 6
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).

All Lessons and Notes
##### Tree - Basic Concepts, Rooted Tree, M-ary Tree
50 mins Video Lesson

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.

### 9. Permutations, Combinations and Discrete Probability

Video Lessons - 2
Revision Notes - 1

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

All Lessons and Notes
##### Permutations and Combinations
47 mins Video Lesson

Rule of Sum, Rule of product, Combination, Arrangements, Permutation, Examples, and other topics.

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