Discrete Mathematics Fundamentals

Mathematics

2023-11-16

Lessons List

Lesson 00 Introduction to Discrete Mathematics | Recommended Books for Discrete Mathematics

Lesson 01 What is Logic Proposition and Propositional Logic

Lesson 02 Logical Connectives in Compound Proposition | Truth Table in Discrete Mathematics

Lesson 03 Converse Inverse and Contrapositive of a Conditional Statement

Lesson 04 Logic Circuits | Logic Gates | Combinatorial Circuit in Discrete Mathematics

Lesson 05 Law of Logic Rules with Examples | Tautology Contradiction Contingency in Discrete Maths

Lesson 06 Law of Logic Rules Practice Examples

Lesson 07 Predicate and its Examples in Discrete Mathematics

Lesson 08 Quantifier and its Examples in Discrete | Universal Uniqueness Existential Quantifiers

Lesson 09 Negating Quantified Expressions | De Morgan s Laws for Quantifiers

Lesson 10 Nested Quantifiers Understanding Statements Involving Nested Quantifiers

Lesson 11 Rules of Inference for Propositional Logic | Rules of Inference in Discrete Mathematics

Lesson 12 Using Rules of Inference to Build Arguments | Rules of Inference Examples

Lesson 13 Rules of Inference for Quantified Statements

Lesson 14 The Resolution Principle Preliminaries | Resolution in Proposition Logic

Lesson 15 What is Fallacies in Discrete Mathematics

Lesson 16 Introduction to Proofs | Methods of Proof Direct Proof

Lesson 17 Part I Indirect Proof | Proof by Contrapositive with Examples

Lesson 18 Part II Indirect Proof | Proof by Contradiction with Examples

Lesson 19 Mistakes in Proof | Common Mistakes in Proofs in Discrete Mathematics

Lesson 20 Part I Proof Methods and Strategies in Discrete Mathematics

Lesson 21 Part II Proof Methods and Strategies in Discrete Mathematics

Lesson 22 Theorem VS Lemma VS Corollary in Discrete Mathematics

Lesson 23 Applications of Propositional Logic in Real Life

Lesson 24 What is Set | Different Types of Numbers | Set Forms | Intervals Notation

Lesson 25 Types of Set in Discrete Mathematics with Examples

Lesson 26 Set Notation and Quantifiers | Truth Set and Quantifier

Lesson 27 All Set Operations and Venn Diagram in Discrete Mathematics

Lesson 28 Set Identities | Generalized Union and Intersection | Method of Identity Proof

Lesson 29 Function in Discrete Mathematics | Domain Codomain Range Image and Preimage of Function

Lesson 30 Function and its Types with Examples in Discrete Mathematics

Lesson 31 Real Valued Integer Valued Function | Function Increasing Decreasing Function

Lesson 32 Compositions of Functions with Examples in Discrete Mathematics

Lesson 33 Inverse Functions with Examples in Discrete Mathematics

Lesson 34 The Graph of Function in Discrete Mathematics | Floor and Ceil Function

Lesson 35 Partial Function VS Total Function in Discrete Mathematics

Lesson 36 Sequence vs Summation | Arithmetic Progression | Geometric Progression

Lesson 37 Series and Summations | Arithmetic Series | Geometric Series in Discrete Mathematics

Lesson 38 Cardinality of Sets | Hilbert s Grand Hotel Paradox | The Countinuum Hypothesis

Lesson 39 Computer Representation of Sets in Discrete Mathematics

Lesson 40 Matrices | Matrix Arithmetic | Transposes and Powers of Matrices | Zero–One Matrices

Lesson 41 Part I 3 1 Algorithm | Properties of Algorithms | Searching and Sorting Algorithms

Lesson 42 Part II 3 1 Algorithm | Naive String Matcher | Greedy Algorithm | The Halting Problem

Lesson 43 The Growth of Function Asymptotic Notation of Algorithm in Discrete Mathematics

Lesson 44 The Growth of Combinations of Functions with Examples in Discrete Mathematics

Lesson 45 Complexity of Algorithms | Complexity of Matrix Multiplication | P VERSUS NP

Lesson 46 Divisibility and Modular Arithmetic Division | Modular Arithmetic | Arithmetic Modulo m

Lesson 47 Integer Representations and Algorithms | Representations of Binary Octal and Hexadecimal

Lesson 48 Primes and Greatest Common Divisors | GCD vs LCM | gcds as Linear Combinations

Lesson 49 Part I Solving Congruences | Linear Congruences with Examples | ax ≡ b mod m

Lesson 50 Part II Solving Congruences | Chinese Remainder Theorem | Fermat s Little Theorem

Lesson 51 Part III Pseudoprime vs Absolute Pseudoprime in Discrete Mathematics with Examples

Lesson 52 Applications of Congruences in Discrete Mathematics with Examples

Lesson 53 Classical Cryptography | Julius Caesar Method of encryption and Decryption with Examples

Lesson 54 Symmetric VS Asymmetric Cryptography | RSA Rivest Shamir Adleman Public key Cryptosystem

Lesson 55 Part I Mathematical Induction in Discrete Mathematics with Examples

Lesson 56 Part II Mathematical Induction Proof examples in Discrete Mathematics

Lesson 57 Strong Induction and Well Ordering | Examples of Proofs Using Strong Induction

Lesson 58 Part I Recursive Definitions and Structural Induction with Examples

Lesson 59 Part II Recursive Definitions and Structural Induction with Examples

Lesson 60 Recursive Algorithms in Discrete Mathematics with Examples 1 to 10 Algorithms

Lesson 61 Program Correctness | Program Verification | Conditional Statements | Loop Invariants

Lesson 62 Counting | Sum Rule vs Product Rule in Discrete Mathematics with Examples

Lesson 63 The Basics of Counting | Combining the Sum and Product Rule | Subtraction Rule

Lesson 64 Pigeonhole Principle | Generalized Pigeonhole Principle in Discrete Mathematics

Lesson 65 Permutation and Combination in Discrete Mathematics with Examples | Combinatorial Proof

Lesson 66 Binomial Coefficients and Identities | Pascal s Identity and Triangle

Lesson 67 Generalized Permutations and Combinations | Combinations with Repetition

Lesson 68 Discrete Probability | Probability Rules| Probabilities of Complements Unions of Events

Lesson 69 Probability Theory | Bernoulli Trials and the Binomial Distribution | Random Variables

Lesson 70 Bayes Theorem | GENERALIZING BAYES THEOREM | Bayesian Spam Filters

Lesson 71 Part I Expected Values | Linearity of Expectations |Average Case Computational Complexity

Lesson 72 Part II Expected Values | The Geometric Distribution | Chebyshev s Inequality

Lesson 73 What is Recurrence Relation | Homogeneous VS Non Homogeneous Recurrence Relations

Lesson 74 Applications of Recurrence Relations in Discrete Mathematics with Examples

Lesson 75 Part I Solving Linear Recurrence Relations | First and Second Order Recurrence Relation

Lesson 76 Part II Linear Nonhomogeneous Recurrence Relations with Constant Coefficients

Lesson 77 Divide and Conquer Algorithms and Recurrence Relations in Discrete Maths with Examples

Lesson 79 Part I Generating Functions with examples in Discrete Mathematics

Lesson 80 Part II Generating Functions Theorems |Useful Facts About Power Series |Counting Problems

Lesson 81 The Principle of Inclusion–Exclusion | Inclusion Exclusion in Discrete Mathematics

Lesson 82 Part I Applications of Inclusion–Exclusion | Alternative Form of Inclusion–Exclusion

Lesson 83 Part II Applications of Inclusion–Exclusion|Num of ONTO Function |Sieve of Eratosthenes

Lesson 84 Part III Number of ONTO Function Continue | Derangements with Examples

Lesson 85 Relations and their Properties | Relation VS Function | Binary Relation

Lesson 86 Combining Relations | Composition of relation | Composing the Parent Relation with Itself

Lesson 87 Representing Relations using Digraphs and Matrices with Examples

Lesson 88 n ary Relations and Their Applications | Database and SQL in Discrete Mathematics

Lesson 89 Representing Relations | Representing Relations Using Matrices and Digraphs

Lesson 90 Closures of Relations | Paths in Directed Graphs | Types of Closures in Discrete Maths

Lesson 91 Finding Transitive Closures | Warshall Algorithm with Example

Lesson 92 Part I Equivalence Relations with Examples in Discrete Mathematics

Lesson 93 Part II Equivalence Classes and Partitions | Partition of a SET

Lesson 94 Part I Partial Orderings in Discrete Mathematics with Examples

Lesson 95 Part II Comparable VS Incomparable in POSET | Totally Ordered Set | Well Ordering |

Lesson 96 Part III Lexicographic Order | Hasse Diagrams | Maximal and Minimal Elements

Lesson 97 Part IV Lattices | Semi lattice vs Join Semi lattice | Topological Sorting

Lesson 98 Graph in Discrete Mathematics | Graph and its Types | Graph Terminology

Lesson 99 Graphs and Graph Models | Application of Graph in Real Life

Lesson 100 Part I Graph Terminology and Special Types of Graphs

Lesson 101 Part II Bipartite Graphs and Matchings | Hall s Marriage Theorem | New Graphs from Old

Lesson 102 Part I Representing Graphs and Graph Isomorphism | Adjacency Lists Incidence Matrices

Lesson 103 Part II Representing Graphs and Graph Isomorphism | Isomorphism Graphs with Applications

Lesson 104 Part I Connectivity | Path Walk and Trail in Graph Discrete Mathematics

Lesson 105 Part II Connectivity | Connectedness in Directed and Undirected Graphs

Lesson 106 Euler and Hamilton Paths | Applications of Euler Paths and Circuits

Lesson 107 Hamilton Paths and Circuits | Applications of Hamilton Circuits

Lesson 108 Understanding Mohammed s Scimitars | Fleury s Algorithm

Lesson 109 Shortest Path Problems | Dijkstra s Algorithm in Discrete Mathematics

Lesson 110 Travelling Salesman Problem | Traveling Salesperson Problem in Discrete Mathematics

Lesson 111 Planar Graphs in Discrete Mathematics | EULER S FORMULA | Kuratowski s Theorem

Lesson 112 Graph Coloring | THE FOUR COLOR THEOREM | Applications of Graph Colorings

Lesson 113 Introduction to Trees | TREE vs GRAPH | Tree terminology and its basic Types

Lesson 114 Introduction to Trees | Properties of Trees | FULL BALANCED m ARY TREES

Lesson 115 Applications of Trees | Prefix Codes | HUFFMAN CODING

Lesson 116 Tree Traversal | Inorder Preorder Postorder Traversal of Binary Trees

Lesson 117 Tree Traversal | Infix Prefix and Postfix Notation with Examples

Lesson 118 Spanning Trees | Kirchhoff s Matrix Tree Theorem | Minimum Spanning Tree

Lesson 119 Depth First Search VS Breadth First Search | Backtracking Applications

Lesson 120 Kruskal s and Prim s Minimum Spanning Tree MST Algorithms

Lesson 121 Boolean Algebra | Boolean Expressions | Boolean Functions in Discrete Mathematics

Lesson 122 Identities of Boolean Algebra | Duality and Abstract Definition of a Boolean Algebra

Lesson 123 SOP vs POS | Min term vs Max term | Functional Completeness

Lesson 124 Logic Gates AND OR NOT NAND NOR XOR XNOR | Combination of Gates | Half and Full Adders

Lesson 125 Minimization of Circuits | Karnaugh Map K Map for 2 3 and 4 Variables

Lesson 126 Minimization of Circuits | Don t Care X Conditions in K Maps

Lesson 127 Minimization of Circuits | The Quine–McCluskey Method

Lesson 128 Part I Languages and Grammars | Phrase Structure Grammars | Automata VS TOC

Lesson 129 Part II Languages and Grammars | Leftmost and Rightmost Derivation | Types of Grammars

Lesson 130 Finite State Machines with Output | Finite State Machine | Deterministic Finite Automata

Lesson 131 Part I Finite State Machines with No Output | Language Recognized by Finite Automata

Lesson 132 Part II Finite State Machines with No Output | Language Recognized by FSAs

Lesson 133 Language Recognition | Regular Expression | Regular Sets and Regular Grammars

Lesson 134 Part I Turing Machines | How Turing Machine Works with Example

Lesson 134 Part II Turing Machines | Using Turing Machines to Recognize Sets | Different Types TMs

Lesson 135 LAST LESSON END OF COURSE Final Words | Discrete Mathematics COURSE OUTCOMES

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Discrete Mathematics was informative and challenging. Gained useful insights into logical and problem-solving techniques. 2025-04-15

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Totally worth the time. 2025-03-12

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Nice Explanation 2025-03-07

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