Discrete Structures | Discrete Mathematics Complete Course
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1 modules • 137 lessons • 43.5 hours of video
Discrete Structures | Discrete Mathematics Complete Course
137 lessons
• 43.5 hours
Discrete Structures | Discrete Mathematics Complete Course
137 lessons
• 43.5 hours
- Lesson 00: Introduction to Discrete Mathematics | Recommended Books for Discrete Mathematics 07:36
- Lesson 01: What is Logic Proposition and Propositional Logic 09:27
- Lesson 02: Logical Connectives in Compound Proposition | Truth Table in Discrete Mathematics 16:38
- Lesson 03: Converse Inverse and Contrapositive of a Conditional Statement 09:51
- Lesson 04: Logic Circuits | Logic Gates | Combinatorial Circuit in Discrete Mathematics 10:49
- Lesson 05: Law of Logic Rules with Examples | Tautology Contradiction Contingency in Discrete Maths 22:52
- Lesson 06: Law of Logic Rules Practice Examples 18:18
- Lesson 07: Predicate and its Examples in Discrete Mathematics 10:38
- Lesson 08: Quantifier and its Examples in Discrete | Universal, Uniqueness Existential Quantifiers 16:12
- Lesson 09: Negating Quantified Expressions | De Morgan’s Laws for Quantifiers 10:37
- Lesson 10: Nested Quantifiers Understanding Statements Involving Nested Quantifiers 13:01
- Lesson 11: Rules of Inference for Propositional Logic | Rules of Inference in Discrete Mathematics 19:06
- Lesson 12: Using Rules of Inference to Build Arguments | Rules of Inference Examples 13:53
- Lesson 13: Rules of Inference for Quantified Statements 18:06
- Lesson 14: The Resolution Principle [Preliminaries] | Resolution in Proposition Logic 08:26
- Lesson 15: What is Fallacies in Discrete Mathematics 07:04
- Lesson 16: Introduction to Proofs | Methods of Proof - Direct Proof 24:52
- Lesson 17 Part I: Indirect Proof | Proof by Contrapositive with Examples 10:44
- Lesson 18 Part II: Indirect Proof | Proof by Contradiction with Examples 19:24
- Lesson 19: Mistakes in Proof | Common Mistakes in Proofs in Discrete Mathematics 08:39
- Lesson 20 Part I: Proof Methods and Strategies in Discrete Mathematics 32:26
- Lesson 21 Part II: Proof Methods and Strategies in Discrete Mathematics 24:02
- Lesson 22: Theorem VS Lemma VS Corollary in Discrete Mathematics 06:05
- Lesson 23: Applications of Propositional Logic in Real Life 09:36
- Lesson 24: What is Set | Different Types of Numbers | Set Forms | Intervals Notation 19:23
- Lesson 25: Types of Set in Discrete Mathematics with Examples 17:46
- Lesson 26: Set Notation and Quantifiers | Truth Set and Quantifier 05:46
- Lesson 27: All Set Operations and Venn Diagram in Discrete Mathematics 13:40
- Lesson 28: Set Identities | Generalized Union and Intersection | Method of Identity Proof 21:54
- Lesson 29: Function in Discrete Mathematics | Domain Codomain Range Image and Preimage of Function 14:16
- Lesson 30: Function and its Types with Examples in Discrete Mathematics 15:02
- Lesson 31: Real Valued & Integer Valued Function | Function Increasing & Decreasing Function 14:09
- Lesson 32: Compositions of Functions with Examples in Discrete Mathematics 14:22
- Lesson 33: Inverse Functions with Examples in Discrete Mathematics 08:26
- Lesson 34: The Graph of Function in Discrete Mathematics | Floor and Ceil Function 13:02
- Lesson 35: Partial Function VS Total Function in Discrete Mathematics 07:19
- Lesson 36: Sequence vs Summation | Arithmetic Progression | Geometric Progression, 40:52
- Lesson 37: Series and Summations | Arithmetic Series | Geometric Series in Discrete Mathematics 24:29
- Lesson 38: Cardinality of Sets | Hilbert's Grand Hotel Paradox | The Countinuum Hypothesis 33:06
- Lesson 39: Computer Representation of Sets in Discrete Mathematics 05:43
- Lesson 40: Matrices | Matrix Arithmetic | Transposes and Powers of Matrices | Zero–One Matrices 23:37
- Lesson 41 Part I: 3.1 Algorithm | Properties of Algorithms | Searching and Sorting Algorithms 33:18
- Lesson 42 Part II: 3.1 Algorithm | Naive String Matcher | Greedy Algorithm | The Halting Problem 23:30
- Lesson 43: The Growth of Function - Asymptotic Notation of Algorithm in Discrete Mathematics 26:07
- Lesson 44: The Growth of Combinations of Functions with Examples in Discrete Mathematics 13:20
- Lesson 45: Complexity of Algorithms | Complexity of Matrix Multiplication | P VERSUS NP 28:37
- Lesson 46: Divisibility and Modular Arithmetic Division | Modular Arithmetic | Arithmetic Modulo m 28:02
- Lesson 47: Integer Representations and Algorithms | Representations of Binary Octal and Hexadecimal 30:07
- Lesson 48: Primes and Greatest Common Divisors | GCD vs LCM | gcds as Linear Combinations 40:30
- Lesson 49 Part I: Solving Congruences | Linear Congruences with Examples | ax ≡ b (mod m) 21:09
- Lesson 50 Part II: Solving Congruences | Chinese Remainder Theorem | Fermat’s Little Theorem 22:24
- Lesson 51 Part III: Pseudoprime vs Absolute Pseudoprime in Discrete Mathematics with Examples 13:51
- Lesson 52: Applications of Congruences in Discrete Mathematics with Examples 19:17
- Lesson 53: Classical Cryptography | Julius Caesar Method of encryption and Decryption with Examples 09:03
- Lesson 54: Symmetric VS Asymmetric Cryptography | RSA Rivest Shamir Adleman Public-key Cryptosystem 20:15
- Lesson 55 Part I: Mathematical Induction in Discrete Mathematics with Examples 15:28
- Lesson 56 Part II: Mathematical Induction Proof examples in Discrete Mathematics 19:59
- Lesson 57: Strong Induction and Well-Ordering | Examples of Proofs Using Strong Induction 17:18
- Lesson 58 Part I: Recursive Definitions and Structural Induction with Examples 27:47
- Lesson 59 Part II: Recursive Definitions and Structural Induction with Examples 29:26
- Lesson 60: Recursive Algorithms in Discrete Mathematics with Examples 1 to 10 Algorithms 27:28
- Lesson 61: Program Correctness | Program Verification | Conditional Statements | Loop Invariants 21:55
- Lesson 62: Counting | Sum Rule vs Product Rule in Discrete Mathematics with Examples 29:39
- Lesson 63: The Basics of Counting | Combining the Sum and Product Rule | Subtraction Rule 18:08
- Lesson 64: Pigeonhole Principle | Generalized Pigeonhole Principle in Discrete Mathematics 20:25
- Lesson 65: Permutation and Combination in Discrete Mathematics with Examples | Combinatorial Proof 24:55
- Lesson 66: Binomial Coefficients and Identities | Pascal’s Identity and Triangle 23:07
- Lesson 67: Generalized Permutations and Combinations | Combinations with Repetition 18:31
- Lesson 68: Discrete Probability | Probability Rules| Probabilities of Complements & Unions of Events 33:17
- Lesson 69: Probability Theory | Bernoulli Trials and the Binomial Distribution | Random Variables 54:10
- Lesson 70: Bayes’ Theorem | GENERALIZING BAYES’ THEOREM | Bayesian Spam Filters 24:46
- Lesson 71 Part I: Expected Values | Linearity of Expectations |Average-Case Computational Complexity 16:53
- Lesson 72 Part II: Expected Values | The Geometric Distribution | Chebyshev’s Inequality 29:48
- Lesson 73: What is Recurrence Relation | Homogeneous VS Non-Homogeneous Recurrence Relations 13:37
- Lesson 74: Applications of Recurrence Relations in Discrete Mathematics with Examples 27:58
- Lesson 75 Part - I: Solving Linear Recurrence Relations | First and Second Order Recurrence Relation 31:48
- Lesson 76 Part II: Linear Nonhomogeneous Recurrence Relations with Constant Coefficients 10:05
- Lesson 77: Divide and Conquer Algorithms and Recurrence Relations in Discrete Maths with Examples 17:56
- Lesson 79 Part I: Generating Functions with examples in Discrete Mathematics 17:42
- Lesson 80 Part II: Generating Functions Theorems |Useful Facts About Power Series |Counting Problems 25:24
- Lesson 81: The Principle of Inclusion–Exclusion | Inclusion Exclusion in Discrete Mathematics 18:45
- Lesson 82 Part I: Applications of Inclusion–Exclusion | Alternative Form of Inclusion–Exclusion 17:10
- Lesson 83: Part II: Applications of Inclusion–Exclusion|Num. of ONTO Function |Sieve of Eratosthenes 10:17
- Lesson 84 Part III: Number of ONTO Function - Continue | Derangements with Examples 09:49
- Lesson 85: Relations and their Properties | Relation VS Function | Binary Relation 20:43
- Lesson 86: Combining Relations | Composition of relation | Composing the Parent Relation with Itself 19:13
- Lesson 87: Representing Relations using Digraphs and Matrices with Examples 13:04
- Lesson 88: n-ary Relations and Their Applications | Database and SQL in Discrete Mathematics 23:24
- Lesson 89: Representing Relations | Representing Relations Using Matrices and Digraphs 31:31
- Lesson 90: Closures of Relations | Paths in Directed Graphs | Types of Closures in Discrete Maths 22:22
- Lesson 91: Finding Transitive Closures | Warshall Algorithm with Example 15:16
- Lesson 92 Part I: Equivalence Relations with Examples in Discrete Mathematics 14:05
- Lesson 93 Part II: Equivalence Classes and Partitions | Partition of a SET 18:15
- Lesson 94 Part I: Partial Orderings in Discrete Mathematics with Examples 13:14
- Lesson 95 Part II: Comparable VS Incomparable in POSET | Totally Ordered Set | Well Ordering | 15:22
- Lesson 96 Part III: Lexicographic Order | Hasse Diagrams | Maximal and Minimal Elements 27:54
- Lesson 97 Part IV: Lattices | Semi-lattice vs Join Semi-lattice | Topological Sorting 15:37
- Lesson 98: Graph in Discrete Mathematics | Graph and its Types | Graph Terminology 16:16
- Lesson 99: Graphs and Graph Models | Application of Graph in Real Life 20:53
- Lesson 100 Part I: Graph Terminology and Special Types of Graphs 30:17
- Lesson 101 Part II: Bipartite Graphs and Matchings | Hall's Marriage Theorem | New Graphs from Old 20:45
- Lesson 102 Part I: Representing Graphs and Graph Isomorphism | Adjacency Lists & Incidence Matrices 16:00
- Lesson 103 Part II: Representing Graphs and Graph Isomorphism | Isomorphism Graphs with Applications 19:21
- Lesson 104 Part I: Connectivity | Path Walk and Trail in Graph Discrete Mathematics 13:46
- Lesson 105 Part II: Connectivity | Connectedness in Directed and Undirected Graphs 10:01
- Lesson 106: Euler and Hamilton Paths | Applications of Euler Paths and Circuits 23:02
- Lesson 107: Hamilton Paths and Circuits | Applications of Hamilton Circuits 12:54
- Lesson 108: Understanding Mohammed's Scimitars | Fleury's Algorithm 13:42
- Lesson 109: Shortest-Path Problems | Dijkstra’s Algorithm in Discrete Mathematics 17:17
- Lesson 110: Travelling Salesman Problem | Traveling Salesperson Problem in Discrete Mathematics 08:35
- Lesson 111: Planar Graphs in Discrete Mathematics | EULER’S FORMULA | Kuratowski’s Theorem 19:23
- Lesson 112: Graph Coloring | THE FOUR COLOR THEOREM | Applications of Graph Colorings 23:12
- Lesson 113: Introduction to Trees | TREE vs GRAPH | Tree terminology and its basic Types 11:00
- Lesson 114: Introduction to Trees | Properties of Trees | FULL & BALANCED m-ARY TREES 30:35
- Lesson 115: Applications of Trees | Prefix Codes | HUFFMAN CODING 20:13
- Lesson 116: Tree Traversal | Inorder Preorder Postorder Traversal of Binary Trees 25:02
- Lesson 117: Tree Traversal | Infix Prefix and Postfix Notation with Examples 14:11
- Lesson 118: Spanning Trees | Kirchhoff's Matrix Tree Theorem | Minimum Spanning Tree 14:51
- Lesson 119: Depth-First Search VS Breadth-First Search | Backtracking Applications 23:11
- Lesson 120: Kruskal's and Prim's Minimum Spanning Tree (MST) Algorithms 14:33
- Lesson 121: Boolean Algebra | Boolean Expressions | Boolean Functions in Discrete Mathematics 19:20
- Lesson 122: Identities of Boolean Algebra | Duality and Abstract Definition of a Boolean Algebra 14:53
- Lesson 123: SOP vs POS | Min-term vs Max-term | Functional Completeness 25:42
- Lesson 124: Logic Gates [AND OR NOT NAND NOR XOR XNOR] | Combination of Gates | Half and Full Adders 23:40
- Lesson 125: Minimization of Circuits | Karnaugh Map - K Map for 2, 3 and 4 Variables 31:16
- Lesson 126: Minimization of Circuits | Don't Care (X) Conditions in K-Maps 14:56
- Lesson 127: Minimization of Circuits | The Quine–McCluskey Method 17:06
- Lesson 128 Part I: Languages and Grammars | Phrase-Structure Grammars | Automata VS TOC 16:46
- Lesson 129 Part II: Languages and Grammars | Leftmost and Rightmost Derivation | Types of Grammars 26:53
- Lesson 130: Finite-State Machines with Output | Finite-State Machine | Deterministic Finite Automata 24:49
- Lesson 131 Part I: Finite-State Machines with No Output | Language Recognized by Finite Automata 15:08
- Lesson 132 Part II: Finite-State Machines with No Output | Language Recognized by FSAs 18:03
- Lesson 133: Language Recognition | Regular Expression | Regular Sets and Regular Grammars 26:43
- Lesson 134 Part I: Turing Machines | How Turing Machine Works with Example 24:11
- Lesson 134 Part II: Turing Machines | Using Turing Machines to Recognize Sets | Different Types TMs 29:34
- Lesson 135 LAST LESSON: END OF COURSE - Final Words | Discrete Mathematics COURSE OUTCOMES 06:04
- How to use FAHAD HUSSAIN YouTube Channel 04:31
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