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Discrete Mathematics Fundamentals

Track :

Mathematics

Lessons no : 136

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What will you learn in this course?
  • Master logical reasoning, propositional and predicate logic, and their applications in computer science and mathematics
  • Apply set theory principles to solve problems involving unions, intersections, and Cartesian products in real-world contexts
  • Utilize combinatorial techniques to count arrangements, permutations, and combinations for practical problem-solving
  • Analyze and interpret graphs, trees, and networks to model relationships and optimize solutions in computer algorithms
  • Solve problems involving functions, relations, and mappings using discrete mathematics concepts and techniques
  • Implement principles of discrete mathematics to develop algorithms and data structures efficiently
  • Understand and apply principles of graph theory to network design, routing, and connectivity problems
  • Use mathematical induction and recursion to prove properties and solve complex discrete problems
  • Explore applications of discrete mathematics in cryptography, coding theory, and information security
  • Develop problem-solving skills through discrete mathematics exercises in logic, set theory, and combinatorics
  • Identify and analyze discrete structures in computer science, engineering, and information technology fields
  • Apply combinatorial reasoning to optimize resource allocation and scheduling problems
  • Utilize graph algorithms to solve shortest path, spanning tree, and network flow problems
  • Interpret mathematical notation and formal proofs to communicate discrete mathematics concepts effectively
  • Leverage discrete mathematics principles to enhance algorithm design and computational efficiency
  • Solve real-world problems using discrete mathematics concepts in data analysis, network analysis, and software development

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Lessons | 136
Lesson 00 Introduction to Discrete Mathematics | Recommended Books for Discrete Mathematics
00:07:36

Lesson 00 Introduction to Discrete Mathematics | Recommended Books for Discrete Mathematics
Lesson 01 What is Logic Proposition and Propositional Logic
00:09:27

Lesson 01 What is Logic Proposition and Propositional Logic
Lesson 02 Logical Connectives in Compound Proposition | Truth Table in Discrete Mathematics
00:16:38

Lesson 02 Logical Connectives in Compound Proposition | Truth Table in Discrete Mathematics
Lesson 03 Converse Inverse and Contrapositive of a Conditional Statement
00:09:51

Lesson 03 Converse Inverse and Contrapositive of a Conditional Statement
Lesson 04 Logic Circuits | Logic Gates | Combinatorial Circuit in Discrete Mathematics
00:10:49

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
00:22:52

Lesson 05 Law of Logic Rules with Examples | Tautology Contradiction Contingency in Discrete Maths
Lesson 06 Law of Logic Rules Practice Examples
00:18:18

Lesson 06 Law of Logic Rules Practice Examples
Lesson 07 Predicate and its Examples in Discrete Mathematics
00:10:38

Lesson 07 Predicate and its Examples in Discrete Mathematics
Lesson 08 Quantifier and its Examples in Discrete | Universal Uniqueness Existential Quantifiers
00:16:12

Lesson 08 Quantifier and its Examples in Discrete | Universal Uniqueness Existential Quantifiers
Lesson 09 Negating Quantified Expressions | De Morgan s Laws for Quantifiers
00:10:37

Lesson 09 Negating Quantified Expressions | De Morgan s Laws for Quantifiers
Lesson 10 Nested Quantifiers Understanding Statements Involving Nested Quantifiers
00:13:01

Lesson 10 Nested Quantifiers Understanding Statements Involving Nested Quantifiers
Lesson 11 Rules of Inference for Propositional Logic | Rules of Inference in Discrete Mathematics
00:19:06

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
00:13:53

Lesson 12 Using Rules of Inference to Build Arguments | Rules of Inference Examples
Lesson 13 Rules of Inference for Quantified Statements
00:18:06

Lesson 13 Rules of Inference for Quantified Statements
Lesson 14 The Resolution Principle Preliminaries | Resolution in Proposition Logic
00:08:26

Lesson 14 The Resolution Principle Preliminaries | Resolution in Proposition Logic
Lesson 15 What is Fallacies in Discrete Mathematics
00:07:04

Lesson 15 What is Fallacies in Discrete Mathematics
Lesson 16 Introduction to Proofs | Methods of Proof Direct Proof
00:24:52

Lesson 16 Introduction to Proofs | Methods of Proof Direct Proof
Lesson 17 Part I Indirect Proof | Proof by Contrapositive with Examples
00:10:44

Lesson 17 Part I Indirect Proof | Proof by Contrapositive with Examples
Lesson 18 Part II Indirect Proof | Proof by Contradiction with Examples
00:19:24

Lesson 18 Part II Indirect Proof | Proof by Contradiction with Examples
Lesson 19 Mistakes in Proof | Common Mistakes in Proofs in Discrete Mathematics
00:08:39

Lesson 19 Mistakes in Proof | Common Mistakes in Proofs in Discrete Mathematics
Lesson 20 Part I Proof Methods and Strategies in Discrete Mathematics
00:32:26

Lesson 20 Part I Proof Methods and Strategies in Discrete Mathematics
Lesson 21 Part II Proof Methods and Strategies in Discrete Mathematics
00:24:02

Lesson 21 Part II Proof Methods and Strategies in Discrete Mathematics
Lesson 22 Theorem VS Lemma VS Corollary in Discrete Mathematics
00:06:05

Lesson 22 Theorem VS Lemma VS Corollary in Discrete Mathematics
Lesson 23 Applications of Propositional Logic in Real Life
00:09:36

Lesson 23 Applications of Propositional Logic in Real Life
Lesson 24 What is Set | Different Types of Numbers | Set Forms | Intervals Notation
00:19:23

Lesson 24 What is Set | Different Types of Numbers | Set Forms | Intervals Notation
Lesson 25 Types of Set in Discrete Mathematics with Examples
00:17:46

Lesson 25 Types of Set in Discrete Mathematics with Examples
Lesson 26 Set Notation and Quantifiers | Truth Set and Quantifier
00:05:46

Lesson 26 Set Notation and Quantifiers | Truth Set and Quantifier
Lesson 27 All Set Operations and Venn Diagram in Discrete Mathematics
00:13:40

Lesson 27 All Set Operations and Venn Diagram in Discrete Mathematics
Lesson 28 Set Identities | Generalized Union and Intersection | Method of Identity Proof
00:21:54

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
00:14:16

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
00:15:02

Lesson 30 Function and its Types with Examples in Discrete Mathematics
Lesson 31 Real Valued Integer Valued Function | Function Increasing Decreasing Function
00:14:09

Lesson 31 Real Valued Integer Valued Function | Function Increasing Decreasing Function
Lesson 32 Compositions of Functions with Examples in Discrete Mathematics
00:14:22

Lesson 32 Compositions of Functions with Examples in Discrete Mathematics
Lesson 33 Inverse Functions with Examples in Discrete Mathematics
00:08:26

Lesson 33 Inverse Functions with Examples in Discrete Mathematics
Lesson 34 The Graph of Function in Discrete Mathematics | Floor and Ceil Function
00:13:02

Lesson 34 The Graph of Function in Discrete Mathematics | Floor and Ceil Function
Lesson 35 Partial Function VS Total Function in Discrete Mathematics
00:07:19

Lesson 35 Partial Function VS Total Function in Discrete Mathematics
Lesson 36 Sequence vs Summation | Arithmetic Progression | Geometric Progression
00:40:52

Lesson 36 Sequence vs Summation | Arithmetic Progression | Geometric Progression
Lesson 37 Series and Summations | Arithmetic Series | Geometric Series in Discrete Mathematics
00:24:29

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
00:33:06

Lesson 38 Cardinality of Sets | Hilbert s Grand Hotel Paradox | The Countinuum Hypothesis
Lesson 39 Computer Representation of Sets in Discrete Mathematics
00:05:43

Lesson 39 Computer Representation of Sets in Discrete Mathematics
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Noor Fathima

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

Reddy yamuna

Very effective course 2025-04-11

MATCHETTI RACHANA

VERY USEFUL INFORMATION. AND IT HELPS A LOT FOR ME. 2025-04-02

BALI VENKATA RAMANA

Nice 2025-03-23

Jyothirmayi Thandraju

It is very helpful course 2025-03-19

Bhadrachalam Anusha

Totally worth the time. 2025-03-12

G Vasantha Vani

Nice Explanation 2025-03-07

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