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Discrete Mathematics
Unlock the Power of Problem Solving. Learn Discrete Mathematics and Master the Foundation of Computer Science.
| star star star star star_half | 4.9 (317 ratings) |
Instructor: Deepak Poonia (MTech IISc Bangalore, GATE CSE AIR 53; 67; 107)
Language: English
Enrolled Learners: 41155
Validity Period: Lifetime
GO Classes Complete Discrete Mathematics and Engineering Mathematics Courses are FREE for all learners. Sign up and start learning.
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Features of the course:
One-Stop Solution for your Complete Best GATE Preparation!!
1. Quality Content: No Rote-learning. No poor understanding. No rote memorization of formulas, tables, or theorems. Understand everything with proofs, intuitions, and ideas.
2. No Prerequisites: Every concept is taught from the basics, without assuming any prior knowledge whatsoever.
3. Daily Homework: Practice material, with solutions, for Every Lecture to test your understanding of concepts of that respective lecture.
4. GATE PYQs Video Solution: Detailed Video Solution of All GATE Previous Years' Questions, with Complete Analysis of each question.
5. Summary Lectures: Short videos that summarize every concept and detail of the course. Helps in quick revision.
6. Quality Practice Sets: Practice Sets from standard resources, with solutions, containing a lot of quality questions for practice.
7. Weekly Quizzes: Every week, there will be a Live Quiz, containing 15-20 questions, to evaluate your understanding of concepts taught in the previous week. The Quiz questions can be seen and solved even after the live quiz is over. The weekly quizzes can be accessed by complete course enrolled students.
8. Doubt Resolution: All of your doubts will be resolved directly by the faculty. There is a dedicated Telegram group for Enrolled Students of Goclasses where our faculty resolve students' Doubts. So, our students don't have to go anywhere else to ask doubts.
| Module 1 - Basic Proof Techniques | |||
| Lecture 1A - Proof Techniques Part 1 - Direct Proofs | |||
| Annotated Notes - Lecture 1A - Proof Techniques Part 1 - Direct Proofs (106 pages) | |||
| Lecture 1B - Proof Techniques Part 2 - Proof by Contrapositive & Contradiction | |||
| Annotated Notes - Lecture 1B - Proof Techniques Part 2 - Proof by Contrapositive & Contradiction (124 pages) | |||
| Lecture 1C - Proof by Mathematical Induction - Proof Technique | |||
| Annotated Notes - Lecture 1C - Proof by Mathematical Induction (54 pages) | |||
| Homework 1 - Proof Techniques - Direct Proof (25 pages) | |||
| Homework 2 - Proof Techniques - Contraposition & Contradiction (22 pages) | |||
| Homework 1,2 Video Solutions - Proof Techniques | |||
| Lecture 2 - Practice Questions on Proof Techniques | |||
| Annotated Notes - Lecture 2 - Practice Questions on Proof Techniques (48 pages) | |||
| Weekly Quiz - Proof Techniques | |||
| Rate & Review | |||
| Module 2 - Introduction to Discrete Mathematics | |||
| Lecture 1 - Introduction to Discrete Mathematics 30:00 | |||
| Summary Lecture 1 - Introduction to Discrete Mathematics 4:00 | |||
| Module 3 - Propositional Logic | |||
| Lecture 1 - Introduction to Mathematical Logic 39:00 | |||
| Annotated Notes - Lecture 1 - Introduction to Mathematical Logic (33 pages) | |||
| Summary Lecture 1 - Introduction to Mathematical Logic 2:00 | |||
| Lecture 2 - Proposition & Propositional Variable 53:00 | |||
| Annotated Notes - Lecture 2 - Proposition & Propositional Variable (48 pages) | |||
| Summary Lecture 2 - Proposition & Propositional Variable, Truth Value 8:00 | |||
| Is it a Proposition?? - A Dumb Question!! | |||
| Lecture 3 - Atomic & Compound Propositions 26:00 | |||
| Annotated Notes - Lecture 3 - Atomic & Compound Propositions (25 pages) | |||
| Summary Lecture 3A - Atomic Proposition. Compound Proposition 5:00 | |||
| Summary Lecture 3B - Logical Connectives 4:00 | |||
| Lecture 4 - Negation Operator - Logical Connectives 21:00 | |||
| Lecture 5 - Conjunction (AND) Operator - Logical Connectives 26:00 | |||
| Lecture 6 - Disjunction (OR) Operator - Logical Connectives 13:00 | |||
| Annotated Notes - Lecture 4,5,6 - Logical Connectives (77 pages) | |||
| Lecture 7 - Exclusive-OR Operator - Logical Connectives 35:00 | |||
| Lecture 8 - NAND NOR Operator - Logical Connectives 7:00 | |||
| Annotated Notes - Lecture 7,8 - Logical Connectives (41 pages) | |||
| Lecture 9 - Implication Operator - Logical Connectives 58:00 | |||
| Lecture 10 - Implication Operator Continued 19:00 | |||
| Annotated Notes - Lecture 9,10 - Implication Operator (80 pages) | |||
| Lecture 11 - Important Points about Implication Operator 20:00 | |||
| Lecture 12 - Necessary & Sufficient Condition - Implication Operator 57:00 | |||
| Lecture 13 - Various English Translations of Implication Statement 28:00 | |||
| Annotated Notes - Lecture 11,12,13 - Implication Operator Continued (111 pages) | |||
| Lecture 14 - Bi-implication Operator - Logical Connective 26:00 | |||
| Annotated Notes - Lecture 14 - Bi-implication Operator (38 pages) | |||
| Lecture 15 - Property Vs Definition - Implication Vs Bi-implication Statements 21:00 | |||
| Annotated Notes - Lecture 15 - Property Vs Definition (24 pages) | |||
| Lecture 16 - Propositional Variable Vs Propositional Formula 40:00 | |||
| Annotated Notes - Lecture 16 - Propositional Variable Vs Propositional Formula (40 pages) | |||
| Homework 1 - Logical Connectives - Propositional Logic (33 pages) | |||
| Homework 2 - Implication Bi-implication - Propositional Logic (17 pages) | |||
| Homework 1,2 Video Solution & Notes | |||
| Lecture 17 - Propositional Formula Revisited 44:00 | |||
| Lecture 18 - Truth Table 25:00 | |||
| Annotated Notes - Lecture 17,18 - Propositional Formula Revisited, Truth Table (80 pages) | |||
| Homework 3 - Standard Questions - Propositional Logic (16 pages) | |||
| Homework 3 Video Solution | |||
| Lecture 19 - Tautology, Contradiction, Contingency 59:00 | |||
| Lecture 20 - By Case Method 29:00 | |||
| Lecture 21 - By Case Method Practice 29:00 | |||
| Lecture 22 - Logical Equivalence 47:00 | |||
| Lecture 23 - Logical Equivalence Practice 32:00 | |||
| Annotated Notes - Lecture 19-23 - Tautology, Equivalence (149 pages) | |||
| Weekly Quiz 1 - Propositional Logic | |||
| Lecture 24 - Converse, Contrapositive of Conditional Statement 20:00 | |||
| Lecture 25 - English-Logic Translation 20:00 | |||
| Lecture 26 - Unless Word - English-Logic Translation 24:00 | |||
| Annotated Notes - Lecture 24-26 - English-Logic Translation, Converse, Unless Word (122 pages) | |||
| Lecture 27 - Logical Laws - Commutative Property 30:00 | |||
| Lecture 28 - Logical Laws - Associative Property 29:00 | |||
| Lecture 29 - Logical Laws - Idempotent Property 12:00 | |||
| Lecture 30 - Logical Laws - Distributive Law 30:00 | |||
| Lecture 31 - Logical Laws - De Morgan's Laws 20:00 | |||
| Lecture 32 - Logical Laws - Implication Laws 9:00 | |||
| Lecture 33 - Simplification Using Logical Laws 53:00 | |||
| Lecture 34 - Analysis of Implication 44:00 | |||
| Annotated Notes - Lecture 27-34 - Logical Laws (200 pages) | |||
| Lecture 35 - Logical Arguments 44:00 | |||
| Lecture 36 - Rules of Inference - Logical Arguments 44:00 | |||
| Annotated Notes - Lecture 35,36 - Logical Arguments (83 pages) | |||
| Lecture 37 - The Inference Symbol 18:00 | |||
| Annotated Notes - Lecture 37 - The Inference Symbol (27 pages) | |||
| Weekly Quiz 2 - Propositional Logic | |||
| Weekly Quiz 3 - Propositional Logic | |||
| Propositional Logic - Summary, GATE PYQs & Practice Questions | |||
| Rate & Review | |||
| Module 4 - First Order Logic | |||
| About First Order Logic | |||
| (OPTIONAL) Lecture 1 - Overview & Need of First Order Logic | |||
| Annotated Notes - Lecture 1 - First Order Logic Motivation & Overview (83 pages) | |||
| Lecture 2 - Objects & Domain in First Order Logic 28:00 | |||
| Lecture 3 - Predicates in First Order Logic 52:00 | |||
| Lecture 4 - Creating Proposition from predicate 22:00 | |||
| Annotated Notes - Lecture 2,3,4 - Objects & Predicates (91 pages) | |||
| Lecture 5 - Quantifiers Introduction 16:00 | |||
| Lecture 6 - Universal Quantifier 46:00 | |||
| Lecture 7 - Existential Quantifier 41:00 | |||
| Lecture 8 - Quantifiers Practice 38:00 | |||
| Lecture 9 - Quantifiers Summary 12:00 | |||
| Annotated Notes - Lecture 5-9 - Quantifiers (150 pages) | |||
| Lecture 10 - Quantifiers Tricky Points 32:00 | |||
| Lecture 11 - English-FOL Translation Part 1 3:00 | |||
| Lecture 12 - English-FOL Translation Part 2 47:00 | |||
| Lecture 13 - English-FOL Translation Part 3 15:00 | |||
| Lecture 14 - English-FOL Translation Part 4 28:00 | |||
| Lecture 15 - English-FOL Translation Part 5 16:00 | |||
| Lecture 16 - English-FOL Translation Part 6 23:00 | |||
| Lecture 17 - English-FOL Translation Part 7 16:00 | |||
| Annotated Notes - Lecture 10-17 - English-FOL Translation (187 pages) | |||
| Lecture 18 - Revision of English-FOL Translation 69:00 | |||
| Lecture 19 - A LOT of Practice of English-FOL Translation 36:00 | |||
| Lecture 20 - Bounded Variable 29:00 | |||
| Lecture 21 - Free Variable Vs Bounded Variable 48:00 | |||
| Lecture 22 - Practice - Bounded Variable Free Variable 33:00 | |||
| Lecture 23 - Important Note About Free Variables 19:00 | |||
| Lecture 24 - Scope of a Quantifier 49:00 | |||
| Annotated Notes - Lecture 20-24 - Free Variable, Bounded Variable, Scope of a Quantifier (151 pages) | |||
| Lecture 25 - Nested Quantifiers Part 1 - Need of Nested Quantifiers 17:00 | |||
| Lecture 26 - Nested Quantifiers Part 2 - All Four Standard Templates 27:00 | |||
| Lecture 27 - Nested Quantifiers Part 3 - Examples, Variations 61:00 | |||
| Annotated Notes - Lecture 25-27 - Nested Quantifiers (109 pages) | |||
| Lecture 28 - More Practice of English - FOL Translation 37:00 | |||
| Lecture 29 - Even More Practice of English - FOL Translation 23:00 | |||
| Annotated Notes - Lecture 18, 19, 28, 29 - English-FOL Translation Examples Part 1-4 (133 pages) | |||
| Lecture 30 - Practice - Free Variable, Bounded Variable, Scope 44:00 | |||
| Annotated Notes - Lecture 30 - Practice - Free Variable, Bounded Variable, Scope (50 pages) | |||
| Homework 1 - Quantifiers - First Order Logic (30 pages) | |||
| Homework 1 - Detailed Video Solutions - First Order Logic | |||
| Lecture 31 - Negation of quantifiers 50:00 | |||
| Annotated Notes - Lecture 31 - Negation of quantifiers (65 pages) | |||
| Lecture 32 - Validity, Satisfiability of a FOL Expression 29:00 | |||
| Lecture 33 - Validity, Satisfiability of a FOL Expression Part 2 38:00 | |||
| Annotated Notes - Lecture 32,33 - Validity, Satisfiability of a FOL Expression (65 pages) | |||
| Lecture 34 - Validity of FOL Expression Involving Implication 22:00 | |||
| Lecture 35 - Equivalence of FOL Expressions 11:00 | |||
| Lecture 36 - Distributive Properties of Quantifiers 45:00 | |||
| Annotated Notes - Lecture 34-36 - Distributive Properties of Quantifiers (58 pages) | |||
| Lecture 37 - Practice - First Order Logic | |||
| Lecture 38 - Null Quantification Rule | |||
| Annotated Notes - Lecture 37,38 - Null Quantification Rule (141 pages) | |||
| Lecture 39 - Arguments in First Order Logic | |||
| Annotated Notes- Lecture 39 - Arguments in First Order Logic (83 pages) | |||
| NOTE About Next Lectures | |||
| OPTIONAL Lecture 1 - Interpretation, Model in Propositional Logic 31:00 | |||
| OPTIONAL Lecture 2 - Interpretation, Model in First Order Logic 43:00 | |||
| Annotated Notes - OPTIONAL Lecture 1,2 - Interpretation, Model in Propositional Logic, FOL (77 pages) | |||
| OPTIONAL Lecture 3 - Uniqueness Quantifier 27:00 | |||
| Annotated Notes - OPTIONAL Lecture 3 - Uniqueness Quantifier (32 pages) | |||
| Optional Lecture 4 - Tautology in First Order Logic 34:00 | |||
| Annotated Notes - Optional Lecture 4 - Tautology in First Order Logic (42 pages) | |||
| First Order Logic - Complete Summary, ALL GATE PYQs & Practice | |||
| Rate & Review | |||
| Module 5 - Set Theory | |||
| Lecture 1 - Set Definition 30:00 | |||
| Lecture 2 - Finite Set, Infinite Set 9:00 | |||
| Lecture 3 - Cardinality of a Set 9:00 | |||
| Lecture 4 - Set Representations 36:00 | |||
| Annotated Notes - Lecture 1-4 - Set (128 pages) | |||
| Lecture 5 - Subset 24:00 | |||
| Annotated Notes - Lecture 5 - Subset (49 pages) | |||
| Lecture 6 - Powerset of a Set 18:00 | |||
| Lecture 7 - Set Operations 51:00 | |||
| Lecture 8 - Set Equality 32:00 | |||
| Annotated Notes - Lecture 6-8 - Set Operations (120 pages) | |||
| Weekly Quiz 1 - Set Theory | |||
| Lecture 9 - Understanding Set Operations 42:00 | |||
| Annotated Notes - Lecture 9 - Understanding Set Operations (41 pages) | |||
| Lecture 10 - Proofs involving Sets, Set Equality, Subset 37:00 | |||
| Lecture 11 - Set Identities 50:00 | |||
| Lecture 12 - Proofs involving Power Sets 13:00 | |||
| Annotated Notes - Lecture 10-12 - Proofs involving Sets (102 pages) | |||
| Practice Set 1 - Set, Subset - Set Theory (Video Solution Below) (27 pages) | |||
| Practice Set 1 - Video Solutions | |||
| Lecture 13 - Ordered Pairs 18:00 | |||
| Lecture 14 - Cartesian Product of Sets 41:00 | |||
| Annotated Notes - Lecture 13,14 - Cartesian Product (81 pages) | |||
| Weekly Quiz 2 - Set Theory | |||
| Lecture 15 - Relations 26:00 | |||
| Lecture 16 - Counting Number of Relations 5:00 | |||
| Lecture 17 - Relation on a Set 33:00 | |||
| Annotated Notes - Lecture 15-17 - Relations (60 pages) | |||
| Lecture 18 - Understanding Relations Part 1 31:00 | |||
| Lecture 19 - Understanding Relations Part 2 47:00 | |||
| Lecture 20 - Types of Binary Relations 2:00 | |||
| Lecture 21 - Reflexive Relation 46:00 | |||
| Annotated Notes - Lecture 18-21 - Understanding Relations & Reflexive Relation (153 pages) | |||
| Lecture 22 - Symmetric Relation 29:00 | |||
| Lecture 23 - Antisymmetric Relation 4:00 | |||
| Annotated Notes - Lecture 22,23 - Symmetric Relation (40 pages) | |||
| Lecture 24 - Antisymmetric Relation Definition 2 11:00 | |||
| Lecture 25 - Asymmetric Relation 32:00 | |||
| Example 1 - Symmetric, Antisymmetric, Asymmetric 15:00 | |||
| Example 2 - Symmetric, Antisymmetric, Asymmetric 17:00 | |||
| Lecture 26 - Transitive Relation 27:00 | |||
| Example 1 - Transitive Relation 6:00 | |||
| Annotated Notes - Lecture 24-26 - Transitive Relation (122 pages) | |||
| Lecture 27 - Equivalence Relation Definition 18:00 | |||
| Annotated Notes - Lecture 27 - Equivalence Relation Definition (23 pages) | |||
| Lecture 28 - Partition of a Set 40:00 | |||
| Annotated Notes - Lecture 28 - Partition of a Set (45 pages) | |||
| Summary Lecture - Partition of a Set 18:00 | |||
| Annotated Notes - Summary Lecture - Partition of a Set (37 pages) | |||
| Lecture 29 - Equivalence Relation Complete Analysis Part 1 78:00 | |||
| Annotated Notes - Lecture 29 - Equivalence Relation Complete Analysis Part 1 (63 pages) | |||
| Practice Set 2 - Relations - Set Theory (Video Solution Below) (48 pages) | |||
| Practice Set 2 - Video Solutions | |||
| Lecture 30 - Equivalence Relation Complete Analysis Part 2 60:00 | |||
| Lecture 31 - Graph of Equivalence Relation 6:00 | |||
| Lecture 32 - Practice Equivalence Relation 9:00 | |||
| Annotated Notes - Lecture 30-32 - Equivalence Relation Complete Analysis Part 2 (76 pages) | |||
| Summary Lecture - Equivalence Relations 35:00 | |||
| Annotated Notes - Summary Lecture - Equivalence Relations (38 pages) | |||
| Practice Set 3 - Equivalence Relations - Set Theory (Video Solution Below) (40 pages) | |||
| Practice Set 3 - Video Solutions | |||
| Lecture 33 - Partial Order Relation 47:00 | |||
| Annotated Notes - Lecture 33 - Partial Order Relation (40 pages) | |||
| Lecture 34 - Total Order Relation 35:00 | |||
| Lecture 35 - Hasse Diagram of POSET 53:00 | |||
| Lecture 36 - Special Elements of POSET 25:00 | |||
| Annotated Notes - Lecture 34-36 - Total Order Relation, Hasse Diagram, Elements of POSET (107 pages) | |||
| Lecture 37 - Practice Questions on Hasse Diagrams 16:00 | |||
| Lecture 38 - Upper Bound, Lower Bound, LUB, GLB 62:00 | |||
| Annotated Notes - Lecture 37,38 - Upper Bound, Lower Bound, LUB, GLB (54 pages) | |||
| Lecture 39 - Practice Questions on GLB, LUB 34:00 | |||
| Lecture 40 - Hasse Diagram of a Total Order Relation 26:00 | |||
| Annotated Notes - Lecture 39,40 - Hasse Diagram of a Total Order Relation (53 pages) | |||
| Lecture 41 - Lattice 15:00 | |||
| Annotated Notes - Lecture 41 - Lattice (19 pages) | |||
| Lecture 42 - Hasse Diagram to Partial Order Relation 7:00 | |||
| Lecture 43 - Hasse Diagram to Partial Order Relation Part 2 31:00 | |||
| Annotated Notes - Lecture 42,43 - Hasse Diagram to Partial Order Relation (30 pages) | |||
| Lecture 44 - Properties of Lattices 28:00 | |||
| Annotated Notes - Lecture 44 - Properties of Lattices (28 pages) | |||
| Lecture 45 - Sublattice 44:00 | |||
| Lecture 46 - Questions on Minimal, Maximal Elements in POSET Part 1 14:00 | |||
| Annotated Notes - Lecture 45,46 - Sublattice (46 pages) | |||
| Lecture 47 - Questions on Minimal, Maximal Elements in POSET Part 2 48:00 | |||
| Annotated Notes - Lecture 47 - Questions on Minimal, Maximal Elements in POSET Part 2 (55 pages) | |||
| Practice Set 4 - Partial Order Relations & Lattices - Set Theory (Video Solution Below) (67 pages) | |||
| Practice Set 4 - Video Solutions | |||
| Lecture 48 - Questions - Maximal, Greatest Elements in a Lattice | |||
| Annotated Notes - Lecture 48 - Questions - Maximal, Greatest Elements in a Lattice (50 pages) | |||
| Lecture 49 - Properties of Every Lattice 22:00 | |||
| Annotated Notes - Lecture 49 - Properties of Every Lattice (22 pages) | |||
| Lecture 50 - Practice Questions on Sublattice 30:00 | |||
| Annotated Notes - Lecture 50 - Practice Questions on Sublattice (26 pages) | |||
| Lecture 51 - Types of Lattices 8:00 | |||
| Lecture 52 - Bounded Lattice 38:00 | |||
| Annotated Notes - Lecture 51, 52 - Bounded Lattice (53 pages) | |||
| Lecture 53 - Identity Property in Lattices, Domination Law 36:00 | |||
| Lecture 54 - Complemented Lattice 20:00 | |||
| Annotated Notes - Lecture 53,54 - Identity Property in Lattices, Complemented Lattice (67 pages) | |||
| Weekly Quiz 13 - Equivalence Relation | |||
| Lecture 55 - Distributive Lattice 56:00 | |||
| Annotated Notes - Lecture 55 - Distributive Lattice (60 pages) | |||
| Lecture 56 - Practice Questions on Types of Lattice 27:00 | |||
| Lecture 57 - Boolean Lattice 30:00 | |||
| Lecture 58 - Why Boolean Lattice is called a Boolean Algebra 19:00 | |||
| Lecture 59 - Complete Analysis of Total Order Relation 9:00 | |||
| Lecture 60 - Complete Analysis of Powerset Lattice 17:00 | |||
| Annotated Notes - Lecture 56-60 - Boolean Lattice (117 pages) | |||
| Lecture 61 - Complete Analysis of Divisibility Relation - Part 1 30:00 | |||
| Lecture 62 - Complete Analysis of Divisibility Relation - Part 2 51:00 | |||
| Annotated Notes - Lecture 61,62 - Division Lattice Dn Complete Analysis (72 pages) | |||
| Lecture 63 - Refinement of a Partition | GATE 2007, 1998 127:00 | |||
| Annotated Notes - Refinement of a Partition (128 pages) | |||
| Lecture 64 - Constructing Total Order from Partial Order - GATE 2024, 1997 119:00 | |||
| Annotated Notes - Constructing Total Order from Partial Order (98 pages) | |||
| Rate & Review | |||
| Module 6 - Function | |||
| Lecture 1 - Function Definition & Terminology 35:00 | |||
| Lecture 2 - Number of Functions 16:00 | |||
| Lecture 3 - Representations of Function, Image of a Subset of Domain 22:00 | |||
| Lecture 4 - Types of Functions - Injective, Surjective, Bijective 36:00 | |||
| Annotated Notes - Lecture 1-4 - Functions (100 pages) | |||
| Lecture 5 - Practice Questions on Types of Functions 34:00 | |||
| Lecture 6 - Set Operations on Relations 13:00 | |||
| Lecture 7 - Composition Operation 52:00 | |||
| Annotated Notes - Lecture 5-7 - Operations on Functions (87 pages) | |||
| Lecture 8 - Inverse of a Function | |||
| Annotated Notes - Lecture 8 - Inverse of a Function (108 pages) | |||
| Weekly Quiz 1 - Functions | |||
| Functions - Summary, Practice & GATE PYQs | |||
| Rate & Review | |||
| Module 7 - Group Theory | |||
| Lecture 1, 2 are OPTIONAL | |||
| (OPTIONAL) Lecture 1 - Abstract Algebra - Introduction & Motivation 33:00 | |||
| (OPTIONAL) Lecture 2 - Abstract Algebra Origin & The Galois Story 15:00 | |||
| Lecture 3 - Abstract Algebra GATE Syllabus 8:00 | |||
| Lecture 4 - Binary Operation & The Closure Property 23:00 | |||
| Lecture 5 - The Associative Property 7:00 | |||
| Lecture 6 - The Identity Property 31:00 | |||
| Annotated Notes - Lecture 1-6 - Abstract Algebra & Binary Operation (114 pages) | |||
| Lecture 7 - Practice Questions on Binary Operation 22:00 | |||
| Lecture 8 - Important Properties of Identity Element 12:00 | |||
| Lecture 9 - The Inverse Property 29:00 | |||
| Lecture 10 - The Commutative Property 3:00 | |||
| Lecture 11 - Classification of Binary Algebraic Structures 31:00 | |||
| Lecture 12 - Practice Questions on Binary Operations 19:00 | |||
| Annotated Notes - Lecture 7-12 - Classification of Binary Algebraic Structures (152 pages) | |||
| Summary Lecture 1 - Introduction to Algebraic Structure 10:00 | |||
| Summary Lecture 2 - Binary Operation, Closure Property 13:00 | |||
| Summary Lecture 3 - Questions on Binary Operation 14:00 | |||
| Summary Lecture 4 - More Questions on Binary Operation 9:00 | |||
| Summary Lecture 5 - Associative, Commutative Property 10:00 | |||
| Summary Lecture 6 - Questions on Associative, Commutative Property 15:00 | |||
| Annotated Notes - Summary Lectures 1-6 - Group Theory (107 pages) | |||
| Practice Set 1 - Group Theory (67 pages) | |||
| Lecture 13 - Properties of Monoid 11:00 | |||
| Lecture 14 - Group Theory Practice Set-1 Question 25 Solution 28:00 | |||
| Lecture 15 - Practice Questions on Monoid, Group 9:00 | |||
| Lecture 16 - nth Roots of Unity is an Abelian Group under Multiplication 30:00 | |||
| Lecture 17 - Addition Modulo n Group 10:00 | |||
| Lecture 18 - Group Properties 18:00 | |||
| Annotated Notes - Lecture 13-18 - Some Important Groups & Group Properties (94 pages) | |||
| Lecture 19 - Associativity & Parentheses 22:00 | |||
| Lecture 20 - Cayley Table 26:00 | |||
| Annotated Notes - Lecture 19, 20 - Cayley Table (46 pages) | |||
| Lecture 21 - Group Properties Part 2 27:00 | |||
| Annotated Notes - Lecture 21 - Group Properties Part 2 (31 pages) | |||
| Lecture 22 - Checking Associative Property in the Cayley Table 14:00 | |||
| Annotated Notes - Lecture 22 - Checking Associative Property in the Cayley Table (13 pages) | |||
| Lecture 23A - Cayley Table of a Group 26:00 | |||
| Annotated Notes - Lecture 23A - Cayley Table of a Group (32 pages) | |||
| Lecture 23B - Practice Question Cayley Table 26:00 | |||
| Annotated Notes - Lecture 23B - Practice Question Cayley Table (20 pages) | |||
| Lecture 24 - Monoid Vs Group 5:00 | |||
| Annotated Notes - Lecture 24 - Monoid Vs Group (4 pages) | |||
| Lecture 25A - Groups of Small Order 15:00 | |||
| Lecture 25B - Groups of Order 4 22:00 | |||
| Lecture 25C - Practice Question - Group of Small Order 16:00 | |||
| Annotated Notes - Lecture 25 - Groups of Small Order (37 pages) | |||
| Lecture 26 - Power of an Element in a Group 23:00 | |||
| Lecture 27A - Subgroup 35:00 | |||
| Lecture 27B - Subgroup Generated by an Element 23:00 | |||
| Annotated Notes - Lecture 26,27 - Subgroup (64 pages) | |||
| Lecture 28 - Relatively Prime Integers (Coprime Numbers) 10:00 | |||
| Lecture 29 - Multiplication Modulo n Group - Unit Group Un 75:00 | |||
| Lecture 30 - Practice Question - Multiplication Modulo Group Un 21:00 | |||
| Annotated Notes - Lecture 28-30 - Multiplication Modulo n Group - Unit Group Un (110 pages) | |||
| Lecture 31 - Practice Question on Subgroup Generated by an Element 15:00 | |||
| Lecture 32A - Order of an Element in a Group 42:00 | |||
| Lecture 32B - Summary Lecture - Order of an Element 13:00 | |||
| Lecture 33 - Cyclic Group 33:00 | |||
| Lecture 34 - Practice Question on Subgroup 18:00 | |||
| Annotated Notes - Lecture 31-34 - Order of an Element & Cyclic Group (104 pages) | |||
| Lecture 35A - A lot of Practice Questions on Groups 64:00 | |||
| Lecture 35B - Some More Practice Questions on Groups 18:00 | |||
| Lecture 36 - Lagrange's Theorem 21:00 | |||
| Lecture 37 - Summary - Groups of Specific Orders 7:00 | |||
| Lecture 38 - Alternative Definitions of Abelian Group 35:00 | |||
| Lecture 39 - Intersection of Subgroups 6:00 | |||
| Lecture 40 - Alternative Definitions of Subgroup 7:00 | |||
| Annotated Notes - Lecture 35-40 - Lagrange's Theorem (187 pages) | |||
| GATE PYQs - Detailed Video Solutions - Group Theory | |||
| Weekly Quiz 16 - Group Theory - With Video Solution Available | |||
| Rate & Review | |||
| Module 8 - Combinatorics | |||
| Lecture 1 - Introduction to Combinatorics 7:00 | |||
| Lecture 2 - The Sum Rule 31:00 | |||
| Lecture 3A - The Product Rule 30:00 | |||
| Lecture 3B - Practice Questions 11:00 | |||
| Lecture 4 - The Subtraction Rule 31:00 | |||
| Annotated Notes - Lecture 1-4 - Basic Counting Principles (95 pages) | |||
| Lecture 5 - Practice Questions 30:00 | |||
| Lecture 6 - Counting By Case 25:00 | |||
| Lecture 7 - The Complement Rule 54:00 | |||
| Lecture 8A - The Division Rule 14:00 | |||
| Annotated Notes - Lecture 5-8A - The Complement, By Case Rule (117 pages) | |||
| Lecture 8B - The Division Rule 51:00 | |||
| Lecture 9 - Factorial, nCr, nPr 14:00 | |||
| Lecture 10 - Permutation & Combination 28:00 | |||
| Lecture 11 - Combination 21:00 | |||
| Annotated Notes - Lecture 8B-11 - Permutation & Combination (112 pages) | |||
| Lecture 12 - Practice Questions & the Most Common Mistake 64:00 | |||
| Lecture 13 - Two Standard Templates & More Practice Questions 18:00 | |||
| Lecture 14A - Combinatorial Arguments 35:00 | |||
| Annotated Notes - Lecture 12-14A - Two Standard Templates & Combinatorial Arguments (136 pages) | |||
| Lecture 14B - Combinatorial Arguments 28:00 | |||
| Lecture 14C - Combinatorial Arguments 28:00 | |||
| Lecture 14D - Practice Combinatorial Arguments 16:00 | |||
| Lecture 15 - Binomial Theorem 26:00 | |||
| Lecture 16 - Bijective Proofs 13:00 | |||
| Lecture 17 - Permutation with Repetition 27:00 | |||
| Annotated Notes - Lecture 14B-17 - Binomial Theorem, Permutation with repetition (94 pages) | |||
| Annotated Notes - Lecture 14D - Practice Combinatorial Arguments (16 pages) | |||
| Lecture 18A - Many Practice Questions 16:00 | |||
| Lecture 18B - Grid Walk Problems in Combinatorics 29:00 | |||
| Lecture 19A - Distributing Objects into Boxes - DODB 33:00 | |||
| Lecture 19B - Practice Questions on DODB Template | |||
| Lecture 20A - IODB Template - Star Bar Problem 30:00 | |||
| Annotated Notes - Lecture 18-20A - Distributing Objects into Boxes - DODB & IOIB (89 pages) | |||
| Annotated Notes - Lecture 19B - Practice Questions on DODB Template (33 pages) | |||
| Lecture 20B - Combination with Repetition - IODB Template 2 30:00 | |||
| Lecture 20C - Non-Negative Integer Solutions - IODB Template 3 30:00 | |||
| Lecture 20D - Multiset Problem - IODB Template 4 10:00 | |||
| Lecture 20E - Non-Decreasing integer Sequence - IODB Template 5 23:00 | |||
| Annotated Notes - Lecture 20B-20E - IODB Templates (97 pages) | |||
| Lecture 20F - Practice Questions - IODB 34:00 | |||
| Lecture 20G - Integer Composition - IODB Template 6 20:00 | |||
| Lecture 21 - DOIB Problem 36:00 | |||
| Lecture 22 - IOIB Problem 18:00 | |||
| Lecture 23 - Summary - Distributing Objects into Boxes | |||
| Annotated Notes - Lecture 20F-23 - DOIB, IOIB Problems (125 pages) | |||
| Lecture 24A - Inclusion Exclusion Principle 76:00 | |||
| Lecture 24B - Practice Questions - Inclusion Exclusion 76:00 | |||
| Annotated Notes - Lecture 24A,24B - Inclusion Exclusion Principle (109 pages) | |||
| Lecture 24C - Derangement - Inclusion Exclusion Principle Application 56:00 | |||
| Lecture 24D - Onto Functions | |||
| Annotated Notes - Lecture 24C,24D - Derangement, Onto Functions (74 pages) | |||
| Lecture 25A - Generating Function 40:00 | |||
| Lecture 25B - Generating Function Part 2 30:00 | |||
| Lecture 25C - Generating Function Part 3 14:00 | |||
| Annotated Notes - Lecture 25A-25C - Generating Function (84 pages) | |||
| Lecture 25D - Practice Questions - Generating Function Part 4 33:00 | |||
| Lecture 25E - AGP Series & Generating Function Part 5 36:00 | |||
| GATE CSE 2022 Question on Generating Function 17:00 | |||
| Lecture 25F - Extended Binomial Theorem - Generating Function - Part 6 40:00 | |||
| GATE CSE 2016 Question on Generating Function 5:00 | |||
| GATE CSE 2017 Question on Ordinary Generating Function 5:00 | |||
| GATE CSE 2018 Question on Generating Function 3:00 | |||
| GATE CSE 2005 Question on Generating Function 4:00 | |||
| TIFR CSE 2010 Question on Generating Function 6:00 | |||
| Lecture 25G - Summary of Generating Function 11:00 | |||
| Annotated Notes - Lecture 25D-25F - Extended Binomial Theorem & Generating Function (164 pages) | |||
| Lecture 26 - Recurrence Relations | |||
| Annotated Notes - Lecture 26 - Recurrence Relations (73 pages) | |||
| Practice Set 1 - Combinatorics - Berkeley University Questions (51 pages) | |||
| Practice Set-1 Solutions - Berkeley Questions - Combinatorics | |||
| Annotated Notes - Practice Set 1 Solutions - Berkeley Questions (163 pages) | |||
| Practice Set 2 - Recurrence Relations ALL Standard Questions - Combinatorics (44 pages) | |||
| Practice Set-2 Solutions - Recurrence Relation Questions - Combinatorics | |||
| Annotated Notes - Practice Set 2 Solution - Recurrence Relations (115 pages) | |||
| Lecture 27A - Pigeonhole Principle | |||
| Annotated Notes - Lecture 27A - Pigeonhole Principle (144 pages) | |||
| Lecture 27B - The Generalized Pigeonhole Principle | |||
| Annotated Notes - Lecture 27B - The Generalized Pigeonhole Principle (136 pages) | |||
| Lecture 27C - Practice - Pigeonhole Principle | |||
| Annotated Notes - Lecture 27C - Practice Pigeon Hole Principle (112 pages) | |||
| Practice Set 3 - Derangement ALL Standard Questions - Combinatorics (36 pages) | |||
| Practice Set 3 Solutions - Derangement - Combinatorics | |||
| Annotated Notes - Practice Set 3 Solutions - Derangement All Questions (169 pages) | |||
| Weekly Quiz 19 - Combinatorics (5 pages) | |||
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| Module 9 - Graph Theory | |||
| Lecture 1 - Why Study Graph Theory - The Motivation 45:00 | |||
| Lecture 2 - Basic Terminology - Graph Theory 34:00 | |||
| Lecture 2B - Basics - Degree, Adjacency 21:00 | |||
| Annotated Notes - Lecture 1-2B - Introduction & Terminology (88 pages) | |||
| Lecture 2C - Practice Questions - Basics 27:00 | |||
| Lecture 3A - Handshaking Theorem 19:00 | |||
| Lecture 3B - Handshaking Theorem for Directed Graphs 11:00 | |||
| Lecture 4A - Cycle, Path, Walk in Simple Graphs 31:00 | |||
| Annotated Notes - Lecture 2C-4A - Handshaking Theorem (77 pages) | |||
| Lecture 4B - Walk, Path Revise & Practice 25:00 | |||
| Lecture 4C - Distance and Diameter 15:00 | |||
| Lecture 5A - Special Type of Graphs 21:00 | |||
| Lecture 5B - Special Type of Graphs Part 2 45:00 | |||
| Lecture 6 - GATE & TIFR Questions on Degree Concept 19:00 | |||
| Lecture 7 - Subgraph 35:00 | |||
| Annotated Notes - Lecture 4B-7 - Walk, Path, Subgraph, Diameter (160 pages) | |||
| GATE CSE 2001 - Number of Simple Graphs 6:00 | |||
| Lecture 8A - Graph Isomorphism Part 1 - Definition 58:00 | |||
| Lecture 8B - GATE 2012 Question - Graph Isomorphism 4:00 | |||
| My OLD Video for GATE 2012 Question | |||
| Lecture 8C - Graph Isomorphism is an Equivalence Relation 5:00 | |||
| Lecture 8D - Graph Complement and Self Complementary Graph 13:00 | |||
| Lecture 8E - Practice - Graph Isomorphism 10:00 | |||
| Lecture 9A - Connected Components 24:00 | |||
| Annotated Notes - Lecture 8A-9A - Graph Isomorphism, Complement, Components (81 pages) | |||
| Lecture 9B - Complement of a Disconnected graph is Connected 35:00 | |||
| Lecture 9C - TIFR CSE 2018 Question 43:00 | |||
| Lecture 9D - A Simple Practice Question 1:00 | |||
| Lecture 10A - Bipartite Graphs 33:00 | |||
| Lecture 10B - Complete Bipartite Graph 9:00 | |||
| Annotated Notes - Lecture 9B-10B - Bipartite Graphs, Graph Complement (82 pages) | |||
| Lecture 10C - Practice Questions - Bipartite Graphs 41:00 | |||
| Lecture 11A - Trees - Part 1 - Cyclic Graphs Acyclic Graph 11:00 | |||
| Lecture 11B - Trees - Part 2 - Tree and Forest Definitions 8:00 | |||
| Lecture 11C - Trees - Part 3 - Many Definitions of Tree 74:00 | |||
| Lecture 11D - Tree Part 4 - Every Tree has at least two vertices of degree 1 10:00 | |||
| Annotated Notes - Lecture 10C-11D - Trees, Rooted Tree (141 pages) | |||
| Lecture 11E - ALL Questions - Trees, Forest 54:00 | |||
| Lecture 12A - Rooted Trees 29:00 | |||
| Lecture 12B - Rooted Tree Part 2 - Binary Tree. Full Binary Tree 46:00 | |||
| Lecture 13A - Questions Related to Components 17:00 | |||
| Annotated Notes - Lecture 11E-13A - Rooted Trees, Binary Tree (161 pages) | |||
| Lecture 13B - Questions on Rooted Trees 34:00 | |||
| Lecture 14A - Clique, Independent Set - Part 1 43:00 | |||
| Lecture 14B - UGC NET CSE 2016 Clique Question 11:00 | |||
| Lecture 14C - Clique, Independent Set - Part 3 18:00 | |||
| Annotated Notes - Lecture 13B-14C - Clique, Independent Set (85 pages) | |||
| Lecture 15A - Vertex Cover, Edge Cover - Part 1 46:00 | |||
| Lecture 15B - Vertex Cover, Edge Cover - Part 2 - Analysis 28:00 | |||
| Lecture 15C - Relation between Vertex Cover & Independent Set 22:00 | |||
| Meme - Relation between Vertex Cover & Independent Set | |||
| Annotated Notes - Lecture 15A-15C - Vertex Cover, Edge Cover (90 pages) | |||
| Lecture 16A - Matching Part 1 - Perfect Matching, Matching Number 51:00 | |||
| Lecture 16B - Matching Part 2 - Matching & Covering Analysis 62:00 | |||
| Annotated Notes - Lecture 16A-16B - Matching (104 pages) | |||
| Lecture 17A - Graph Coloring Part 1 - Vertex Coloring 47:00 | |||
| Lecture 17B - Graph Coloring Part 2 - Greedy Algorithm for Vertex Coloring 41:00 | |||
| Lecture 17C - Graph Coloring Part 3 - All GATE TIFR Questions 53:00 | |||
| Annotated Notes - Lecture 17A-17C - Graph Coloring - Vertex Coloring (119 pages) | |||
| Lecture 17D - Graph Coloring Part 4 - Brooks Theorem for Vertex Coloring 9:00 | |||
| Lecture 17E - Graph Coloring Part 5 - Edge Coloring 40:00 | |||
| Annotated Notes - Lecture 17D-17E - Edge Coloring (57 pages) | |||
| Lecture 18 - Graph Realization Problem - Havel Hakimi Theorem 73:00 | |||
| Annotated Notes - Lecture 18 - Graph Realization Problem - Havel Hakimi Theorem (59 pages) | |||
| Lecture 19A - Cut Vertex, Cut Edge 62:00 | |||
| Lecture 19B - Connectivity Number, Vertex Cut, Edge Cut 69:00 | |||
| Annotated Notes - Lecture 19A-19B - Connectivity Number, Cut (131 pages) | |||
| Lecture 20A - Strongly Connected Components - Part 1 59:00 | |||
| Lecture 20B - Weakly Connected Graph 4:00 | |||
| Lecture 20C - Strongly Connected Components - Part 3 - Associated DAG 26:00 | |||
| Annotated Notes - Lecture 20A-20C - Strongly Connected Components (102 pages) | |||
| Lecture 21A - Euler Circuit & Graph | |||
| Lecture 21B - Hamiltonian Cycle & Graphs | |||
| Annotated Notes - Lecture 21A-21B - Euler Graph & Hamiltonian Graph (232 pages) | |||
| Euler & Hamiltonian Cycles - ALL Previous Exam Questions | |||
| Lecture 22A - Planar Graph Introduction 38:00 | |||
| Lecture 22B - Planar Graphs - Faces & Degree of a face | |||
| Annotated Notes - Lecture 22A-22B - Planar Graphs (181 pages) | |||
| Lecture 22C - Planar Graph - Euler Formula | |||
| Lecture 22D - Planar Graphs - Some Important Results & Four Color Theorem 49:00 | |||
| Annotated Notes - Lecture 22C-22D - Planar Graph - Euler Formula (179 pages) | |||
| Lecture 23A - Adjacency Matrix, Adjacency List 7:00 | |||
| Lecture 23B - GATE 1987-9d Adjacency List | |||
| Lecture 23C - GATE 1988-2xvi Adjacency Matrix | |||
| Lecture 23D - TIFR CSE 2015 Adjacency Matrix 6:00 | |||
| Annotated Notes - Lecture 23 - Adjacency Matrix, Adjacency List (16 pages) | |||
| Lecture 24A - Powers of Adjacency Matrix of a Graph 93:00 | |||
| Lecture 24B - Applications of Powers of Adjacency Matrix of a Graph 73:00 | |||
| Annotated Notes - Lecture 24A-24B - Powers of Adjacency Matrix of a Graph (120 pages) | |||
| Lecture 24C - Applications of Powers of Adjacency Matrix Part 2 121:00 | |||
| Annotated Notes - Lecture 24C - Applications of Powers of Adjacency Matrix Part 2 (84 pages) | |||
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| Students' Hand Written Notes | |||
| Notes by Quantum City (AIR 107, GATE CS 2024, Shreyas Rathod) - Discrete Mathematics Notes (114 pages) | |||
| Propositional Logic Notes - Students Notes by Abhishek Patel (47 pages) | |||
| First Order Logic Notes - Students Notes by Abhishek Patel (63 pages) | |||
| Handwritten Notes by Karan Agrawal (AIR 102 GATE CS 2024) - Discrete Mathematics | |||
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| 1.0 Basics (40 pages) | |||
| 3.0 Propositional Logic (57 pages) | |||
| 4.0 First Order Logic (68 pages) | |||
| 5.0 Set Theory (115 pages) | |||
| 6.0 Functions (27 pages) | |||
| 7.0 Group Theory (54 pages) | |||
| 8.0 Combinatorics (99 pages) | |||
| 9.0 Graph Theory (116 pages) | |||
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