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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 (149 ratings) |
Instructor: Deepak Poonia (MTech IISc Bangalore, GATE CSE AIR 53; 67; 107)
Language: English
Enrolled Learners: 23118
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 understadning. No By-hearting of formulas, tables or theorems. Understand everything with proofs-intuitions-ideas.
2. No Prerequisites: Every concept is taught from basics, without assuming any prior knowledge whatsoever.
3. Daily Homeworks: 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 which summarises everything 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, solved even after tha live quiz is over.
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 faculties resolve students' Doubts. So, our students don't have to go anywhere else for asking doubts.
| Module 1 - Fundamentals of Computer Science | |||
| Lecture 1 - Summation - Sigma notation, Shifting Indices, & Properties of Sigma | |||
| Annotated Notes - Lecture 1 - Summation (43 pages) | |||
| Homework 1 - Fundamental Course - Summation (16 pages) | |||
| Lecture 2 - Sequence & Series | |||
| Annotated Notes - Lecture 2 - Sequence & Series (57 pages) | |||
| Homework 2 - Fundamental Course - Sequence & Series (13 pages) | |||
| Lecture 3 - Geometric Progression | |||
| Annotated Notes - Lecture 3 - Geometric Progression (57 pages) | |||
| Homework 3 - Fundamental Course - Geometric Progression (13 pages) | |||
| Lecture 4A - Modular Arithmetic | |||
| Annotated Notes - Lecture 4A - Modular Arithmetic (64 pages) | |||
| Homework 4 - Fundamental Course - Modular Arithmetic (9 pages) | |||
| Lecture 4B - Modular Arithmetic Part 2 | |||
| Annotated Notes - Lecture 4B - Modular Arithmetic Part 2 (70 pages) | |||
| Homework 5 - Fundamental Course - Modular Arithmetic (22 pages) | |||
| Lecture 5A - Logarithm Definition and All Properties 61:00 | |||
| Lecture 5B - Logarithm Exercise Questions 26:00 | |||
| Lecture 5C - Logarithm Questions, Graph, and Log in Computer science 42:00 | |||
| Annotated Notes - Lecture 5A-5C - Logarithms and Properties (110 pages) | |||
| (NEW) Lecture 6 - GATE PYQs on Fundamental Topics (Series and Logarithms) 112:00 | |||
| Annotated Notes - Lecture 6 - GATE PYQs on Fundamental Topics (81 pages) | |||
| Lecture 7A - Proof Techniques Part 1 - Direct Proofs | |||
| Annotated Notes - Lecture 7A - Proof Techniques Part 1 - Direct Proofs (106 pages) | |||
| Homework 6 - Proof Techniques Part 1 - Direct Proof (25 pages) | |||
| Lecture 7B - Proof Techniques Part 2 - Proof by Contrapositive & Contradiction | |||
| Annotated Notes - Lecture 7B - Proof Techniques Part 2 - Proof by Contrapositive & Contradiction (124 pages) | |||
| Homework 7 - Proof Techniques Part 2 - Contraposition & Contradiction (22 pages) | |||
| Lecture 7C - Proof by Mathematical Induction - Proof Technique | |||
| Annotated Notes - Lecture 7C - Proof by Mathematical Induction (54 pages) | |||
| Lecture 8 - Proof Techniques Homework 6,7 Solutions | |||
| Annotated Notes - Lecture 8 - Proof Techniques Homework 6,7 Solutions (85 pages) | |||
| (NEW) Lecture 9 - Practice Questions on Proof Techniques | |||
| Annotated Notes - Lecture 9 - Practice Questions on Proof Techniques (48 pages) | |||
| Weekly Quiz 1 - Fundamental Course - Sequence, Series & Modular Arithmetic | |||
| Weekly Quiz 2 - Proof Techniques - Fundamental Course | |||
| 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 | |||
| Propositional Logic Complete Summary & GATE PYQs | |||
| 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 | |||
| Rate & Review | |||
| Propositional Logic - Summary, GATE PYQs & Practice Questions | |||
| Module 4 - First Order Logic | |||
| First Order Logic - Complete Summary, ALL GATE PYQs & Practice | |||
| 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) | |||
| Rate & Review | |||
| First Order Logic - Complete Summary, ALL GATE PYQs & Practice | |||
| 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) | |||
| (NEW) Refinement of a Partition | GATE 2007, 1998 127:00 | |||
| Annotated Notes - Refinement of a Partition (128 pages) | |||
| (NEW) 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 | |||
| (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 Question - GATE CSE 1989 - Number of Commutative Binary Operations 15:00 | |||
| GATE Question - GATE CSE 1994 | Associative Non-Commutative Operation on N 8:00 | |||
| GATE Question - GATE CSE 2013 - Binary operation ⊕ Question 11:00 | |||
| GATE Question - GATE CSE IT 2006 - Identity Element 10:00 | |||
| GATE Question - GATE CSE 2003 - Binary Operators + and * 14:00 | |||
| GATE Question - GATE CSE 1988 - Abelian Group 7:00 | |||
| GATE Question - GATE CSE 1992 - Group of Even Order 14:00 | |||
| Weekly Quiz 16 - Group Theory - With Video Solution Available | |||
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| 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 18 - Many Practice Questions 16:00 | |||
| 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 Disconnected Graph 34:00 | |||
| 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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