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Unlock the Power of Problem Solving. Learn Discrete Mathematics and Master the Foundation of Computer Science.
Instructor: Deepak Poonia (MTech IISc Bangalore, GATE CSE AIR 53; 67; 107)
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 | |||
| Lecture 1B - Proof Techniques Part 2 - Proof by Contrapositive & Contradiction | |||
| Annotated Notes - Lecture 1B - Proof Techniques Part 2 - Proof by Contrapositive & Contradiction | |||
| Lecture 1C - Proof by Mathematical Induction - Proof Technique | |||
| Annotated Notes - Lecture 1C - Proof by Mathematical Induction | |||
| Homework 1 - Proof Techniques - Direct Proof | |||
| Homework 2 - Proof Techniques - Contraposition & Contradiction | |||
| Homework 1,2 Video Solutions - Proof Techniques | |||
| Lecture 2 - Practice Questions on Proof Techniques | |||
| Annotated Notes - Lecture 2 - Practice Questions on Proof Techniques | |||
| Weekly Quiz - Proof Techniques | |||
| Rate & Review | |||
| Module 2 - Introduction to Discrete Mathematics | |||
| Lecture 1 - Introduction to Discrete Mathematics | |||
| Summary Lecture 1 - Introduction to Discrete Mathematics | |||
| Module 3 - Propositional Logic | |||
| Lecture 1 - Introduction to Mathematical Logic | |||
| Annotated Notes - Lecture 1 - Introduction to Mathematical Logic | |||
| Summary Lecture 1 - Introduction to Mathematical Logic | |||
| Lecture 2 - Proposition & Propositional Variable | |||
| Annotated Notes - Lecture 2 - Proposition & Propositional Variable | |||
| Summary Lecture 2 - Proposition & Propositional Variable, Truth Value | |||
| Is it a Proposition?? - A Dumb Question!! | |||
| Lecture 3 - Atomic & Compound Propositions | |||
| Annotated Notes - Lecture 3 - Atomic & Compound Propositions | |||
| Summary Lecture 3A - Atomic Proposition. Compound Proposition | |||
| Summary Lecture 3B - Logical Connectives | |||
| Lecture 4 - Negation Operator - Logical Connectives | |||
| Lecture 5 - Conjunction (AND) Operator - Logical Connectives | |||
| Lecture 6 - Disjunction (OR) Operator - Logical Connectives | |||
| Annotated Notes - Lecture 4,5,6 - Logical Connectives | |||
| Lecture 7 - Exclusive-OR Operator - Logical Connectives | |||
| Lecture 8 - NAND NOR Operator - Logical Connectives | |||
| Annotated Notes - Lecture 7,8 - Logical Connectives | |||
| Lecture 9 - Implication Operator - Logical Connectives | |||
| Lecture 10 - Implication Operator Continued | |||
| Annotated Notes - Lecture 9,10 - Implication Operator | |||
| Lecture 11 - Important Points about Implication Operator | |||
| Lecture 12 - Necessary & Sufficient Condition - Implication Operator | |||
| Lecture 13 - Various English Translations of Implication Statement | |||
| Annotated Notes - Lecture 11,12,13 - Implication Operator Continued | |||
| Lecture 14 - Bi-implication Operator - Logical Connective | |||
| Annotated Notes - Lecture 14 - Bi-implication Operator | |||
| Lecture 15 - Property Vs Definition - Implication Vs Bi-implication Statements | |||
| Annotated Notes - Lecture 15 - Property Vs Definition | |||
| Lecture 16 - Propositional Variable Vs Propositional Formula | |||
| Annotated Notes - Lecture 16 - Propositional Variable Vs Propositional Formula | |||
| Homework 1 - Logical Connectives - Propositional Logic | |||
| Homework 2 - Implication Bi-implication - Propositional Logic | |||
| Homework 1,2 Video Solution & Notes | |||
| Lecture 17 - Propositional Formula Revisited | |||
| Lecture 18 - Truth Table | |||
| Annotated Notes - Lecture 17,18 - Propositional Formula Revisited, Truth Table | |||
| Homework 3 - Standard Questions - Propositional Logic | |||
| Homework 3 Video Solution | |||
| Lecture 19 - Tautology, Contradiction, Contingency | |||
| Lecture 20 - By Case Method | |||
| Lecture 21 - By Case Method Practice | |||
| Lecture 22 - Logical Equivalence | |||
| Lecture 23 - Logical Equivalence Practice | |||
| Annotated Notes - Lecture 19-23 - Tautology, Equivalence | |||
| Weekly Quiz 1 - Propositional Logic | |||
| Lecture 24 - Converse, Contrapositive of Conditional Statement | |||
| Lecture 25 - English-Logic Translation | |||
| Lecture 26 - Unless Word - English-Logic Translation | |||
| Annotated Notes - Lecture 24-26 - English-Logic Translation, Converse, Unless Word | |||
| Lecture 27 - Logical Laws - Commutative Property | |||
| Lecture 28 - Logical Laws - Associative Property | |||
| Lecture 29 - Logical Laws - Idempotent Property | |||
| Lecture 30 - Logical Laws - Distributive Law | |||
| Lecture 31 - Logical Laws - De Morgan's Laws | |||
| Lecture 32 - Logical Laws - Implication Laws | |||
| Lecture 33 - Simplification Using Logical Laws | |||
| Lecture 34 - Analysis of Implication | |||
| Annotated Notes - Lecture 27-34 - Logical Laws | |||
| Lecture 35 - Logical Arguments | |||
| Lecture 36 - Rules of Inference - Logical Arguments | |||
| Annotated Notes - Lecture 35,36 - Logical Arguments | |||
| Lecture 37 - The Inference Symbol | |||
| Annotated Notes - Lecture 37 - The Inference Symbol | |||
| 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 | |||
| Lecture 2 - Objects & Domain in First Order Logic | |||
| Lecture 3 - Predicates in First Order Logic | |||
| Lecture 4 - Creating Proposition from predicate | |||
| Annotated Notes - Lecture 2,3,4 - Objects & Predicates | |||
| Lecture 5 - Quantifiers Introduction | |||
| Lecture 6 - Universal Quantifier | |||
| Lecture 7 - Existential Quantifier | |||
| Lecture 8 - Quantifiers Practice | |||
| Lecture 9 - Quantifiers Summary | |||
| Annotated Notes - Lecture 5-9 - Quantifiers | |||
| Lecture 10 - Quantifiers Tricky Points | |||
| Lecture 11 - English-FOL Translation Part 1 | |||
| Lecture 12 - English-FOL Translation Part 2 | |||
| Lecture 13 - English-FOL Translation Part 3 | |||
| Lecture 14 - English-FOL Translation Part 4 | |||
| Lecture 15 - English-FOL Translation Part 5 | |||
| Lecture 16 - English-FOL Translation Part 6 | |||
| Lecture 17 - English-FOL Translation Part 7 | |||
| Annotated Notes - Lecture 10-17 - English-FOL Translation | |||
| Lecture 18 - Revision of English-FOL Translation | |||
| Lecture 19 - A LOT of Practice of English-FOL Translation | |||
| Lecture 20 - Bounded Variable | |||
| Lecture 21 - Free Variable Vs Bounded Variable | |||
| Lecture 22 - Practice - Bounded Variable Free Variable | |||
| Lecture 23 - Important Note About Free Variables | |||
| Lecture 24 - Scope of a Quantifier | |||
| Annotated Notes - Lecture 20-24 - Free Variable, Bounded Variable, Scope of a Quantifier | |||
| Lecture 25 - Nested Quantifiers Part 1 - Need of Nested Quantifiers | |||
| Lecture 26 - Nested Quantifiers Part 2 - All Four Standard Templates | |||
| Lecture 27 - Nested Quantifiers Part 3 - Examples, Variations | |||
| Annotated Notes - Lecture 25-27 - Nested Quantifiers | |||
| Lecture 28 - More Practice of English - FOL Translation | |||
| Lecture 29 - Even More Practice of English - FOL Translation | |||
| Annotated Notes - Lecture 18, 19, 28, 29 - English-FOL Translation Examples Part 1-4 | |||
| Lecture 30 - Practice - Free Variable, Bounded Variable, Scope | |||
| Annotated Notes - Lecture 30 - Practice - Free Variable, Bounded Variable, Scope | |||
| Homework 1 - Quantifiers - First Order Logic | |||
| Homework 1 - Detailed Video Solutions - First Order Logic | |||
| Lecture 31 - Negation of quantifiers | |||
| Annotated Notes - Lecture 31 - Negation of quantifiers | |||
| Lecture 32 - Validity, Satisfiability of a FOL Expression | |||
| Lecture 33 - Validity, Satisfiability of a FOL Expression Part 2 | |||
| Annotated Notes - Lecture 32,33 - Validity, Satisfiability of a FOL Expression | |||
| Lecture 34 - Validity of FOL Expression Involving Implication | |||
| Lecture 35 - Equivalence of FOL Expressions | |||
| Lecture 36 - Distributive Properties of Quantifiers | |||
| Annotated Notes - Lecture 34-36 - Distributive Properties of Quantifiers | |||
| Lecture 37 - Practice - First Order Logic | |||
| Lecture 38 - Null Quantification Rule | |||
| Annotated Notes - Lecture 37,38 - Null Quantification Rule | |||
| Lecture 39 - Arguments in First Order Logic | |||
| Annotated Notes- Lecture 39 - Arguments in First Order Logic | |||
| NOTE About Next Lectures | |||
| OPTIONAL Lecture 1 - Interpretation, Model in Propositional Logic | |||
| OPTIONAL Lecture 2 - Interpretation, Model in First Order Logic | |||
| Annotated Notes - OPTIONAL Lecture 1,2 - Interpretation, Model in Propositional Logic, FOL | |||
| OPTIONAL Lecture 3 - Uniqueness Quantifier | |||
| Annotated Notes - OPTIONAL Lecture 3 - Uniqueness Quantifier | |||
| Optional Lecture 4 - Tautology in First Order Logic | |||
| Annotated Notes - Optional Lecture 4 - Tautology in First Order Logic | |||
| First Order Logic - Complete Summary, ALL GATE PYQs & Practice | |||
| Rate & Review | |||
| Module 5 - Set Theory | |||
| Lecture 1 - Set Definition | |||
| Lecture 2 - Finite Set, Infinite Set | |||
| Lecture 3 - Cardinality of a Set | |||
| Lecture 4 - Set Representations | |||
| Annotated Notes - Lecture 1-4 - Set | |||
| Lecture 5 - Subset | |||
| Annotated Notes - Lecture 5 - Subset | |||
| Lecture 6 - Powerset of a Set | |||
| Lecture 7 - Set Operations | |||
| Lecture 8 - Set Equality | |||
| Annotated Notes - Lecture 6-8 - Set Operations | |||
| Weekly Quiz 1 - Set Theory | |||
| Lecture 9 - Understanding Set Operations | |||
| Annotated Notes - Lecture 9 - Understanding Set Operations | |||
| Lecture 10 - Proofs involving Sets, Set Equality, Subset | |||
| Lecture 11 - Set Identities | |||
| Lecture 12 - Proofs involving Power Sets | |||
| Annotated Notes - Lecture 10-12 - Proofs involving Sets | |||
| Practice Set 1 - Set, Subset - Set Theory (Video Solution Below) | |||
| Practice Set 1 - Video Solutions | |||
| Lecture 13 - Ordered Pairs | |||
| Lecture 14 - Cartesian Product of Sets | |||
| Annotated Notes - Lecture 13,14 - Cartesian Product | |||
| Weekly Quiz 2 - Set Theory | |||
| Lecture 15 - Relations | |||
| Lecture 16 - Counting Number of Relations | |||
| Lecture 17 - Relation on a Set | |||
| Annotated Notes - Lecture 15-17 - Relations | |||
| Lecture 18 - Understanding Relations Part 1 | |||
| Lecture 19 - Understanding Relations Part 2 | |||
| Lecture 20 - Types of Binary Relations | |||
| Lecture 21 - Reflexive Relation | |||
| Annotated Notes - Lecture 18-21 - Understanding Relations & Reflexive Relation | |||
| Lecture 22 - Symmetric Relation | |||
| Lecture 23 - Antisymmetric Relation | |||
| Annotated Notes - Lecture 22,23 - Symmetric Relation | |||
| Lecture 24 - Antisymmetric Relation Definition 2 | |||
| Lecture 25 - Asymmetric Relation | |||
| Example 1 - Symmetric, Antisymmetric, Asymmetric | |||
| Example 2 - Symmetric, Antisymmetric, Asymmetric | |||
| Lecture 26 - Transitive Relation | |||
| Example 1 - Transitive Relation | |||
| Annotated Notes - Lecture 24-26 - Transitive Relation | |||
| Lecture 27 - Equivalence Relation Definition | |||
| Annotated Notes - Lecture 27 - Equivalence Relation Definition | |||
| Lecture 28 - Partition of a Set | |||
| Annotated Notes - Lecture 28 - Partition of a Set | |||
| Summary Lecture - Partition of a Set | |||
| Annotated Notes - Summary Lecture - Partition of a Set | |||
| Lecture 29 - Equivalence Relation Complete Analysis Part 1 | |||
| Annotated Notes - Lecture 29 - Equivalence Relation Complete Analysis Part 1 | |||
| Practice Set 2 - Relations - Set Theory (Video Solution Below) | |||
| Practice Set 2 - Video Solutions | |||
| Lecture 30 - Equivalence Relation Complete Analysis Part 2 | |||
| Lecture 31 - Graph of Equivalence Relation | |||
| Lecture 32 - Practice Equivalence Relation | |||
| Annotated Notes - Lecture 30-32 - Equivalence Relation Complete Analysis Part 2 | |||
| Summary Lecture - Equivalence Relations | |||
| Annotated Notes - Summary Lecture - Equivalence Relations | |||
| Practice Set 3 - Equivalence Relations - Set Theory (Video Solution Below) | |||
| Practice Set 3 - Video Solutions | |||
| Lecture 33 - Partial Order Relation | |||
| Annotated Notes - Lecture 33 - Partial Order Relation | |||
| Lecture 34 - Total Order Relation | |||
| Lecture 35 - Hasse Diagram of POSET | |||
| Lecture 36 - Special Elements of POSET | |||
| Annotated Notes - Lecture 34-36 - Total Order Relation, Hasse Diagram, Elements of POSET | |||
| Lecture 37 - Practice Questions on Hasse Diagrams | |||
| Lecture 38 - Upper Bound, Lower Bound, LUB, GLB | |||
| Annotated Notes - Lecture 37,38 - Upper Bound, Lower Bound, LUB, GLB | |||
| Lecture 39 - Practice Questions on GLB, LUB | |||
| Lecture 40 - Hasse Diagram of a Total Order Relation | |||
| Annotated Notes - Lecture 39,40 - Hasse Diagram of a Total Order Relation | |||
| Lecture 41 - Lattice | |||
| Annotated Notes - Lecture 41 - Lattice | |||
| Lecture 42 - Hasse Diagram to Partial Order Relation | |||
| Lecture 43 - Hasse Diagram to Partial Order Relation Part 2 | |||
| Annotated Notes - Lecture 42,43 - Hasse Diagram to Partial Order Relation | |||
| Lecture 44 - Properties of Lattices | |||
| Annotated Notes - Lecture 44 - Properties of Lattices | |||
| Lecture 45 - Sublattice | |||
| Lecture 46 - Questions on Minimal, Maximal Elements in POSET Part 1 | |||
| Annotated Notes - Lecture 45,46 - Sublattice | |||
| Lecture 47 - Questions on Minimal, Maximal Elements in POSET Part 2 | |||
| Annotated Notes - Lecture 47 - Questions on Minimal, Maximal Elements in POSET Part 2 | |||
| Practice Set 4 - Partial Order Relations & Lattices - Set Theory (Video Solution Below) | |||
| 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 | |||
| Lecture 49 - Properties of Every Lattice | |||
| Annotated Notes - Lecture 49 - Properties of Every Lattice | |||
| Lecture 50 - Practice Questions on Sublattice | |||
| Annotated Notes - Lecture 50 - Practice Questions on Sublattice | |||
| Lecture 51 - Types of Lattices | |||
| Lecture 52 - Bounded Lattice | |||
| Annotated Notes - Lecture 51, 52 - Bounded Lattice | |||
| Lecture 53 - Identity Property in Lattices, Domination Law | |||
| Lecture 54 - Complemented Lattice | |||
| Annotated Notes - Lecture 53,54 - Identity Property in Lattices, Complemented Lattice | |||
| Weekly Quiz 13 - Equivalence Relation | |||
| Lecture 55 - Distributive Lattice | |||
| Annotated Notes - Lecture 55 - Distributive Lattice | |||
| Lecture 56 - Practice Questions on Types of Lattice | |||
| Lecture 57 - Boolean Lattice | |||
| Lecture 58 - Why Boolean Lattice is called a Boolean Algebra | |||
| Lecture 59 - Complete Analysis of Total Order Relation | |||
| Lecture 60 - Complete Analysis of Powerset Lattice | |||
| Annotated Notes - Lecture 56-60 - Boolean Lattice | |||
| Lecture 61 - Complete Analysis of Divisibility Relation - Part 1 | |||
| Lecture 62 - Complete Analysis of Divisibility Relation - Part 2 | |||
| Annotated Notes - Lecture 61,62 - Division Lattice Dn Complete Analysis | |||
| Lecture 63 - Refinement of a Partition | GATE 2007, 1998 | |||
| Annotated Notes - Refinement of a Partition | |||
| Lecture 64 - Constructing Total Order from Partial Order - GATE 2024, 1997 | |||
| Annotated Notes - Constructing Total Order from Partial Order | |||
| Rate & Review | |||
| Module 6 - Function | |||
| Lecture 1 - Function Definition & Terminology | |||
| Lecture 2 - Number of Functions | |||
| Lecture 3 - Representations of Function, Image of a Subset of Domain | |||
| Lecture 4 - Types of Functions - Injective, Surjective, Bijective | |||
| Annotated Notes - Lecture 1-4 - Functions | |||
| Lecture 5 - Practice Questions on Types of Functions | |||
| Lecture 6 - Set Operations on Relations | |||
| Lecture 7 - Composition Operation | |||
| Annotated Notes - Lecture 5-7 - Operations on Functions | |||
| Lecture 8 - Inverse of a Function | |||
| Annotated Notes - Lecture 8 - Inverse of a Function | |||
| 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 | |||
| (OPTIONAL) Lecture 2 - Abstract Algebra Origin & The Galois Story | |||
| Lecture 3 - Abstract Algebra GATE Syllabus | |||
| Lecture 4 - Binary Operation & The Closure Property | |||
| Lecture 5 - The Associative Property | |||
| Lecture 6 - The Identity Property | |||
| Annotated Notes - Lecture 1-6 - Abstract Algebra & Binary Operation | |||
| Lecture 7 - Practice Questions on Binary Operation | |||
| Lecture 8 - Important Properties of Identity Element | |||
| Lecture 9 - The Inverse Property | |||
| Lecture 10 - The Commutative Property | |||
| Lecture 11 - Classification of Binary Algebraic Structures | |||
| Lecture 12 - Practice Questions on Binary Operations | |||
| Annotated Notes - Lecture 7-12 - Classification of Binary Algebraic Structures | |||
| Summary Lecture 1 - Introduction to Algebraic Structure | |||
| Summary Lecture 2 - Binary Operation, Closure Property | |||
| Summary Lecture 3 - Questions on Binary Operation | |||
| Summary Lecture 4 - More Questions on Binary Operation | |||
| Summary Lecture 5 - Associative, Commutative Property | |||
| Summary Lecture 6 - Questions on Associative, Commutative Property | |||
| Annotated Notes - Summary Lectures 1-6 - Group Theory | |||
| Practice Set 1 - Group Theory | |||
| Lecture 13 - Properties of Monoid | |||
| Lecture 14 - Group Theory Practice Set-1 Question 25 Solution | |||
| Lecture 15 - Practice Questions on Monoid, Group | |||
| Lecture 16 - nth Roots of Unity is an Abelian Group under Multiplication | |||
| Lecture 17 - Addition Modulo n Group | |||
| Lecture 18 - Group Properties | |||
| Annotated Notes - Lecture 13-18 - Some Important Groups & Group Properties | |||
| Lecture 19 - Associativity & Parentheses | |||
| Lecture 20 - Cayley Table | |||
| Annotated Notes - Lecture 19, 20 - Cayley Table | |||
| Lecture 21 - Group Properties Part 2 | |||
| Annotated Notes - Lecture 21 - Group Properties Part 2 | |||
| Lecture 22 - Checking Associative Property in the Cayley Table | |||
| Annotated Notes - Lecture 22 - Checking Associative Property in the Cayley Table | |||
| Lecture 23A - Cayley Table of a Group | |||
| Annotated Notes - Lecture 23A - Cayley Table of a Group | |||
| Lecture 23B - Practice Question Cayley Table | |||
| Annotated Notes - Lecture 23B - Practice Question Cayley Table | |||
| Lecture 24 - Monoid Vs Group | |||
| Annotated Notes - Lecture 24 - Monoid Vs Group | |||
| Lecture 25A - Groups of Small Order | |||
| Lecture 25B - Groups of Order 4 | |||
| Lecture 25C - Practice Question - Group of Small Order | |||
| Annotated Notes - Lecture 25 - Groups of Small Order | |||
| Lecture 26 - Power of an Element in a Group | |||
| Lecture 27A - Subgroup | |||
| Lecture 27B - Subgroup Generated by an Element | |||
| Annotated Notes - Lecture 26,27 - Subgroup | |||
| Lecture 28 - Relatively Prime Integers (Coprime Numbers) | |||
| Lecture 29 - Multiplication Modulo n Group - Unit Group Un | |||
| Lecture 30 - Practice Question - Multiplication Modulo Group Un | |||
| Annotated Notes - Lecture 28-30 - Multiplication Modulo n Group - Unit Group Un | |||
| Lecture 31 - Practice Question on Subgroup Generated by an Element | |||
| Lecture 32A - Order of an Element in a Group | |||
| Lecture 32B - Summary Lecture - Order of an Element | |||
| Lecture 33 - Cyclic Group | |||
| Lecture 34 - Practice Question on Subgroup | |||
| Annotated Notes - Lecture 31-34 - Order of an Element & Cyclic Group | |||
| Lecture 35A - A lot of Practice Questions on Groups | |||
| Lecture 35B - Some More Practice Questions on Groups | |||
| Lecture 36 - Lagrange's Theorem | |||
| Lecture 37 - Summary - Groups of Specific Orders | |||
| Lecture 38 - Alternative Definitions of Abelian Group | |||
| Lecture 39 - Intersection of Subgroups | |||
| Lecture 40 - Alternative Definitions of Subgroup | |||
| Annotated Notes - Lecture 35-40 - Lagrange's Theorem | |||
| 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 | |||
| Lecture 2 - The Sum Rule | |||
| Lecture 3A - The Product Rule | |||
| Lecture 3B - Practice Questions | |||
| Lecture 4 - The Subtraction Rule | |||
| Annotated Notes - Lecture 1-4 - Basic Counting Principles | |||
| Lecture 5 - Practice Questions | |||
| Lecture 6 - Counting By Case | |||
| Lecture 7 - The Complement Rule | |||
| Lecture 8A - The Division Rule | |||
| Annotated Notes - Lecture 5-8A - The Complement, By Case Rule | |||
| Lecture 8B - The Division Rule | |||
| Lecture 9 - Factorial, nCr, nPr | |||
| Lecture 10 - Permutation & Combination | |||
| Lecture 11 - Combination | |||
| Annotated Notes - Lecture 8B-11 - Permutation & Combination | |||
| Lecture 12 - Practice Questions & the Most Common Mistake | |||
| Lecture 13 - Two Standard Templates & More Practice Questions | |||
| Lecture 14A - Combinatorial Arguments | |||
| Annotated Notes - Lecture 12-14A - Two Standard Templates & Combinatorial Arguments | |||
| Lecture 14B - Combinatorial Arguments | |||
| Lecture 14C - Combinatorial Arguments | |||
| Lecture 14D - Practice Combinatorial Arguments | |||
| Lecture 15 - Binomial Theorem | |||
| Lecture 16 - Bijective Proofs | |||
| Lecture 17 - Permutation with Repetition | |||
| Annotated Notes - Lecture 14B-17 - Binomial Theorem, Permutation with repetition | |||
| Annotated Notes - Lecture 14D - Practice Combinatorial Arguments | |||
| Lecture 18A - Many Practice Questions | |||
| Lecture 18B - Grid Walk Problems in Combinatorics | |||
| Lecture 19A - Distributing Objects into Boxes - DODB | |||
| Lecture 19B - Practice Questions on DODB Template | |||
| Lecture 20A - IODB Template - Star Bar Problem | |||
| Annotated Notes - Lecture 18-20A - Distributing Objects into Boxes - DODB & IOIB | |||
| Annotated Notes - Lecture 19B - Practice Questions on DODB Template | |||
| Lecture 20B - Combination with Repetition - IODB Template 2 | |||
| Lecture 20C - Non-Negative Integer Solutions - IODB Template 3 | |||
| Lecture 20D - Multiset Problem - IODB Template 4 | |||
| Lecture 20E - Non-Decreasing integer Sequence - IODB Template 5 | |||
| Annotated Notes - Lecture 20B-20E - IODB Templates | |||
| Lecture 20F - Practice Questions - IODB | |||
| Lecture 20G - Integer Composition - IODB Template 6 | |||
| Lecture 21 - DOIB Problem | |||
| Lecture 22 - IOIB Problem | |||
| Lecture 23 - Summary - Distributing Objects into Boxes | |||
| Annotated Notes - Lecture 20F-23 - DOIB, IOIB Problems | |||
| Lecture 24A - Inclusion Exclusion Principle | |||
| Lecture 24B - Practice Questions - Inclusion Exclusion | |||
| Annotated Notes - Lecture 24A,24B - Inclusion Exclusion Principle | |||
| Lecture 24C - Derangement - Inclusion Exclusion Principle Application | |||
| Lecture 24D - Onto Functions | |||
| Annotated Notes - Lecture 24C,24D - Derangement, Onto Functions | |||
| Lecture 25A - Generating Function | |||
| Lecture 25B - Generating Function Part 2 | |||
| Lecture 25C - Generating Function Part 3 | |||
| Annotated Notes - Lecture 25A-25C - Generating Function | |||
| Lecture 25D - Practice Questions - Generating Function Part 4 | |||
| Lecture 25E - AGP Series & Generating Function Part 5 | |||
| GATE CSE 2022 Question on Generating Function | |||
| Lecture 25F - Extended Binomial Theorem - Generating Function - Part 6 | |||
| GATE CSE 2016 Question on Generating Function | |||
| GATE CSE 2017 Question on Ordinary Generating Function | |||
| GATE CSE 2018 Question on Generating Function | |||
| GATE CSE 2005 Question on Generating Function | |||
| TIFR CSE 2010 Question on Generating Function | |||
| Lecture 25G - Summary of Generating Function | |||
| Annotated Notes - Lecture 25D-25F - Extended Binomial Theorem & Generating Function | |||
| Lecture 26 - Recurrence Relations | |||
| Annotated Notes - Lecture 26 - Recurrence Relations | |||
| Practice Set 1 - Combinatorics - Berkeley University Questions | |||
| Practice Set-1 Solutions - Berkeley Questions - Combinatorics | |||
| Annotated Notes - Practice Set 1 Solutions - Berkeley Questions | |||
| Practice Set 2 - Recurrence Relations ALL Standard Questions - Combinatorics | |||
| Practice Set-2 Solutions - Recurrence Relation Questions - Combinatorics | |||
| Annotated Notes - Practice Set 2 Solution - Recurrence Relations | |||
| Lecture 27A - Pigeonhole Principle | |||
| Annotated Notes - Lecture 27A - Pigeonhole Principle | |||
| Lecture 27B - The Generalized Pigeonhole Principle | |||
| Annotated Notes - Lecture 27B - The Generalized Pigeonhole Principle | |||
| Lecture 27C - Practice - Pigeonhole Principle | |||
| Annotated Notes - Lecture 27C - Practice Pigeon Hole Principle | |||
| Practice Set 3 - Derangement ALL Standard Questions - Combinatorics | |||
| Practice Set 3 Solutions - Derangement - Combinatorics | |||
| Annotated Notes - Practice Set 3 Solutions - Derangement All Questions | |||
| Weekly Quiz 19 - Combinatorics | |||
| Rate & Review | |||
| Module 9 - Graph Theory | |||
| Lecture 1 - Why Study Graph Theory - The Motivation | |||
| Lecture 2 - Basic Terminology - Graph Theory | |||
| Lecture 2B - Basics - Degree, Adjacency | |||
| Annotated Notes - Lecture 1-2B - Introduction & Terminology | |||
| Lecture 2C - Practice Questions - Basics | |||
| Lecture 3A - Handshaking Theorem | |||
| Lecture 3B - Handshaking Theorem for Directed Graphs | |||
| Lecture 4A - Cycle, Path, Walk in Simple Graphs | |||
| Annotated Notes - Lecture 2C-4A - Handshaking Theorem | |||
| Lecture 4B - Walk, Path Revise & Practice | |||
| Lecture 4C - Distance and Diameter | |||
| Lecture 5A - Special Type of Graphs | |||
| Lecture 5B - Special Type of Graphs Part 2 | |||
| Lecture 6 - GATE & TIFR Questions on Degree Concept | |||
| Lecture 7 - Subgraph | |||
| Annotated Notes - Lecture 4B-7 - Walk, Path, Subgraph, Diameter | |||
| GATE CSE 2001 - Number of Simple Graphs | |||
| Lecture 8A - Graph Isomorphism Part 1 - Definition | |||
| Lecture 8B - GATE 2012 Question - Graph Isomorphism | |||
| My OLD Video for GATE 2012 Question | |||
| Lecture 8C - Graph Isomorphism is an Equivalence Relation | |||
| Lecture 8D - Graph Complement and Self Complementary Graph | |||
| Lecture 8E - Practice - Graph Isomorphism | |||
| Lecture 9A - Connected Components | |||
| Annotated Notes - Lecture 8A-9A - Graph Isomorphism, Complement, Components | |||
| Lecture 9B - Complement of a Disconnected graph is Connected | |||
| Lecture 9C - TIFR CSE 2018 Question | |||
| Lecture 9D - A Simple Practice Question | |||
| Lecture 10A - Bipartite Graphs | |||
| Lecture 10B - Complete Bipartite Graph | |||
| Annotated Notes - Lecture 9B-10B - Bipartite Graphs, Graph Complement | |||
| Lecture 10C - Practice Questions - Bipartite Graphs | |||
| Lecture 11A - Trees - Part 1 - Cyclic Graphs Acyclic Graph | |||
| Lecture 11B - Trees - Part 2 - Tree and Forest Definitions | |||
| Lecture 11C - Trees - Part 3 - Many Definitions of Tree | |||
| Lecture 11D - Tree Part 4 - Every Tree has at least two vertices of degree 1 | |||
| Annotated Notes - Lecture 10C-11D - Trees, Rooted Tree | |||
| Lecture 11E - ALL Questions - Trees, Forest | |||
| Lecture 12A - Rooted Trees | |||
| Lecture 12B - Rooted Tree Part 2 - Binary Tree. Full Binary Tree | |||
| Lecture 13A - Questions Related to Components | |||
| Annotated Notes - Lecture 11E-13A - Rooted Trees, Binary Tree | |||
| Lecture 13B - Questions on Rooted Trees | |||
| Lecture 14A - Clique, Independent Set - Part 1 | |||
| Lecture 14B - UGC NET CSE 2016 Clique Question | |||
| Lecture 14C - Clique, Independent Set - Part 3 | |||
| Annotated Notes - Lecture 13B-14C - Clique, Independent Set | |||
| Lecture 15A - Vertex Cover, Edge Cover - Part 1 | |||
| Lecture 15B - Vertex Cover, Edge Cover - Part 2 - Analysis | |||
| Lecture 15C - Relation between Vertex Cover & Independent Set | |||
| Meme - Relation between Vertex Cover & Independent Set | |||
| Annotated Notes - Lecture 15A-15C - Vertex Cover, Edge Cover | |||
| Lecture 16A - Matching Part 1 - Perfect Matching, Matching Number | |||
| Lecture 16B - Matching Part 2 - Matching & Covering Analysis | |||
| Annotated Notes - Lecture 16A-16B - Matching | |||
| Lecture 17A - Graph Coloring Part 1 - Vertex Coloring | |||
| Lecture 17B - Graph Coloring Part 2 - Greedy Algorithm for Vertex Coloring | |||
| Lecture 17C - Graph Coloring Part 3 - All GATE TIFR Questions | |||
| Annotated Notes - Lecture 17A-17C - Graph Coloring - Vertex Coloring | |||
| Lecture 17D - Graph Coloring Part 4 - Brooks Theorem for Vertex Coloring | |||
| Lecture 17E - Graph Coloring Part 5 - Edge Coloring | |||
| Annotated Notes - Lecture 17D-17E - Edge Coloring | |||
| Lecture 18 - Graph Realization Problem - Havel Hakimi Theorem | |||
| Annotated Notes - Lecture 18 - Graph Realization Problem - Havel Hakimi Theorem | |||
| Lecture 19A - Cut Vertex, Cut Edge | |||
| Lecture 19B - Connectivity Number, Vertex Cut, Edge Cut | |||
| Annotated Notes - Lecture 19A-19B - Connectivity Number, Cut | |||
| Lecture 20A - Strongly Connected Components - Part 1 | |||
| Lecture 20B - Weakly Connected Graph | |||
| Lecture 20C - Strongly Connected Components - Part 3 - Associated DAG | |||
| Annotated Notes - Lecture 20A-20C - Strongly Connected Components | |||
| Lecture 21A - Euler Circuit & Graph | |||
| Lecture 21B - Hamiltonian Cycle & Graphs | |||
| Annotated Notes - Lecture 21A-21B - Euler Graph & Hamiltonian Graph | |||
| Euler & Hamiltonian Cycles - ALL Previous Exam Questions | |||
| Lecture 22A - Planar Graph Introduction | |||
| Lecture 22B - Planar Graphs - Faces & Degree of a face | |||
| Annotated Notes - Lecture 22A-22B - Planar Graphs | |||
| Lecture 22C - Planar Graph - Euler Formula | |||
| Lecture 22D - Planar Graphs - Some Important Results & Four Color Theorem | |||
| Annotated Notes - Lecture 22C-22D - Planar Graph - Euler Formula | |||
| Lecture 23A - Adjacency Matrix, Adjacency List | |||
| Lecture 23B - GATE 1987-9d Adjacency List | |||
| Lecture 23C - GATE 1988-2xvi Adjacency Matrix | |||
| Lecture 23D - TIFR CSE 2015 Adjacency Matrix | |||
| Annotated Notes - Lecture 23 - Adjacency Matrix, Adjacency List | |||
| Lecture 24A - Powers of Adjacency Matrix of a Graph | |||
| Lecture 24B - Applications of Powers of Adjacency Matrix of a Graph | |||
| Annotated Notes - Lecture 24A-24B - Powers of Adjacency Matrix of a Graph | |||
| Lecture 24C - Applications of Powers of Adjacency Matrix Part 2 | |||
| Annotated Notes - Lecture 24C - Applications of Powers of Adjacency Matrix Part 2 | |||
| Rate & Review | |||
| Students' Hand Written Notes | |||
| Notes by Quantum City (AIR 107, GATE CS 2024, Shreyas Rathod) - Discrete Mathematics Notes | |||
| Propositional Logic Notes - Students Notes by Abhishek Patel | |||
| First Order Logic Notes - Students Notes by Abhishek Patel | |||
| Handwritten Notes by Karan Agrawal (AIR 102 GATE CS 2024) - Discrete Mathematics | |||
| Rate & Review | |||
| 1.0 Basics | |||
| 3.0 Propositional Logic | |||
| 4.0 First Order Logic | |||
| 5.0 Set Theory | |||
| 6.0 Functions | |||
| 7.0 Group Theory | |||
| 8.0 Combinatorics | |||
| 9.0 Graph Theory | |||
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