IIT Madras Discrete Maths Lectures: Discrete Mathematics
BSMA300159 lectures12 weeks
Weeks
- Week 15 lecturesIntroduction to Discrete Mathematics · Introduction to Sets and Basic Set Concepts · Set Operations and Set Identities · Functions and Types of Functions · Sequences and Summations
- Week 25 lecturesIntroduction to Propositional Logic and Truth Tables · Propositional Logic: Satisfiability, Validity, and Applications · Propositional Logic: Axioms, Rules of Inference, Logical Equivalence · Predicate Logic · Predicate Logic and Normal Forms in Predicate Logic
- Week 35 lecturesMathematical Proof Techniques: Introduction and Direct Proof · Proof by Contraposition and Contradiction · Proofs of Equivalence and Counterexamples · Mathematical Induction · Strong Induction and Advanced Applications
- Week 45 lecturesCardinality of Sets, Finite & Infinite Sets, and Countable Sets · Uncountable Sets and Properties of Countable Sets · Introduction to Recursion and Recursive Definitions · Recursive Definition of Sets and Structural Induction · Recursive Definition of Trees and Graphs
- Week 55 lecturesCounting Techniques – Product Rule · Counting Techniques – Sum Rule · Counting Techniques – Subtraction Rule & Division Rule · Permutations – Counting Ordered Arrangements · Combinations – Counting Unordered Selections
- Week 65 lecturesPigeonhole Principle and Generalized Pigeonhole Principle · Binomial Theorem and Binomial Coefficients · Generalized Permutations and Combinations · Permutations and Combinations with Indistinguishable Objects · Stirling Numbers of the Second Kind and Onto Functions
- Week 75 lecturesGenerating Functions and Their Applications in Counting · Introduction to Recurrence Relations and Tower of Hanoi · Applications of Recurrence Relations in Counting · Generating Permutations and Combinations Algorithms · Inclusion-Exclusion Principle and Derangements
- Week 83 lecturesOperations on Relations and Matrix Representation · Relations as Graphs and Closure of Relations · Transitive Closure of Relations and Warshall's Algorithm
- Week 95 lecturesEquivalence Relations and Partial Orders · Partial Orders, Hasse Diagrams and Lattices · Boolean Algebra · Boolean Identities · Representing Boolean Functions
- Week 105 lecturesGraph Theory: Basic Concepts and Applications · Graph Terminology, Degree of Vertices and Special Graphs · Bipartite Graphs and Matchings · Graph Operations, Representations and Isomorphism · Graphs: Paths and Connectivity
- Week 113 lecturesSpecial Paths in Graphs: Euler and Hamilton Paths · Weighted Graphs and Shortest Paths · Graph Coloring and Applications
- Week 125 lecturesProperties of Trees and m-ary Trees · Tree Traversal Algorithms · Applications of Tree Traversals and Spanning Trees · Introduction to Abstract Algebra · Abstract Algebra - Groups
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