Math Foundation C4Z71M1R9W

URI	`m2://res/C4Z71M1R9W`
Kind	course
Creators	Sukumar D (instructor)
Date	2026-10-27
Scope	in

Expressions

e1: edition

Language	en
Date	2026-10-27

m1: page, IIT Hyderabad (record). nptel 111106003
m2: page, 2026-10-27 (record). nptel 111106003

Contents

part 1: Week 1
session 1: Mathematical Statements
session 2: Negation of statements
session 3: Universal and existential quantifiers
session 4: Negation rules to quantified statements
session 5: Nested quantifiers and their negation rules
session 6: Review of statements, negation, and quantifiers
part 2: Week 2
session 7: Compound Statements
session 8: Compound Statements with Quantifiers
session 9: Implications and their negation
session 10: Converse and Related Implications
session 11: Biconditionals (If and Only If)
session 12: Contrapositive and Week 2 Review
part 3: Week 3
session 13: Proofs in Mathematics
session 14: Direct Proof Method
session 15: Contrapositive Proof
session 16: Proof by Contradiction
session 17: Proving Equivalence
session 18: Induction & Counterexamples
part 4: Week 4
session 19: Basic Set Terminology
session 20: Empty Set, Subsets and Power Sets
session 21: Equality of Sets
session 22: Describing Sets and Proving Equality
session 23: Union and Intersection
session 24: Complement and Difference
part 5: Week 5
session 25: Family of Sets
session 26: Union of a Family
session 27: Intersection of a Family
session 28: Disjoint and Pairwise Disjoint Families
session 29: Cartesian Product
session 30: Worked Examples and Review
part 6: Week 6
session 31: Functions: Definition and Examples
session 32: Functions: More Examples
session 33: Injective Functions
session 34: Onto Functions
session 35: Bijections
session 36: Review: Functions
part 7: Week 7
session 37: Functions: Graphical View
session 38: Composition of Functions
session 39: Inverse Functions
session 40: Graph of the Inverse Function
session 41: Bijections between Intervals
session 42: Review: Composition and Inverses (W6 + W7)
part 8: Week 8
session 43: Cantor’s Theorem
session 44: Image of Subsets under Functions — 1
session 45: Image of Subsets under Functions — 2
session 46: Inverse Image of Subsets under Functions
session 47: Inverse Image of Subsets under Functions - 2
session 48: Review: Images and Inverse Images
part 9: Week 9
session 49: Relations: Definition and Examples
session 50: Properties of Relations I - The Four Properties
session 51: Properties of Relations II - More Examples, Digraphs, and Matrices
session 52: Equivalence Relations
session 53: Equivalence Classes and Partitions
session 54: Equivalence Classes and Partitions
part 10: Week 10
session 55: The Induction Principle
session 56: The Strong Induction Principle
session 57: The Well-Ordering Principle and the Division Algorithm
session 58: Equivalence of the Three Principles
session 59: Worked Examples: gcd and Bezout
session 60: Review: Pitfalls and the Whole Picture
part 11: Week 11
session 61: Cardinality: Comparing Sizes via Bijections
session 62: The Schroder-Bernstein Theorem
session 63: Knaster-Tarski and the Proof of Schroder-Bernstein
session 64: Finite Sets and the Pigeonhole Principle
session 65: Countable and Uncountable Sets
session 66: Comparing Cardinality
part 12: Week 12
session 67: Order Relations: Definition and Examples
session 68: Restriction, Chains, and Bounds
session 69: Maximum, Minimum, Maximal, Minimal, and LUB/GLB
session 70: Hasse Diagrams and Intervals
session 71: Well-Ordering, Zorn's Lemma, and the Axiom of Choice
session 72: The Product of a Family

Catalogue records

nptel: 111106003 (manifestation)
nptel_video: 111106003 (manifestation)