NOC:Set Theory and Mathematical Logic

Lecture 1 - Introduction to Set Theory

Lecture 2 - Operations on Sets, and Functions

Lecture 3 - Bijective Functions

Lecture 4 - Equivalence Relations and Partitions

Lecture 5 - Cantor-Schroder-Bernstein Theorem

Lecture 6 - Natural Numbers in ZF Set Theory

Lecture 7 - Standard Number Systems in ZF Set Theory

Lecture 8 - (Finitary) Power Sets and Countability

Lecture 9 - Bijections of the set of real numbers: Dedekind cut and Cantor's middle-third set

Lecture 10 - Bijections of the real numbers: Continued Fractions

Lecture 11 - Principles of Mathematical Induction

Lecture 12 - Ordinal Numbers

Lecture 13 - Ordinal Arithmetic

Lecture 14 - Cardinal Numbers and Cardinal Arithmetic

Lecture 15 - Tutorial - Week 4

Lecture 16 - Partial Orders

Lecture 17 - Lattices

Lecture 18 - Equivalents of the Axiom of Choice (AC): Zorn's Lemma (ZL) and Well-ordering theorem (WOT)

Lecture 19 - Tutorial - Week 5

Lecture 20 - Boolean Algebras

Lecture 21 - Stone's Representation Theorems for Boolean Algebras

Lecture 22 - Some Exercises on Boolean Algebras

Lecture 23 - Ultrafilters in Boolean Algebras

Lecture 24 - Introduction to Mathematical Logic

Lecture 25 - Propositional Logic: Language, Formulas and Valuations

Lecture 26 - Propositional Logic: Logical Equivalence and Lindenbaum-Tarski Algebra

Lecture 27 - Tutorial - Week 7

Lecture 28 - Propositional Logic: Normal Forms of Formulas and Adequacy of Connectives

Lecture 29 - Propositional Logic: Semantic Consequence Relation

Lecture 30 - Propositional Logic: Syntactic Consequence Relation

Lecture 31 - Deduction Theorem (Continued...)

Lecture 32 - Tutorial - Week 8

Lecture 33 - Propositional Logic: Consistency and Soundness Theorem

Lecture 34 - Propositional Logic: Completeness Theorem - Part I

Lecture 35 - Propositional Logic: Completeness Theorem - Part II

Lecture 36 - Compactness Theorem and Konig's Lemma

Lecture 37 - Tutorial - Week 9

Lecture 38 - Introduction to First-Order Predicate Logic

Lecture 39 - Predicate Logic: Terms and Formulas

Lecture 40 - Predicate Logic: Validity of Formulas

Lecture 41 - Tutorial - Week 10

Lecture 42 - Predicate Logic Substructures, Semantic Consequence Relation, and Models of Theories

Lecture 43 - Predicate Logic: Standard Logical Equivalences, Normal Forms, and Definable Sets

Lecture 44 - Tutorial - Week 11

Lecture 45 - Hyperreal Numbers

Lecture 46 - Predicate Logic: Ultraproduct of Structures and Los's Theorem

Lecture 47 - Predicate Logic: Compactness Theorem

Lecture 48 - Tutorial - Week 12

Lecture 49 - Predicate Logic: Lowenheim-Skolem Theorems

Lecture 50 - Predicate Logic: Reduced Products, Categoricity

Lecture 51 - Predicate Logic: Categoricity (Continued...) and Quantifier Elimination

Lecture 52 - Godel's Incompleteness Theorems