August 23, 2023: Introduction to formalization of statements, Truth values of statements, Logical equivalence, calculating a few Truth Tables. (Notes)
August 29, 2023: De Morgan's laws, Conditional and Biconditional statements, many examples of logical equivalences, tautologies, and contradictions. (Notes)
Reference for logic of compound statements: Notes.
August 31, 2023: Introduction to set theory, basic operations on sets like unions, intersections, complements, the notion of cardinality, and relation between sets. (Notes)
Sep 05, 2023: Complements, Direct products, Venn diagrams, and proving De Morgan's laws. (Notes)
Sep 07, 2023: Power sets, domain, codomain, and range of a function, recurrence relations. (Notes)
Sep 12, 2023: Injective, surjective functions, inverse of a function, solving together problems on basic set theory. (Problem set)
Reference for basic set theory: Sections 0.3-0.4 of "Discrete Mathematics: An Open Introduction".
Sep 19, 2023: Different techniques of proofs and a few examples. (Notes)
Sep 21, 2023: More examples of proofs. (Notes)
Sep 26, 2023: Problem session. (Problem set)
Propositional logic examples
Problem set for midterm I.
Oct 05, 2023: Midterm I
Oct 17, 2023: Unique factorization and Division algorithm. (Notes)
Oct 24, 2023: Relations on sets with examples. (Notes)
Oct 26, 2023: Going through homework problems (Notes), Mathematical Induction I (Notes)
Oct 31, 2023: More applications of the first induction principle. (Reference: Sec 5.2-5.3 of the book by Susanna S. Epp)
Nov 01, 2023: Problem set for Midterm 2A. (Notes)
Nov 03, 2023: Midterm 2A (1,2) (Solutions - 1,2)
Nov 07, 2023: Recursion relations (Notes)
Nov 09, 2023: Review and Quiz 04
Problem set for Midterm 2B
Midterm 2B: Friday 11/10 - Sunday 11/12.
New topic - Quantitative Thinking
Nov 16, 2023: Basic Counting Techniques. (Notes, Problem Set)
Nov 21, 2023: Selections and Arrangements. (Notes, Video)
Problem set on Selections and Arrangements
Nov 27, 2023: Review session, Quiz 05.
Nov 30, 2023: Midterm 3.
Dec 05, 2023: Final exam review, Binomial Theorem. (Final Problem Set, Notes)
Dec 07, 2023: Review for final, application of the Binomial Theorem. (Notes)