Lectures

Zoom Link

Date Topics Slides Book Video
1/20/21 Overview, Intro to Proofs .pdf 1.1, 1.5, 1.7, 1.8 link
1/22/21 Proofs, Propositions, Predicates, Quantifiers .pdf 1.1, 1.2, 1.8, 1.9 link
1/25/21 Introduction to Set theory .pdf 4.1 link
1/27/21 Laws of set theory, Introduction to Logic .pdf 3, 3.1, 3.2, 3.3 link
1/29/21 Laws of Logic, normal forms .pdf 3.3, 3.4, 3.5, 3.6 link
2/1/21 Logic continued .pdf 3.3, 3.4 link
2/3/21 relations .pdf 4.4 link
2/5/21 Equivalence relation, Partial order, function .pdf 4.3, 4.4, 9.5, 9.11 link
2/8/21 more functions, Bijections .pdf 4.4, 5.1 link
2/10/21 countably infinite, induction .pdf 5.2, 6.1 link .pdf(annotated)
2/12/21 induction continued, strong induction .pdf 6.1, 6.2, 6.3 link .pdf(annotated)
2/15/21 NO CLASS
2/17/21 Introduction to number theory .pdf 8.1, 8.2 link .pdf(annotated)
2/19/21 modular arithmetics .pdf 8.5 link .pdf(annotated)
2/22/21 gcd, prime factorization .pdf 8.2, 8.3 link .pdf(annotated)
2/24/21 inverse, fermat little thm and Euler thm .pdf 8.6, 8.7 link .pdf(annotated)
2/26/21 Crypthography .pdf 8.4, 8.8, 8.9 link .pdf(annotated)
3/1/21 Counting: the product rule, the sum rule .pdf 15.2 link .pdf(annotated)
3/3/21 Counting: permutations, the division rule .pdf 15.2,15.3,15.4, 15.5 link .pdf(annotated)
3/5/21 combinations, counting with repititions .pdf 15.5, 15.6 link .pdf(annotated)
3/8/21 Counting by complement, Priciple of inclusion exclusion .pdf 15.12 link .pdf(annotated)
3/10/21 Midterm Q&A .pdf --- link
3/12/21 Counting: pigeonhole principle, binomial theorem .pdf 15.7, 15.10, 15.13 link .pdf(annotated)
3/15/21 Pascal Triangle, Discrete Probability .pdf 17.4 link .pdf(annotated)
3/17/21 Discrete Probability: uniform distribution, counting and probability .pdf 17.4 link .pdf(annotated)
3/19/21 Principle of inclusion exclusion for probability, the union bound .pdf 17.4 link .pdf(annotated)
3/22/21 Discrete Probability:conditional probability .pdf 17.5, 17.6 link .pdf(annotated)
3/24/21 Discrete Probability: conditional/Bayes rule .pdf 17.5,17.6,17.1 link .pdf(annotated)
3/26/21 Discrete Probability:Bayes rule/ random variables .pdf 18.1 link .pdf(annotated)
3/29/21 Random variables, Expectation .pdf 18.2, 18.4 link .pdf(annotated)
3/31/21 linearity of expectation/ Graph Theory .pdf 18.5, 11.1 link .pdf(annotated)
4/2/21 Graph Theory .pdf 9.3, 11.1, 11.3, 11.4 link .pdf(annotated)
4/5/21 Graph Theory: connectivity .pdf 11.8,11.9 link .pdf(annotated)
4/7/21 Graph Theory: shoretest paths/trees .pdf 11.11 link .pdf(annotated)
4/9/21 NO CLASS
4/12/21 NO CLASS .pdf --- link
4/14/21 Q & A .pdf --- link