# Lectures

### Lectures

Only very high-level class notes will be released: they are meant to reinforce the lecture, not replace it. Lecture topics are tentative. You are highly encouraged to attend all lectures and write your own notes.

Date Topics Book Sections
January 25 Lecture 1: Proof, Set, Subset

4.1

January 27 Lecture 2: Proposition, Predicate, Proof by Contradiction

1.1, 1.2, 1.8

January 30 Lecture 3: Rational Numbers, Set, Set-Builder Notation, Cardinality, Set Operations, Power Set

4.1, 5.1

February 01 Lecture 4: Element Method, Quantifiers, Existential Proof, Constructive Proof, Proof by Cases

1.7, 3.6

February 03 Lecture 5: Cartesian Product, Relation, Properties of Relations, Equivalence Relation, Equivalence Class, Partition

4.2, 4.4, 9.11, 9.12

February 06 Lecture 6: Function

4.3

February 08 Lecture 7: Injectivity, Surjectivity, Bijectivity, Cardinality of Sets

4.4, 5.1, 5.2, 15.1

February 10 Lecture 8: Bijective Proof, Induction I

15.1, 6.1

February 13 Lecture 9: Induction II, Strong Induction

6.2, 6.3

February 15 Lecture 10: Divisibility, Primes

2.3, 8.1

February 17 Lecture 11: Division Algorithm, GCD, Euclidean Algorithm, Relative Primes

8.2, 8.3, 8.7

February 22 Lecture 12: Modular Arithmetic I, Congruence Properties

8.5

February 24 Lecture 13: Modular Arithmetic II, Fermat's Little Theorem

8.5

February 27 Lecture 14: Modular Arithmetic III, Euler's Totient Function, Encryption

8.6, 8.7

March 01 Lecture 15: RSA Encryption

8.8

March 03 Lecture 16: Logical Operators, Conditional, Proposition, Predicate, Truth Tables

3.1, 3.3, 3.4

March 06 Lecture 17: Biconditional, Inverse, Converse, Contrapositive, Tautology, Contradiction, Quantification II, Logical Algebra

3.1, 3.3, 3.4

March 08 Lecture 18: Combinatorial Circuits, Binary Representation

Not in book!

Not in book!

March 13 Lecture 20: Feedback Circuits, RS Latch, Clocks

Not in book!

March 15 Lecture 21: D Latch, D Flip-flop, 2-bit Counter

Not in book!

March 17 Lecture 22: Counting, Permutations, Factorials, Binomial Coefficient, Binomial Theorem

15.1, 15.3, 15.5, 15.7

March 20 Lecture: Cancelled

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March 22 Lecture 23: Binomial Coefficient Properties, Inclusion/Exclusion

15.12

March 24 Lecture 24: Derangements, Ice Cream Scoop Problem

Not in book!

April 03 Lecture 25: Pigeonhole Principle, Strong Pigeonhole Principle

15.10

April 05 Lecture 26: Asymptotics, Big-O, Big-Theta, Big-Omega

14.7

April 07 Lecture 27: Asymptotic Equality, Little-O, Stirling's Formula

14.5, 14.7

April 10 Lecture 28: Probability, Sample Space, Event, Distributions

17.1, 17.2, 17.3

April 12 Lecture 29: Conditional Probability, Independence

17.5, 17.6

April 14 Lecture 30: Law of Total Probability, Bayes' Rule, Extended Bayes' Rule

17.5

April 17 Lecture 31: The Monty Hall Problem

17.1

April 19 Lecture 32: Random Variables, Expected Value, Binomial Random Variable, Indicator Random Variable, Linearity of Expectation

18.1, 18.2, 18.4, 18.5

April 21 Lecture 33: Computational Complexity

Not in book!

April 24 Lecture 34: Variance

18.3, 18.4

April 26 Lecture 35: Graph Theory

11

April 28 Lecture 36: PrÃ¼fer Code

Not in book!

May 01 Lecture 37: Markov Chains

Not in book!