Notes

There is no textbook for this class. Instead, there is a set of comprehensive lecture notes. Make sure you revisit the notes after every lecture, and multiple times thereafter: you should be aware that it will likely take several readings before you fully understand the material. Each note may be covered in one or more lectures. See Policies for more information.

• Note 0: Review of Sets, Notation
• Note 1: Propositional Logic
• Note 2: Proofs
• Note 3: Induction
• Note 4: Stable Marriage
• Note 5: Graph Theory
• Note 6: Modular Arithmetic
• Note 7: Public Key Cryptography
• Note 8: Polynomials
• Note 9: Error Correcting Codes
• Note 10: Infinity and Uncountability
• Note 11: Self-Reference and Uncomputability
• Note 12: Counting
• Note 13: Introduction to Discrete Probability
• Note 14: Conditional Probability
• Note 15: Random Variables: Distribution & Expectation
• Note 16: Random Variables: Variance & Covariance
• Note 17: Applications
• Note 18: Concentration Inequalities and LLN
• Note 19: Geometric and Poisson Distributions
• Note 20: Continuous Probability Distributions
• Note 21: Finite Markov Chains

Discussions

The discussion sections will not cover new material, but rather will give you additional practice solving problems. You can attend any discussion section you like. However, if there are fewer desks than students, then students will be admitted to the section on a first-come first-served basis and others will have to attend an alternative section. See Policies for more information.

• Discussion 00a: Propositional Logic
• Discussion 00b: Proofs
• Discussion 01a: Induction
• Discussion 01b: Stable Marriage
• Discussion 02a: Graphs I
• Discussion 02b: Graphs II
• Discussion 03a: Modular Arithmetic I
• Discussion 03b: Modular Arithmetic II
• Discussion 04a: RSA
• Discussion 04b: Polynomials, Secret Sharing, Error-Correcting Codes
• Discussion 05a: Error-Correcting Codes, Countability

Homeworks

Homeworks are graded for accuracy and it is highly recommended that you do them. Your lowest two homework scores will be dropped, but these drops should be reserved for emergencies. No additional allowances will be made for late or missed homeworks: please do not contact us about missed homeworks or late submissions. See Policies for more information.

• Homework 00: Course Logistics
• Homework 01: Propositional Logic, Proofs
• Homework 02: Induction, Stable Marriage
• Homework 03: Graphs
• Homework 04: Modular Arithmetic
• Homework 05: RSA
• Homework 06: Polynomials, Error Correcting Codes
• Homework 07: Countability, Computability, Counting
• Homework 08: Counting, Introducion to Probability
• Homework 09: Independence, Random Variables
• Homework 10: Variance, Joint Distributions
• Homework 11: Applications, Inequalities
• Homework 12: Geometric and Poisson Distributions, Continuous Random Variables
• Homework 13: Continuous Random Variables, Markov Chains

Lecture Schedule

• Lec 1 (1/22): Intro & Propositional Logic (Note 1)
• Lec 2 (1/24): Proofs (Note 2)
• Lec 3 (1/29): Induction (Note 3)
• Lec 4 (1/31): Stable Marriage (Note 4)
• Lec 5 (9/6): Graph Theory I (Note 5)
• Lec 6 (9/11): Graph Theory II (Note 5)
• Lec 7 (9/13): Modular Arithmetic (Note 6)
• Lec 8 (9/18): RSA (Note 7)
• Lec 9 (9/20): Polynomials (Note 8)
• Lec 10 (9/27): Error-Correcting Codes (Note 9)
• Lec 11 (10/2): Infinity Countability (Note 10)
• Lec 12 (10/4): Self-Ref and Uncomputability (Note 11)
• Lec 13 (10/9): Counting (Note 12)
• Lec 14 (10/4): Introduction to Probability (Note 13)
• Lec 15 (10/16): Conditional Probability (Note 14)
• Lec 16 (10/18): Combinations of Events (Note 14)
• Lec 17 (10/23): Random Variables I (Note 15)
• Lec 18 (10/25): Random Variables II (Note 16)
• Lec 19 (10/30): Applications (Note 17)
• Lec 20 (11/6): Concentration Inequality, LLN (Note 18)
• Lec 21 (11/8): Geometric and Poisson Dist'n (Note 19)
• Lec 22 (11/13): Continuous Distributions I (Note 20)
• Lec 23 (11/15): Continuous Distributions II (Note 20)
• Lec 24 (11/27): Markov Chains I (Note 21)
• Lec 25 (11/29): Markov Chains II (Note 21)