CS 70 at UC Berkeley

# Discrete Mathematics and Probability Theory

Lecture: TuTh 3:30-5:00pm, Wheeler 150

## Professor Alistair Sinclair

sinclair (at) berkeley (dot) edu

Office Hours: M 1:15-2:15PM, W 1:15-2:15PM, 677 Soda Hall

## Professor Yun S. Song

yss (at) berkeley (dot) edu

Office Hours: W 11am-12pm, 629 Soda Hall; Th 5:15-6:15pm, 304B Stanley Hall

### Week 0 Overview

## Welcome to CS70!

### Week 1 Overview

## Propositional Logic, Proofs, Induction

### Week 2 Overview

## Stable Marriage, Graph Theory

### Week 3 Overview

## Graph Theory, Modular Arithmetic

### Week 4 Overview

## Public Key Cryptography, Polynomials

### Week 5 Overview

## Error Correcting Codes, Countability

### Week 6 Overview

## Midterm 1, Counting

- Discussion 6b (solution)
- Homework 5 (TeX) (solution)
- Homework 6 (TeX) (solution)

### Week 7 Overview

## Counting

### Week 8 Overview

## Introduction to Probability, Conditional Probability

### Week 9 Overview

## Conditional Probability, Random Variables I

### Week 10 Overview

## Random Variables II, Concentration Inequalities, Law of Large Numbers

### Week 11 Overview

## Midterm 2, Hashing and Load Balancing

### Week 12 Overview

## Geometric and Poisson, Continuous Probability Distributions

### Week 13 Overview

## Continuous Probability Distributions, Thanksgiving Break

### Week 14 Overview

## Markov Chains, Decidability

## 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: Counting
- Note 12: Introduction to Discrete Probability
- Note 13: Conditional Probability
- Note 14: Random Variables: Distribution & Expectation
- Note 15: Random Variables: Variance & Covariance
- Note 16: Concentration Inequalities and LLN
- Note 17: Applications: Hashing and Load Balancing
- Note 18: Geometric and Poisson Distributions
- Note 19: Continuous Probability Distributions
- Note 20: Finite Markov Chains
- Note 21: Self-Reference and Uncomputability

## Discussions

The discussion sections are specifically designed to consolidate the material covered in lectures and in the notes. It is highly recommended that you attend both discussions each week. You may attend any discussion section, but we recommend that you settle on a weekly two-section pair (with the same TA) as early as possible in the semester. If a particular section is too full, then students will be admitted on a first-come first-served basis and others will have to attend an alternative section. All sections are equivalent: they all cover the same material. See Policies for more information.

- Discussion 1: Propositional Logic, Proofs (solution)
- Discussion 1b: Quiz (Logic, Proofs) (solution)
- Discussion 2: Induction, Stable Marriage (solution)
- Discussion 2b: Quiz (Induction, Stable Marriage) (solution)
- Discussion 3: Graph Theory (solution)
- Discussion 3b: Quiz (Graph Theory) (solution)
- Discussion 4: Modular Arithmetic and RSA (solution)
- Discussion 4b: Quiz (Modular Arithmetic and RSA) (solution)
- Discussion 5: Polynomials and Error-Correcting Codes (solution)
- Discussion 6: Countability (solution)
- Discussion 6b: Quiz (Countability) (solution)
- Discussion 7: Counting (solution)
- Discussion 7b: Quiz (Counting) (solution)
- Discussion 8: Counting and Probability (solution)
- Discussion 8b: Quiz (Counting and Probability) (solution)
- Discussion 9: Conditional Probability and Combinations of Events (solution)
- Discussion 9b: Quiz (Conditional Probability and Combinations of Events) (solution)
- Discussion 10: Random Variables (solution)
- Discussion 11: Concentration Inequalities, LLN and Applications (solution)
- Discussion 11b: Quiz (Concentration Inequalities, LLN and Applications) (solution)
- Discussion 12: Geometric and Poisson Distributions (solution)
- Discussion 12b: Quiz (Geometric and Poisson Distributions) (solution)
- Discussion 13: Continuous Distributions (solution)
- Discussion 14: Markov Chains (solution)

## Homeworks

There will be weekly required homeworks, again designed to consolidate your understanding of the course material. It is highly recommended that you attempt all homeworks. 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.

- HW 00: Course Logistics (TeX) (Sol)
- HW 1: Propositional Logic, Proofs (TeX) (Sol)
- HW 2: Induction, Stable Marriage (TeX) (Sol)
- HW 3: Graph Theory (TeX) (Sol)
- HW 4: Modular Arithmetic and RSA (TeX) (Sol)
- HW 5: Polynomials and Error-Correcting Codes (TeX) (Sol)
- HW 6: Countability (TeX) (Sol)
- HW 7: Counting (TeX) (Sol)
- HW 8: Counting and Probability (TeX) (Sol)
- HW 9: Conditional Probability and Combinations of Events (TeX) (Sol)
- HW 10: Random Variables (TeX) (Sol)
- HW 11: Concentration Inequalities, LLN and Applications (TeX) (Sol)
- HW 12: Geometric and Poisson Distributions (TeX) (Sol)
- HW 13: Continuous Distributions and Markov Chains (TeX) (Sol)

## Lecture Schedule

- Lecture 1 (8/29): Introduction & Logic (Note 1)
- Lecture 2 (9/3): Proofs (Note 2)
- Lecture 3 (9/5): Induction (Note 3)
- Lecture 4 (9/10): Stable Marriage (Note 4)
- Lecture 5 (9/12): Graphs I (Note 5)
- Lecture 6 (9/17): Graphs II (Note 5)
- Lecture 7 (9/19): Modular Arithmetic (Note 6)
- Lecture 8 (9/24): Public Key Cryptography: RSA (Note 7)
- Lecture 9 (9/26): Polynomials (Note 8)
- Lecture 10 (10/1): Error-Correcting Codes (Note 9)
- Lecture 11 (10/3): Countability (Note 10)
- Lecture 12 (10/15): Counting I (Note 11)
- Lecture 13 (10/17): Counting II (Note 11)
- Lecture 14 (10/22): Introduction to Probability (Note 12)
- Lecture 15 (10/24): Conditional Probability (Note 13)
- Lecture 16 (10/24): Combinations of Events (Note 13)
- Lecture 17 (10/29): Random Variables I (Note 14)
- Lecture 18 (11/5): Random Variables II (Note 15)
- Lecture 19 (11/7): Concentration Inequalities and LLN (Note 16)
- Lecture 20 (11/14): Applications (Note 17)
- Lecture 21 (11/19): Geometric and Poisson Distributions (Note 18)
- Lecture 22 (11/21): Continuous Distributions I (Note 19)
- Lecture 23 (11/26): Continuous Distributions II (Note 19)
- Lecture 24 (12/3): Finite Markov Chains (Note 20)
- Lecture 25 (12/5): Self-Reference and Uncomputability (Note 21)