CS 70 at UC Berkeley

# Discrete Mathematics and Probability Theory

Lecture: TTh 8-9:30am, Zoom

## Professor Satish Rao

satishr (at) cs (dot) berkeley (dot) edu

Office Hours: Monday 3-4 (See piazza @443 for zoom link.) And by appointment.

### Week 0 Overview

## Propositional Logic

### Week 1 Overview

## Proofs, Induction

### Week 2 Overview

## Stable Matching

### Week 3 Overview

## Graphs, Modular Arithmetic

### Week 4 Overview

## Modular Arithmetic, Public Key Cryptography

### Week 5 Overview

## Polynomials and Error-Correcting Codes

### Week 6 Overview

## Counting

## 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: Sets and Mathematical Notation
- Note 1: Propositional Logic
- Note 2: Proofs
- Note 3: Induction
- Note 4: Stable Matching
- Note 5: Graph Theory
- Note 6: Modular Arithmetic
- Note 7: Public Key Cryptography (RSA)
- Note 8: Polynomials
- Note 9: Error Correcting Codes
- Note 10: Counting

## Discussions

Discussions will be held over Zoom. The discussion sections are specifically designed to consolidate the material covered in lectures and in the notes. It is highly recommended that you attend all discussions each week. You should attend the discussion that you signed up for, since attendance for that discussion will be graded. All sections are equivalent: they all cover the same material. See Policies for more information.

- Discussion 0: Introduction, Logic (solution)
- Discussion 01a: Proofs (solution)
- Discussion 01b: Induction (solution)
- Discussion 02a: Stable Matching (solution)
- Discussion 02b: Graphs I (solution)
- Discussion 03a: Graphs II (solution)
- Discussion 03b: Modular Arithmetic (solution)
- Discussion 04a: Modular Arithmetic (CRT) (solution)
- Discussion 04b: RSA (solution)
- Discussion 05a: Polynomials, Secret Sharing (solution)
- Discussion 05b: Error Correcting Codes (solution)
- Discussion 06a: Counting (solution)
- Discussion 06b: Counting II (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 this drop 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: Logistics and Review (Sol)
- HW 01: Proofs and Induction (Sol)
- HW 02: Induction and Stable Matching (Sol)
- HW 03: Graphs (Sol)
- HW 04: Modular Arithmetic and RSA (Sol)
- HW 05: RSA and Secret Sharing (Sol)
- HW 06: Error Correcting Codes and Counting (Sol)
- HW 07: Counting

## (Tentative) Lecture Schedule

- Lecture 1 : Introduction & Logic. Slides: (full) (6up) (Note 1)
- Lecture 2 : Proofs. Slides: (full) (6up) (Note 2)
- Lecture 3 : Induction. Slides: (full) (6up) (Note 3)
- Lecture 4 : Stable Matching. Slides: (full) (6up) (Note 4)
- Lecture 5 : Graphs I. Slides: (full) (6up) (Note 5)
- Lecture 6 : Graphs II. Slides: (full) (6up) (Note 5)
- Lecture 7 : Modular Arithmetic. Slides: (full) (6up) (Note 6)
- Lecture 8 : Modular Arithmetic. Slides: (full) (6up) (Note 6)
- Lecture 9 : CRT/FLT/Public Key. Slides: (full) (6up) (Note 7)
- Lecture 10 : Polynomials/Secret Sharing. Slides: (full) (6up) (Note 8)
- Lecture 11 : Errors: Erasures and Corrections. Slides: (full) (6up) (Note 9)
- Lecture 12 : Counting I. Slides: (full) (6up) (Note 10)
- Lecture 13 : Counting II/Midterm Review. Slides: (full) (6up) (Note 10)
- Lecture : Midterm(no lecture)
- Lecture 14: Countability
- Lecture 15: Computability/Self Reference
- Lecture 16: Probability
- Lecture 17: Conditional Probability
- Lecture 18: Combination of Events
- Lecture 19: Random Variables I
- Lecture 20: Random Variables II
- Lecture 21: Concentration Inequalities and LLN
- Lecture 22: Applications
- Lecture 23: Geometric and Poisson Distributions
- Lecture 24: Continuous Distributions I
- Lecture 25: Continuous Distributions II
- Lecture : Thanksgiving.
- Lecture 26: Markov Chains I
- Lecture 27: TBA