CS 70 at UC Berkeley
Discrete Mathematics and Probability Theory
Lectures: M/T/W/Th 2-3:30 p.m., 155 Dwinelle
Instructor Vrettos Moulos
vrettos (at) berkeley (dot) edu
Office Hours: W 4-5 p.m., F 2:30-3:30 p.m., 212 Cory
Week 1 Overview
Propositional Logic, Proofs, Induction
Week 2 Overview
Stable Marriage, Graph Theory, Countability, Computability
- Note 4 : Stable Marriage
- Note 5 : Graph Theory
- Note 10 : Infinity and Uncountability
- Note 11 : Self-Reference and Uncomputability
- Discussion 02a
- Discussion 02b
- Discussion 02c
- Discussion 02d
- Homework 01 (TeX)
- Homework 02
Notes
There is no textbook for this class. Instead, there is a set of fairly comprehensive lecture notes. Make sure you revisit the notes after lecture. Each note may be covered in one or more lectures. See Syllabus for more information.
- Note 0: Review of Sets, Notation (PDF)
- Note 1: Propositional Logic (PDF)
- Note 2: Proofs (PDF)
- Note 3: Induction (PDF)
- Note 4: Stable Marriage (PDF)
- Note 5: Graph Theory (PDF)
- Note 6: Modular Arithmetic (PDF)
- Note 7: Bijections and RSA (PDF)
- Note 8: Polynomials (PDF)
- Note 9: Error Correcting Codes (PDF)
- Note 10: Infinity and Uncountability (PDF)
- Note 11: Self-Reference and Uncomputability (PDF)
- Note 12: Counting (PDF)
- Note 13: Introduction to Discrete Probability (PDF)
- Note 14: Conditional Probability (PDF)
- Note 15: Two Killer Applications (PDF)
- Note 16: Random Variables: Distribution and Expectation (PDF)
- Note 17: Variance (PDF)
- Note 18: Chebyshev's Inequality (PDF)
- Note 19: Some Important Distributions (PDF)
- Note 20: Continuous Probability (PDF)
- Note 24: Markov Chains (PDF)
- Note 25a: Review of Probability (PDF)
- Note 25b: Probability: An Overview (PDF)
- Note 26: Estimation (PDF)
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 who are officially enrolled in that section will get seating priority. See Syllabus for more information.
- Discussion 01a: Propositional Logic (solution)
- Discussion 01b: Proofs (solution)
- Discussion 01c: Induction (solution)
- Discussion 01d: Induction (solution)
- Discussion 02a: Graph Theory
- Discussion 02b: Graph Theory
- Discussion 02c:
- Discussion 02d:
- Discussion 03a: Modular Arithmetic
- Discussion 03b: Modular Arithmetic, Bijections
- Discussion 04a: Fermat's Little Theorem, RSA
- Discussion 04b: Polynomials
- Discussion 05a: Lagrange Interpolation, Erasure Codes, Secret Sharing
- Discussion 05b: Berlekamp-Welch
- Discussion 06a: Uncountability, Uncomputability
- Discussion 06b: Counting
- Discussion 07a: Basic Probability
- Discussion 07b: Conditional Probability
- Discussion 08a: Random Variables, Binomial Distribution
- Discussion 08b: Union Bound, Geometric Distribution, Poisson Distribution
Homeworks
All homeworks are graded for accuracy and it is highly-recommended that you do them. Your lowest homework score will be dropped, but this drop should be reserved for emergencies. See Syllabus for more information.
- Homework 00: Course Logistics (TeX)
- Homework 01: Propositional Logic, Proofs, Induction (TeX)
- Homework 02: Induction, Stable Marriage, Graph Theory
- Homework 03: Graph Theory
- Homework 04: Modular Arithmetic
- Homework 05: Chinese Remainder Theorem, RSA, Polynomials
- Homework 06: Polynomials, Secret Sharing, Error Correcting Codes, Uncountability
- Homework 07: Uncountability, Uncomputability, Counting
- Homework 08: Combinatorial Proofs, Probability Spaces, Conditional Probability, Independence