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
Week 3 Overview
Counting, Probability
Week 4 Overview
Conditional Probability, Discrete Random Variables, Expectation
- Note 14 : Conditional Probability
- Note 16 : Random Variables: Distribution and Expectation
- Note 17 : Variance
- Note 19 : Some Important Distributions
- Discussion 04a (solution)
- Discussion 04b (solution)
- Discussion 04c (solution)
- Discussion 04d (solution)
- Homework 03 (TeX) (solution)
- Homework 04 (TeX) (solution)
Week 5 Overview
Variance, Continuous Probability
- Note 16 : Random Variables: Distribution and Expectation
- Note 17 : Variance
- Note 19 : Some Important Distributions
- Note 20 : Continuous Probability
- Discussion 05a (solution)
- Discussion 05b (solution)
- Discussion 05c (solution)
- Discussion 05d (solution)
- Homework 04 (TeX) (solution)
- Homework 05 (TeX) (solution)
Week 6 Overview
Probability Inequalities, Markov Chains
Week 7 Overview
Modular Arithmetic, RSA, Error-Correcting Codes
Week 8 Overview
Final
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: Stable Marriage (solution)
- Discussion 02b: Graph Theory (solution)
- Discussion 02c: Graph Theory (solution)
- Discussion 02d: Countability, Computability (solution)
- Discussion 03a: Counting (solution)
- Discussion 03b: Counting (solution)
- Discussion 03c: Introduction to Probability (solution)
- Discussion 04a: Conditional Probability (solution)
- Discussion 04b: Bayes Rule, Independence (solution)
- Discussion 04c: Random Variables, Distributions (solution)
- Discussion 04d: Expectation, Joint Distributions (solution)
- Discussion 05a: Variance, Covariance (solution)
- Discussion 05b: Indicators, Conditional Distributions, Memoryless Property (solution)
- Discussion 05c: Uniform Distribution, Exponential Distribution (solution)
- Discussion 05d: Continuous Conditioning, Normal Distribution (solution)
- Discussion 06a: Markov's Inequality, Chebyshev's Inequality, WLLN (solution)
- Discussion 06b: Entropy, Relative Entropy, Chernoff Bound (solution)
- Discussion 06c: Markov Chains I (solution)
- Discussion 06d: Markov Chains II (solution)
- Discussion 07a: Modular Arithmetic (solution)
- Discussion 07b: Chinese Remainder Theorem, RSA (solution)
- Discussion 07c: RSA (solution)
- Discussion 07d: Polynomials, Secret Sharing (solution)
- Discussion 08a: Polynomials (solution)
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) (solution)
- Homework 02: Stable Marriage, Graph Theory, Countability, Computability (TeX) (solution)
- Homework 03: Counting, Introduction to Probability (TeX) (solution)
- Homework 04: Random Variables, Distributions, Expectation (TeX) (solution)
- Homework 05: Variance, Coupon Collector, Continuous Probability (TeX) (solution)
- Homework 06: WLLN, Entropy, Chernoff Bound, Markov Chains (TeX) (solution)
- Homework 07: Modular Arithmetic, RSA, Error-Correcting Codes (TeX) (solution)