The class starts by providing a fundamental grounding in combinatorics, and then quickly moves into the basics of probability theory. We will then cover many essential concepts in probability theory, including particular probability distributions, properties of probabilities, and mathematical tools for analyzing probabilities. Finally, the last third of the class will focus on data analysis and machine learning as a means for seeing direct applications of probability in this exciting and quickly growing subfield of computer science.

The schedule is subject to change by the management at any time.

Week Monday Wednesday Friday
1


Suggested reading: Ch. 1.1-1.2

Jun 26th

Counting

Administrivia
Slides
Lecture Notes



Chapter 1.3-1.6

Jun 28th

Permutations and Combinations

Calculation Reference
Slides
Lecture Notes



Chapter 2.1-2.5, 2.7

Jun 30th

Axioms of Probability

Slides
Lecture Notes
Serendipity Demo

2


Chapter 3.1-3.3

Jul 3rd

Conditional Probability,
Bayes' Theorem

Slides
Lecture Notes
Bayes Demo


Due: PSet #1
Chapter 3.4-3.5

Jul 5th

Independence

Slides
Lecture Notes



Chapter 4.1-4.5

Jul 7th

Random Variables,
Expectation, Variance

Slides
Lecture Notes

3


Chapter 4.6

Jul 10th

Bernoulli and Binomial

Slides
Lecture Notes


Due: PSet #2
Chapter 4.7

Jul 12th

Poisson Random Variables

Slides
Lecture Notes



Chapter 4.8-4.10

Jul 14th

More Discrete Distributions

Slides
Lecture Notes

4


Chapter 5.1-5.3, 5.5

Jul 17th

Continuous Random Variables

Slides
Lecture Notes


Due: PSet #3
Chapter 5.4

Jul 19th

Normal Distribution

Slides
Lecture Notes
Calculator



Chapter 6.1-6.3

Jul 21st

Joint Distributions

Slides
Lecture Notes

5


Chapter 6.4-6.5

Jul 24th

Independent Random Variables

Midterm: Tue 7:00-9:00p

Slides
Lecture Notes



Chapter 5.6.1, 5.6.4

Jul 26th

Conditional Distributions,
Beta Distribution

Slides
Lecture Notes
Beta Demo



Chapter 7.3-7.4

Jul 28th

Covariance and Correlation


Slides
Lecture Notes

6

Due: PSet #4
Chapter 7.5-7.6

Jul 31st

Advanced Expectation

Slides
Lecture Notes



Aug 2nd

Samples and Bootstrapping

Slides
Lecture Notes



Chapter 8.1-8.2, 8.4-8.5

Aug 4th

Probability Bounds

Slides
Lecture Notes

7

Due: PSet #5
Chapter 8.3

Aug 7th

Central Limit Theorem

Lecture Notes



Lecture notes

Aug 9th

Maximum Likelihood,
Maximum A Posteriori

Slides
Lecture Notes
Likelihood Demo



Lecture notes

Aug 11th

Naive Bayes

Slides
Lecture Notes

8


Lecture notes

Aug 14th

Logistic Regression

Slides
Lecture Notes


Due: PSet #6
Lecture notes

Aug 16th

Deep Learning Intro,
CS 109 Overview

Slides
Lecture Notes
Review Session Problems

Aug 19th (Saturday)

Final exam: Sat 12:15-3:15pm