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.

Note on slides: In class I sometimes use slides to facilitate lecture. On their own they are not a great study resource. Here is a link to the slides directory in case you have use for them.

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

Week Monday Wednesday Friday
1

Read: Ch. 1.1 - 1.2

Apr 1st

1: Counting

Read: Ch. 1.3 - 1.6

Apr 3rd

2: Permutations and Combinations

Read: Ch. 2.1 - 2.5, 2.7

Apr 5th

3: Axioms of Probability
2

Read: Ch. 3.1 - 3.3

Apr 8th

4: Conditional and Bayes

Read: Lecture handout

Apr 10th

5: Independence
Due: PSet #1
Read: Ch 3.4 - 3.5

Apr 12th

6: E[X] of Random Vars
3

Read: Chapter 4.1-4.4

Apr 15th

7: Var(X) of Random Vars

Read: Chapter 4.5-4.6

Apr 17th

8: Poisson Distribution

Read: Chapter 4.7-4.10

Apr 19th

9: Continuous Distributions
4
Due: PSet #2
Read: Chapter 5.1-5.3

Apr 22nd

10: Normal Distribution

Read: Chapter 5.4-5.6

Apr 24th

11: Multivariable Models

Read: Chapter 6.1

Apr 26th

12: Continuous Multivariable
5

Read: Chapter 6.2-6.3

Apr 29th

13: Conditional Distributions
Due: PSet #3
Read: Chapter 6.4-6.5

May 1st

14: Multivariate Properties

Read: Chapter 7.1-7.2

May 3rd

15: Cov and Corr
6
Midterm: Tuesday, May 7th
Read: Chapter 7.3-7.4

May 6th

16: Great Expectations

Read: Chapter 7.5-7.6

May 8th

17: Beta

Read: Chapter 7.7

May 10th

18: Central Limit Theorem
7

Read: Chapter 8.1-8.2, 8.5

May 13th

19: Sampling
Due: PSet #4
Read: Chapter 8.3-8.4

May 15th

20: General Inference

Read: Lecture Handout

May 17th

21: Parameters and MLE
8

Read: Lecture Handout

May 20th

22: Gradient Ascent

Read: Lecture Handout

May 22nd

23: Maximum A Posteriori

Due: PSet #5

May 24th

24: Naive Bayes
9

May 27th

Memorial Day
No class

Read: Lecture handout

May 29st

25: Logistic Regression

Read: Lecture handout

May 31st

26: Deep Learning
10

No reading

June 3rd

27: CS109 Overview

Due: PSet #6

June 5th

28: Beyond CS109

Final: June 11th

June 7th

Exams
No class