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 3rd

Counting

Slides
Lecture Notes
Administrivia



Read: Ch. 1.3 - 1.6

Apr 5th

Permutations and Combinations

Slides
Lecture Notes
Calculation Ref



Read: Ch. 2.1 - 2.5, 2.7

Apr 7th

Axioms of Probability

Slides
Lecture Notes
Serendipity Demo

2


Chapter 3.1-3.3

Apr 10th

Conditional Probability, Bayes Theorem

Slides
Lecture Notes
Bayes Demo



Read: Lecture Handout

Apr 12th

Independence

Slides
Lecture Notes


Due: PSet #1
Chapter 3.4-3.5

Apr 14th

Random Variables

Slides
Lecture Notes

3


Read: Chapter 4.1-4.4

Apr 17th

Variance, Bernoulli and Binomial

Slides
Lecture Notes



Read: Chapter 4.5-4.6

Apr 19th

Poisson and More

Slides
Lecture Notes
Hurricane Demo



Read: Chapter 4.7-4.10

Apr 21st

Continuous Random Variables

Slides
Lecture Notes

4

Due PSet #2
Read: Chapter 5.1-5.3

Apr 24th

Normal Distribution

Slides
Lecture Notes
Calculator



Read: Chapter 5.4-5.6

Apr 26th

Joint Distributions

Slides
Lecture Notes



Read: Chapter 6.1

Apr 28th

Continuous Joint Distributions

Slides
Lecture Notes
Logo Demo

5


Read: Chapter 6.2-6.3

May 1st

Properties of Joint Distributions

Slides
Lecture Notes


Due: PSet #3
Read: Chapter 6.4-6.5

May 3rd

Convolution and Joint Conditional

Slides
Lecture Notes



Read: Chapter 7.1-7.2

May 5th

Beta Distributions

Slides
Lecture Notes
Beta Demo

6

Midterm: Tuesday, May 9th
Read: Chapter 7.3-7.4

May 8th

Great Expectations

Slides
Lecture Notes



Read: Chapter 7.5-7.6

May 10th

Covariance and Correlation

Slides
Lecture Notes



Read: Chapter 7.7

May 12th

Samples

Slides
Lecture Notes
Bootstrap Demo

7


Read: Chapter 8.1-8.2, 8.5

May 15th

Central Theorems

Slides
Lecture Notes
Central Limit Theorem


Due: PSet #4
Read: Chapter 8.3-8.4

May 17th

Parameters and MLE

Slides
Lecture Notes
Likelihood



Read: Lecture Handout

May 19th

Maximum A Posteriori

Slides
Lecture Notes

8


Read: Lecture Handout

May 22nd

Naive Bayes

Slides
Lecture Notes



Read: Lecture Handout

May 24th

Logistic Regression

Slides
Lecture Notes


Due: PSet #5
Read: Lecture Handout

May 26th

Towards Deep Learning

Slides
Lecture Notes

9

May 29th

Memorial Day
No class



Read: Lecture Handout

May 31st

Deep Learning

Slides
Lecture Notes



Read: Lecture Handout

Jun 2nd

The Future of Probability
10


Read: Lecture Handout

Jun 5th

CS109 Overview


Due: PSet #6

Jun 7th

Final Review Session