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

Sept 25th

Counting

Slides
Lecture Notes
Administrivia



Read: Ch. 1.3 - 1.6

Sept 27th

Permutations and Combinations

Lecture Notes
Calculation Reference



Read: Ch. 2.1 - 2.5, 2.7

Sept 29th

Axioms of Probability

Slides
Lecture Notes
Serendipity Demo
2


Chapter 3.1-3.3

Oct 2nd

Conditional Probability, Bayes Theorem
Slides
Lecture Notes
Medical Test Demo


Read: Lecture Handout

Oct 4th

Independence

Slides
Lecture Notes
Section 1

Due: PSet #1
Chapter 3.4-3.5

Oct 6th

Random Variables


Slides
Lecture Notes
3


Read: Chapter 4.1-4.4

Oct 9th

Variance, Bernoulli and Binomial

Slides
Lecture Notes


Read: Chapter 4.5-4.6

Oct 11th

Poisson and More


Slides
Lecture Notes
Section 2


Read: Chapter 4.7-4.10

Oct 13th

Continuous Random Variables


Slides
Lecture Notes
Jurors
4

Due PSet #2
Read: Chapter 5.1-5.3

Oct 16th

Normal Distribution

Slides
Lecture Notes
Normal CDF Demo


Read: Chapter 5.4-5.6

Oct 18th

Joint Distributions

Slides
Lecture Notes
Section 3


Read: Chapter 6.1

Oct 20th

Continuous Joint Distributions

Slides
Lecture Notes
5


Read: Chapter 6.2-6.3

Oct 23rd

Properties of Joint Distributions

Slides
Lecture Notes

Due: PSet #3
Read: Chapter 6.4-6.5

Oct 25th

Tracking in 2D Continuous Space
Slides
Lecture Notes
Section 4


Read: Chapter 7.1-7.2

Oct 27th

Convolution

Slides
Lecture Notes
Practice Midterm
6


Read: Chapter 7.3-7.4

Oct 30th

Beta

Slides
Lecture Notes
Beta Demo

Midterm: Thursday, Nov 2nd
Read: Chapter 7.5-7.6

Nov 1st

Great Expectations

Slides
Lecture Notes


Read: Chapter 7.7

Nov 3rd

Covariance and Correlation

Slides
Lecture Notes
7


Read: Chapter 8.1-8.2, 8.5

Nov 6th

Samples

Slides
Lecture Notes
Bootstrapping

Due: PSet #4
Read: Chapter 8.3-8.4

Nov 8th

Central Limit Theorem

Slides
Lecture Notes
CLT Demo


Read: Lecture Handout

Nov 10th

Parameters and MLE

Slides
Lecture Notes
Likelihood Demo
8


Read: Lecture Handout

Nov 13th

Gradient Ascent

Slides
Lecture Notes


Read: Lecture Handout

Nov 15th

Maximum A Posteriori

Slides
Lecture Notes

Due: PSet #5
Read: Lecture Handout

Nov 17th

Naive Bayes

Slides
Lecture Notes
9

Nov 20th

Thanksgiving
No class



Nov 22nd

Thanksgiving
No class



Nov 24th

Thanksgiving
No class

10


Nov 27th

Logistic Regression

Slides
Lecture Notes


Nov 29th

Deep Learning I

Slides
Lecture Notes


Dec 1st

Deep Learning II

Slides
See yesterday's notes
11


Dec 4th

Final Review

Slides


Dec 6th

CS109 Overview

Slides


Due: PSet #6

Dec 8th

Dead Day
No class