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 [Soln]

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


Read: Chapter 5.4-5.6

Oct 18th

Joint Distributions



Read: Chapter 6.1

Oct 20th

Continuous Joint Distributions

5


Read: Chapter 6.2-6.3

Oct 23rd

Properties of Joint Distributions

Due: PSet #3
Read: Chapter 6.4-6.5

Oct 25th

Convolution and Joint Conditional


Read: Chapter 7.1-7.2

Oct 27th

Beta Distributions

6


Read: Chapter 7.3-7.4

Oct 30th

Great Expectations

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

Nov 1st

Covariance and Correlation


Read: Chapter 7.7

Nov 3rd

Samples
7


Read: Chapter 8.1-8.2, 8.5

Nov 6th

Central Theorems

Due: PSet #4
Read: Chapter 8.3-8.4

Nov 8th

Parameters and MLE


Read: Lecture Handout

Nov 10th

Maximum A Posteriori
8


Read: Lecture Handout

Nov 13th

Naive Bayes


Read: Lecture Handout

Nov 15th

Logistic Regression

Due: PSet #5
Read: Lecture Handout

Nov 17th

Intro to Deep Learning
9

Nov 20th

Thanksgiving
No class



Nov 22nd

Thanksgiving
No class



Nov 24th

Thanksgiving
No class

10


Nov 27th

CS109 Overview


Nov 29th

Deep Learning II


Dec 1st

Probabilistic Graphical Models
11


Dec 4th

CS109 Overview


Dec 6th

Final Review


Due: PSet #6

Dec 8tb

Dead Day
No class