$\DeclareMathOperator{\p}{Pr}$ $\DeclareMathOperator{\P}{Pr}$ $\DeclareMathOperator{\c}{^C}$ $\DeclareMathOperator{\or}{ or}$ $\DeclareMathOperator{\and}{ and}$ $\DeclareMathOperator{\var}{Var}$ $\DeclareMathOperator{\E}{E}$ $\DeclareMathOperator{\std}{Std}$ $\DeclareMathOperator{\Ber}{Bern}$ $\DeclareMathOperator{\Bin}{Bin}$ $\DeclareMathOperator{\Poi}{Poi}$ $\DeclareMathOperator{\Uni}{Uni}$ $\DeclareMathOperator{\Exp}{Exp}$ $\DeclareMathOperator{\N}{N}$ $\DeclareMathOperator{\R}{\mathbb{R}}$ $\newcommand{\d}{\, d}$

Schedule

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.

Overview of Topics


Counting Theory

Core Probability

Random Variables

Probabilistic Models

Uncertainty Theory

Machine Learning

Lecture Plan

Lecture content is subject to change by the management at any time.

1
# Weekday Date Topic Notes
Week 1
3
1 Monday Sept 26 Counting
4
2 Wednesday Sept 28 Combinatorics PSet 1 out
5
3 Friday Sept 30 What is Probability?
Week 2
7
4 Monday Oct 3 Conditional Probability and Bayes
8
5 Wednesday Oct 5 Independence
9
6 Friday Oct 7 Random Variables and Expectation PSet 1 in / PSet 2 out
Week 3
11
7 Monday Oct 10 Variance Bernoulli Binomial
12
8 Wednesday Oct 12 Poisson
13
9 Friday Oct 14 Continuous Random Variables
Week 4
15
10 Monday Oct 17 Normal Distribution PSet 2 in / PSet 3 out
16
11 Wednesday Oct 19 Joint Distributions
17
12 Friday Oct 21 Inference
Week 5
19
13 Monday Oct 24 Inference II
14 Wednesday Oct 26 Modelling
15 Friday Oct 28 General Inference PSet 3 in
Week 6
- Monday Oct 31 No Class
- Tuesday Nov 1 Midterm Midterm: 7 - 9pm
16 Wednesday Nov 2 Beta PSet 4 out
17 Friday Nov 4 Adding Random Variables
Week 7
18 Monday Nov 7 Central Limit Theorem
19 Wednesday Nov 9 Bootstraping and P-Values
20 Friday Nov 11 Algorithmic Analysis PSet 4 in / PSet 5 out
Week 8
21 Monday Nov 14 M.L.E.
22 Wednesday Nov 16 M.A.P.
23 Friday Nov 18 Naive Bayes
Withdraw deadline
Week 9
24 Monday Nov 28 Logistic Regression PSet 5 in / PSet 6 out
25 Wednesday Nov 30 Deep Learning
26 Friday Dec 2 Fairness
Week 10
27 Monday Dec 5 Advanced Probability Challenge in
28 Wednesday Dec 7 Future of Probability PSet 6 in
29 Friday Dec 9 No Class Final: Thurs, Dec 13th, 8:30 - 11:30am

Readings

This quarter we are writing a Course Reader for CS109 which is free and written for the course. You can optionally read from Sheldon Ross, A First Course in Probability (10th Ed.), Prentice Hall, 2018. The corresponding readings can be found Win 21 schedule. The textbook's 8th and 9th editions have the same readings and section headers.