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

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


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
 Lecture Day Date Topic Notes
2
 Week 1
3
 1 Mon Sept 22 What is Probability
4
 2 Wed Sept 24 Conditional Probability and Bayes
5
 3 Fri Sept 26 Independence
6
 Week 2
7
 4 Mon Sept 29 Random Variables and Binomial
8
 5 Wed Oct 1 Moments
9
 6 Fri Oct 3 Poisson PSet 1 Due
10
 Week 3
11
 7 Mon Oct 6 Continuous Random Variables
12
 8 Wed Oct 8 Normal Distribution
13
 9 Fri Oct 10 Probabilistic Models PSet 2 Due
14
 Week 4
15
 10 Mon Oct 13 Inference
16
 11 Wed Oct 15 General Inference
17
 12 Fri Oct 17 Multinomial PSet 3 Due
18
 Week 5
19
 13 Mon Oct 20 Beta Midterm PEP
20
 14 Wed Oct 22 Central Limit Theorem
21
 15 Fri Oct 24 Review PSet 4 Due
22
 Week 6
23
 - Mon Oct 27 Midterm (No Lecture) Midterm 7p
25
 16 Wed Oct 29 Bootstraping and P-Values
26
 17 Fri Oct 31 Algorithmic Analysis
27
 Week 7
28
 18 Mon Nov 3 Information Theory
29
 19 Wed Nov 5 Divergence
30
 20 Fri Nov 7 MLE PSet 5 Due
31
 Week 8
32
 21 Mon Nov 10 Logistic Regression
33
 22 Wed Nov 12 Comparing Classifiers
34
 23 Fri Nov 14 Deep Learning
35
 Week 9
36
 24 Mon Nov 17 Beyond Classification PSet 6 Due
37
 25 Wed Nov 19 Application/Practice
38
 26 Fri Nov 21 Application/Practice
39
 Week 10
40
 27 Mon Dec 1 Diffusion Final PEP
41
 28 Wed Dec 3 Future of Probability Pset 7 Due/Challenge In
42
 - Fri Dec 5 No Class

Readings

This quarter we are writing a new Course Reader for CS109 which is free and written for the course. You can access the previous course reader Fall 2024 Course Reader. 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.