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

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

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.