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

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 June 26 Counting
4
 2 Wednesday June 28 Combinatorics PSet 1 out
5
 3 Friday June 30 What is Probability?
Week 2
7
 4 Monday July 3 Conditional Probability and Bayes
8
 5 Wednesday July 5 Independence
9
 6 Friday July 7 Random Variables and Expectation PSet 2 out
Week 3
11
 7 Monday July 10 Variance Bernoulli Binomial PSet 1 in
12
 8 Wednesday July 12 Poisson
13
 9 Friday July 14 Continuous Random Variables
Week 4
15
 10 Monday July 17 Normal Distribution PSet 2 in / PSet 3 out
16
 11 Wednesday July 19 Joint Distributions
17
 12 Friday July 21 Continuous Joint
Week 5
19
 13 Monday July 24 Inference
- Tuesday July 25 Midterm Midterm: 7 - 9pm
14 Wednesday July 26 Modelling
15 Friday July 28 General Inference PSet 4 out
Week 6
16 Monday July 31 Beta PSet 3 in
17 Wednesday Aug 2 Adding Random Variables
18 Friday Aug 4 Central Limit Theorem PSet 5 out
Week 7
19 Monday Aug 7 Bootstraping and P-Values PSet 4 in
20 Wednesday Aug 9 Algorithmic Analysis
21 Friday Aug 11 M.L.E./M.A.P. PSet 6 out
Week 8
22 Monday Aug 14 Naive Bayes / Logistic Regression PSet 5 in
23 Wednesday Aug 16 Logistic Regression
- Friday Aug 18 No Class Final: Sat, Aug 19th, 3:30 - 6:30pm, Pset 6 in

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.