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

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
2
Week 1
3
1 Mon Jan 3 Counting
4
2 Wed Jan 5 Combinatorics PSet 1 out
5
3 Fri Jan 7 What is Probability?
6
Week 2
7
4 Mon Jan 10
Conditional Probability and Bayes
8
5 Wed Jan 12 Independence
9
6 Fri Jan 14
Random Variables and Expectation
PSet 1 in / PSet 2 out
10
Week 3
11
Mon Jan 17 No Class (MLK Day)
12
7 Wed Jan 19
Variance Bernoulli Binomial
13
8 Fri Jan 21 Poisson
14
Week 4
15
9 Mon Jan 24
Continuous Random Variables
PSet 2 in / PSet 3 out
16
10 Wed Jan 26 Normal Distribution
17
11 Fri Jan 28 Joint Distributions
18
Week 5
19
12 Mon Jan 31 Continuous Joint
20
13 Wed Feb 2 Inference
21
14 Fri Feb 4 Modelling PSet 3 in
22
Week 6
23
Mon Feb 7 No Class (Break)
24
Tue Feb 8 Midterm
Midterm: 7 - 9pm
25
15 Wed Feb 9 General Inference PSet 4 out
26
16 Fri Feb 11 Beta
27
Week 7
28
17 Mon Feb 14 Adding
29
18 Wed Feb 16 Central Limit Theorem
30
19 Fri Feb 18
Bootstraping and P-Values
PSet 4 in / PSet 5 out
31
Week 8
32
Mon Feb 21
No Class (Presidents Day)
33
20 Wed Feb 23 Algorithmic Analysis
34
21 Fri Feb 25 M.L.E.
Withdraw deadline
35
Week 9
36
22 Mon Feb 28 M.A.P.
PSet 5 in / PSet 6 out
37
23 Wed Mar 2 Naive Bayes
38
24 Fri Mar 4 Logistic Regression
39
Week 10
40
25 Mon Mar 7 Deep Learning Challenge in
41
26 Wed Mar 9 Future of Probability PSet 6 in
42
Fri Mar 11 No Class (Break)
Final: Thurs, Mar 17th, 12:15 - 3:15pm

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.