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

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 Monday Jan 6 Counting
4
 2 Wednesday Jan 8 Combinatorics
5
 3 Friday Jan 10 What is Probability?
6
 Week 2
7
 4 Monday Jan 13 Conditional Probability and Bayes
8
 5 Wednesday Jan 15 Independence PSet 1 Due
9
 6 Friday Jan 17 Random Variables and Binomial
10
 Week 3
11
 - Monday Jan 20 No Class (MLK Jr Day)
12
 7 Wednesday Jan 22 Moments
13
 8 Friday Jan 24 Poisson PSet 2 Due
14
 Week 4
15
 9 Monday Jan 27 Continuous Random Variables
16
 10 Wednesday Jan 29 Normal Distribution
17
 11 Friday Jan 31 Probabilistic Models PSet 3 Due
18
 Week 5
19
 12 Monday Feb 3 Inference PEP 1
20
 13 Wednesday Feb 5 General Inference
21
 14 Friday Feb 7 Multinomial PSet 4 Due
22
 Week 6
23
 - Monday Feb 10 No Class (Break)
24
 - Tuesday Feb 11 Midterm Midterm: 7 - 9pm
25
 15 Wednesday Feb 12 Beta
26
 16 Friday Feb 14 Central Limit Theorem
27
 Week 7
28
 - Monday Feb 17 No Class (President's Day)
29
 17 Wednesday Feb 19 Sampling Statistics
30
 18 Friday Feb 21 Bootstraping and P-Values PSet 5 Due
31
 Week 8
32
 19 Monday Feb 25 Algorithmic Analysis
33
 20 Wednesday Feb 27 Information Theory
34
 21 Friday Feb 28 M.L.E
35
 Week 9
36
 22 Monday Mar 3 Logistic Regression PSet 6 Due
37
 23 Wednesday Mar 5 Comparing Classifiers
38
 24 Friday Mar 7 Beyond Classification
39
 Week 10
40
 25 Monday Mar 10 Deep Learning PEP 2
41
 26 Wednesday Mar 12 Diffusion
42
 27 Friday Mar 14 No Class PSet 7 Due

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 ReaderYou 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.