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

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.

Lecture Plan
Lecture Day Date Topic Notes
Week 1
1 Mon Jan 5 What is Probability
2 Wed Jan 7 Conditional Probability
3 Fri Jan 9 Bayes Theorem
Week 2
4 Mon Jan 12 Counting and Combinatorics
5 Wed Jan 14 Random Variables and Binomial
6 Fri Jan 16 Moments PSet 1 Due
Week 3
- Mon Jan 19 No lecture (MLK)
7 Wed Jan 21 Poisson
8 Fri Jan 23 Continuous Random Variables PSet 2 Due
Week 4
9 Mon Jan 26 Normal Distribution
10 Wed Jan 28 Probabilistic Models
11 Fri Jan 30 Inference PSet 3 Due
Week 5
12 Mon Feb 2 General Inference Midterm PEP
13 Wed Feb 4 Multinomial
14 Fri Feb 6 Beta PSet 4 Due
Week 6
- Mon Feb 9 No lecture
- Tue Feb 10 Midterm Midterm
15 Wed Feb 11 Central Limit Theorem + SEM
16 Fri Feb 13 Algorithmic Analysis
Week 7
- Mon Feb 16 No lecture (President's Day)
17 Wed Feb 18 Information Theory
18 Fri Feb 20 Bootstrapping and P-Values PSet 5 Due
Week 8
19 Mon Feb 23 MLE
20 Wed Feb 25 Logistic Regression
21 Fri Feb 27 Comparing Classifiers
Week 9
22 Mon Mar 2 Deep Learning PSet 6 Due
23 Wed Mar 4 Beyond Classification
24 Fri Mar 6 Applications / Practice
Week 10
25 Mon Mar 9 Applications / Practice Final PEP
26 Wed Mar 11 Applications / Practice Challenge In
- Fri Mar 13 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 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.

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