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

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.

1
 Lecture Day Date Topic Notes
2
 Week 1
3
 1 Wed Sept 23 What is Probability?
4
 2 Fri Sept 25 Conditional Probability Out: PSet #1
5
 Week 2
6
 3 Mon Sept 28 Bayes Theorem
7
 4 Wed Sept 30 Counting and Combinatorics
8
 5 Fri Oct 2 Random Variables and Expectation
9
 Week 3
10
 6 Mon Oct 5 Moments Due: Pset #1 / Out: PSet #2
11
 7 Wed Oct 7 Poisson
12
 8 Fri Oct 9 Continuous Random Variables
13
 Week 4
14
 9 Mon Oct 12 Normal Distribution Due: Pset #2 / Out: Pset #3
15
 10 Wed Oct 14 Probabilistic Models
16
 11 Fri Oct 16 Inference
17
 Week 5
18
 12 Mon Oct 19 General Inference Due: Pset #3 / Out: Pset #4
19
 13 Wed Oct 21 Multinomial
20
 - Thu Oct 22 Midterm Midterm 6:30pm
21
 14 Fri Oct 23 Beta
22
 Week 6
23
 15 Mon Oct 26 Central Limit Theorem
24
 16 Wed Oct 28 Bootstrapping and P-Values Due: Pset #4 / Out: Pset #5
25
 17 Fri Oct 30 Algorithm Analysis
26
 Week 7
27
 18 Mon Nov 2 Information Theory
28
 19 Wed Nov 4 MLE
29
 20 Fri Nov 6 Logistic Regression Due: Pset #5 / Out: Pset #6
30
 Week 8
31
 21 Mon Nov 9 Comparing Classifiers
32
 22 Wed Nov 11 Deep Learning
33
 23 Fri Nov 13 Diffusion
34
 Week 9
35
 24 Mon Nov 16 Beyond Classification
36
 25 Wed Nov 18 Applications
37
 26 Fri Nov 20 Applications
38
 Week 10
39
 - Mon Nov 23 NO CLASS (Thanksgiving Break)
40
 - Wed Nov 25 NO CLASS (Thanksgiving Break)
41
 - Fri Nov 27 NO CLASS (Thanksgiving Break)
42
 Week 11
43
 27 Mon Nov 30 Applications
44
 28 Wed Dec 2 Beyond CS109
45
 - Fri Dec 4 No lecture
46
 - Wed Dec 9 Final Exam 3:30-6:30pm

Readings

This course has a Course Reader for CS109 which is free and written for the course. You can also read from Sheldon Ross, A First Course in Probability (10th Ed.), Prentice Hall, 2018. The textbook's 8th and 9th editions have the same readings and section headers.

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