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

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 at any time.

1
 # Weekday Date Topic Notes
Week 1
3
 1 Monday June 24 Counting
4
 2 Wednesday June 26 Combinatorics PSet 1 out
5
 3 Friday June 28 What is Probability?
Week 2
7
 4 Monday July 1 Conditional Probability and Bayes
8
 5 Wednesday July 3 Independence
9
 6 Friday July 5 Random Variables and The Binomial PSet 1 in, PSet 2 out
Week 3
11
 7 Monday July 8 Bernoulli, Geometric, Expectation, Variance
12
 8 Wednesday July 10 Poisson
13
 9 Friday July 12 Continuous Random Variables PSet 2 in, PSet 3 out
Week 4
15
 10 Monday July 15 Normal Distribution
16
 11 Wednesday July 17 Joint Distributions
17
 12 Friday July 19 Inference
Week 5
19
 13 Monday July 22 Modelling PSet 3 in on Sunday
- Tuesday July 23 Midterm
14 Wednesday July 24 General Inference PSet 4 out
15 Friday July 26 Beta
Week 6
16 Monday July 29 Adding Random Variables
17 Wednesday July 31 Central Limit Theorem
18 Friday Aug 2 Bootstraping and P-Values PSet 5 out
Week 7
19 Monday Aug 5 Algorithmic Analysis PSet 4 in
20 Wednesday Aug 7 M.L.E. + M.A.P
21 Friday Aug 9 Naive Bayes
Week 8
22 Monday Aug 12 Logistic Regression PSet 5 in
23 Wednesday Aug 14 Machine Learning Challenge in
- Friday Aug 16 No Class Final: Sat, Aug 17th, 3:30 - 6:30pm