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.

While we do not have required reading for this class, the suggested readings come from the optional textbook S. Ross, A First Course in Probability (9th Ed.), Pearson Prentice Hall, 2013. Copies of the book are available for purchase at the Stanford Bookstore, and are also available on reserve in the Engineering Library.

Note on slides: The slides I present in class are meant to facilitate lecture. On their own, they are not a great study resource, so you are strongly encouraged to watch the lectures as well. The lectures are available on mvideox.stanford.edu until the end of the quarter.

The schedule is subject to change by the management at any time.

Week Monday Wednesday Friday
1

Suggested Reading:
Ch. 1.1 - 1.2

June 25th

Counting

Slides
Lecture Notes
Administrivia



Read: Ch. 1.3 - 1.6

June 27th

Permutations and Combinations

Slides
Lecture Notes
Calculation Reference



Read: Ch. 2.1 - 2.5, 2.7

June 29th

Axioms of Probability



Slides
Lecture Notes
2


Read: Chapter 3.1-3.3

July 2nd

Conditional Probability, Bayes Theorem

Slides
Lecture Notes
Medical Test Demo

July 4th

Independence Day
No class


Due: PSet #1
Read: Chapter 3.4-3.5

July 6th

Independence


Slides
Lecture Notes
3


Read: Chapter 4.1-4.5

July 9th

Random Variables
and Expectation
Slides
Lecture Notes


Read: Chapter 4.6

July 11th

Variance,
Bernoulli, and Binomial
Slides
Lecture Notes

Due: PSet #2
Read Chapter 4.7-4.10

July 13th

Poisson and More


Slides
Lecture Notes
4


Read: Chapter 5.1-5.3

July 16th

Continuous Random Variables


Slides
Lecture Notes


Read: Chapter 5.4-5.6

July 18th

Normal Distribution

Slides
Lecture Notes
Normal CDF Demo

Due: PSet #3
Read: Chapter 6.1-6.3

July 20th

Joint Distributions

Slides
Lecture Notes
5

Midterm: Tue 7:00-9:00p
Read: Chapter 6.4-6.5

July 23rd

Independent Random Variables



Read: Chapter 6.4, 5.6.1, 5.6.4

July 25th

Conditional Distributions,
Beta Distribution


Read: Chapter 7.3-7.4

July 27th

Correlation and Covariance

6

Due: PSet #4
Read: Chapter 7.1-7.2

July 30th

Advanced Expectation



Read: Lecture Notes

Aug 1st

Samples/Bootstrapping



Read: Chapter 8.1-8.2, 8.4-8.5

Aug 3rd

Probability bounds

7

Due: PSet #5
Read: Chapter 8.3

Aug 6th

Central Limit Theorem



Read: Lecture Notes

Aug 8th

Maximum Likelihood,
Maximum A Posteriori


Read: Lecture Notes

Aug 10th

Naive Bayes

8

Due: PSet #6
Lecture Notes

Aug 13th

Logistic Regression

Aug 15th



Read: Lecture Notes
Course Review

Aug 17th

Final exam: 3:30-6:30pm