Course Syllabus

In the area below, provide basic, standard course information ahead of registration period to help students make informed course choices. Click the EDIT button and input your responses by over-writing the field description below each bolded heading. Consult the IT Help knowledge base or reach out to FAS Academic Technology at atg@fas.harvard.edu for assistance.

Course goals:

A solid mathematical foundation of probability theory up to the central limit theorem. Probability theory is full of applications. You can see a list of 10 nice stories in this video. https://www.youtube.com/watch?v=4u8Nlmek4yY

Course format:

This is a lecture course. We will develop the topic from scratch in a rigorous manner by defining what a probability space is, what random variables are. No previous exposure to probability theory is needed. 

Typical enrollees:

Students who have seen  multivariable calculus and linear algebra. 

When is course typically offered?

This course is offered in the spring and is traditionally a small course. 

What can students expect from you as an instructor?

The course will not teach from a book but develop the material fresh going into topics that are not covered as well like correlated random variables, examples from different parts of mathematics. There will be notes in style similar to Math 136 from the fall 2024 one can see here.

most websites from old courses are still online at  https://people.math.harvard.edu/~knill/teach/index.html

Assignments and grading:

One homework per week closely related to what we do in class. One midterm take home (including a small in class quiz) and final paper. 

Sample reading list:

See for example https://people.math.harvard.edu/~knill/teaching/mathe320_2022/unit08

Enrollment cap, selection process, notification:

This is usually a small course. There are no enrollment caps

Past syllabus:

We will develop the topic new but draw from  chapters 1-3 from this text  https://people.math.harvard.edu/~knill/books/KnillProbability.pdf

We first set the mathematical frame work of probability spaces, random variables and independence, conditional probability. then define expectation and variance. After putting the tools together, we will look at the law of large numbers, the central limit theorem. As for discrete process, we look at Markov process and random walks. 

Absence and late work policies:

We keep a weekly HW schedule.