This is the webpage for the course of Math 151 – Introduction to Probability.

**Lecture times:** Tuesday and Thursday 9:00 AM – 10:20 AM (Room: 380-380X).

**Instructor:** Jacopo Borga, jborga_at_stanford.edu. **Office hours:** Thursday 11:00-12:15 AM (Building 380, Room 382-Q2).

**Assistant:** Zhihan Li, zhihanli@stanford.edu. **Office hours:** Mondays and Fridays 11:30 AM-1:30 PM (Building 380, Room 381A).

**Description: **This is a first course in probability theory, similar in content to STAT 116, but with more emphasis on mathematical foundations and analytical manipulations. To start with, we will loosely follow these lecture notes written by Prof. Sourav Chatterjee, though we may end up diverging from the notes later on. There is no required textbook.

As a prerequisite for this course, students are assumed to have some knowledge of multivariable calculus (as in MATH 52 or MATH 61C), and be comfortable with proofs and have maturity in analysis (as in MATH 115).

**Program**: We will loosely follow these lecture notes written by Prof. Sourav Chatterjee. Here is a tentative program for this course:

*Week 1:* Basic Concepts

*Week 2:* Conditional probability and independence

*Week 3:* Discrete random variables

*Week 4:* Continuous random variables

*Week 5:* Expected Value + Midterm exam

*Week 6:* Expected Value

*Week 7:* Variance and covariance

* Week 8:* Inequalities

*Week 9:* Limit Theorems

*Week 10:* Markov Chains

**Exercises: **A new homework (with 50 points) will be posted at the start of every week (or earlier), and should be submitted on Gradescope by 10PM the following Monday. I will set up Gradescope to actually accept submissions until a day later, as a grace period in case of last-minute technical difficulties. Any other delay will be not accepted (i.e., no grading for late submissions). Also, your lowest homework score will be dropped from consideration.

You are permitted (and encouraged!) to discuss the problems with other students, but you must write up the solutions yourself. Please work out problems neatly — do not hand in your scratch work.

**Midterm exam: **Thursday, February 9 at 9:00 AM – 10:20 AM (Room: 380-380X).

**Final exam:** Wednesday, March 22 at 8:30 AM-11:30 AM (Room: ??).

**Grading: **Judgement based on Midterm exam mark (30%), Final exam mark (40%) and on consistent Homework (30%).