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

**IMPORTANT NEWS: **The first 3 weeks of lectures will be ONLINE on Zoom (but not recorded!). From Week 4 on, we will return to have in-presence lectures.

The office hours of the course assistant Pranav Nuti will be in-presence starting from Week 4 (but online on Week 1-2-3).

This plan might change according to possible modifications in Stanford mandates and travel restrictions.

**Lecture times:** Tuesday+Thursday 9:45 AM – 11:15 AM (60-109)

**Instructor:** Jacopo Borga, jborga_at_stanford.edu. **Office hours:** Tuesday 8:30-9:30 AM.

**Assistant:** Pranav Nuti, pranavn_at_stanford.edu. **Office hours:** Monday 5:00 PM- 7:00 PM, Thursday 5:00 PM- 7:00 PM.

**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:* Bonus topics, e.g. Markov Chains, Entropy, Probabilistic Method

**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 3 at 9:45 AM – 11:15 AM.

**Final exam:** Wednesday, March 16 at 8:30 AM-11:30 AM.

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