I will also assign homework from the textbook. This are mostly meant to check that you are following along with the class material.

The final grade will be based on HWs (10%), midterms (50%) and final (40%).

We will also discuss personal projects to be completed together with the final. To prepare a good project it is necessary to start as soon as possible. I can propose subjects for possible projects but I'd prefer if you find a problem involving probability theory you are interested in and that can be analyzed with the tools you will learn in class.

**Basics**: The probability framework, Conditional probability, Bayesâ€™ theorem, Independent events.**Random Variables**: Discrete and Continuous r.v., Joint distributions, Expectations, variance, covariance**Convergence Theorems**: Convergence in probability and in distribution, Law of Large Numbers, Central Limit Theorem, Large deviations.**Optional arguments (time permitting)**: Markov Chains, Random Walks, Convergence to Equilibrium.

**First week.**

Material covered: Chapter 1 sections 1.1 to 1.5.

Lecture notes: 8/25

Exercises: 1.10, 1.17, 1.21, 1.27, 1.30.

**Second week.**

Material covered: Chapter 1 sections 1.6 to 1.9.

Lecture notes: 8/30,
9/1

Exercises: 1.44, 1.52.

Problems: 9, 14, 17.

**First HW collection: 9/1**. HW must be uploaded to canvas before the beginning of class.

Solution set for the first HW.

**Third week.**

Chapter 2 sections 2.1, 2.2, 2.4.

Lecture notes: 9/6, 9/8.

Exercises: 2.10, 2.11, 2.24.

**Forth week.**

Material covered: Chapter 2 sections 2.3 and 2.5, Chapter 3 sections 3.1 and 3.2.

Lecture notes: 9/15, 9/19.

Class recording: 9/15, 9/19.

Exercises: 3.8.

Problems for Chapter 2: 4, 5, 7.

**Second HW collection: 9/20.** Solution set for the second HW.

**Fifth week.**

Material covered: Chapter 3 section 3.3 to 3.5 and Chapter 4 section 4.1 and 4.2.

Lecture notes: 9/20, 9/22.

Class recording: 9/20.

Exercises: 3.25, 3.42, 4.18.

Problems for Chapter 3: 4, 7.

**Sixth week.**

Material covered: Chapter 4 section 4.3 and 4.4 and Chapter 5 section 5.1.

Lecture notes: 9/27, 9/29 review.

Exercises: 4.41, 5.13.

Problems for Chapter 4: 5.

**The first midterm** will be posted on Tuesday 10/4 and will be due on Thursday 10/6 before class. It will cover Chapter 1 to 4 of the book. Here is some practice material from previous years: Spring 19, Spring 20, Spring 21 (take home). Some more examples thanks to prof. Houdré: Spring 18 and Fall 18.

**Third HW collection: 10/4.** Solution set for the third HW.

Solution set for the first midterm.

**Seventh week.**

Material covered: Chapter 5 sections 5.2 and 5.6

Lecture notes: 10/04, 10/06.

Exercises: 5.18, 5.30, 5.32, 5.54.

Problems for Chapter 5: 7, 11

**Eighth week.**

Material covered: Chapter 6 sections 6.1 to 6.4.

Lecture notes: 10/13.

Exercises: 6.14, 6.26, 6.36, 6.45.

**Fourth HW collection: 10/25.**

**Ninth week.**

Material covered: Chapter 6 sections 6.5 to 6.8.

Lecture notes: 10/20

Exercises: 6.55, 6.61, 6.70, 6.80.

Problems: 6, 20

**Tenth week.**

Material covered: Chapter 7 section 2 to 4.

Lecture notes: 10/25, 10/27

Exercises: 7.10, 7.36.

Solution set for the forth HW.

The second midterm will be on Tuesday 11/8 and will be due on Thursday 11/10 before class. It will cover up to Chapter 6 included and concentrate on Chapter 5 and 6 of the book. Here is some practice material from previous years: Spring 19, Spring 21. Some more examples thanks to prof. Houdré: Spring 18 and Fall 18.

**Eleventh week.**

Material covered: Chapter 7 sections 5 and 6.

Lecture notes: 11/1, 11/3

Exercises: 7.60, 7.75, 7.96.

Problems for chapter 7: 8, 11.

**Fifth HW collection: 11/22.**

If you want to work on a **personal project** for improving your final grade this is the moment to decide. Here you can find a couple of past project I enjoyed. The project should be 5 to 10 page long and contain a complete discussion of a probability related problem. Please see me after class or at HO for more information.

Solution set for the second midterm.

**Twelfth week.**

Material covered: Chapter 8 sections 1 to 3.

Lecture notes: 11/8, 11/10

Exercises: 8.10, 8.11, 8.21

**Thirteenth week.**

Material covered: Chapter 8 sections 4 to 5.

Lecture notes: 11/15, 11/17

Exercises:8.32, 8.42

Problems for chapter 8: 5, 14

**Fourteenth week.**

Material covered: Introduction to Stochastic Processes.

Lecture notes: 11/22

**Fifteenth week.**

Material covered: Markov Chains.

Lecture notes: 11/29, 12/01

The final will be posted on Tuesday 12/13 around 11am and will be due on Thursday 12/15 before 2:10pm. It will cover from Chapter 1 to Chapter 8 included. Here is some practice material from previous years: Spring 19, Spring 21.