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 differential equation 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 and Second week.**

Material covered: Chapter 1 sections 1.1 to 1.9.

Exercises: 1.10, 1.17, 1.21, 1.27, 1.30, 1.44, 1.52.

Problems: 9, 14, 17.

Solution set for the first HW.

**Third week.**

Chapter 2 sections 2.1, 2.2, 2.4.

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.

Exercises: 2.10, 2.11, 3.8.

Problems for Chapter 2: 4, 5, 7.

**Fifth week.**

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

Exercises: 3.25, 3.42, 4.18.

Problems: 4, 7.

Solution set for the second HW.

**Sixth week.**

Material covered: Chapter 4 section 4.3 and 4.4 Chapter 5 section 5.1 to 5.4.

Exercises: 4.41, 5.13, 5.18, 5.30, 5.32.

Problems: 5.

The first midterm will be posted on Thursday February 25. It will cover Chapter 1 to 5.4 of the book. Here is some practice material from previous years thanks to prof. Houdré: Spring 18 and Fall 18 plus Spring 19.

Solution set for the third HW.Solution set for the first midterm.

**Seventh week.**

Material covered: Chapter 5 sections 5.5 and 5.6, Review for midterm.

Exercises: 5.54.

Problems: 7, 11

**Eighth week.**

Material covered: Chapter 6 sections 6.1 to 6.4.

Exercises: 6.14, 6.26, 6.36, 6.45, 6.55.

**Ninth week.**

Material covered: Chapter 6 sections 6.5 to 6.8 and section 7.1.

Exercises: 6.61, 6.70, 6.80.

Problems: 6, 20

**Tenth week.**

Material covered: Chapter 7 section 2 to 4.

Exercises: 7.10, 7.36.

>Solution set for the forth and fifth HW.

**Eleventh week.**

Material covered: Chapter 7 sections 5 and 6.

Exercises: 7.60, 7.75, 7.96.

Problems for chapter 7: 8, 11.

The second midterm will be on Thursday April 1st. It will cover up to Chapter 6 and concentrate on Chapter 5 and 6 of the book. Here is some practice material from previous years thanks to prof. Houdré: Spring 18 and Fall 18 and my Spring 19.

Solution set for the second midterm.

**Twelfth week.**

Material covered: Chapter 8 sections 1 and 2.

Exercises: 8.10, 8.11, 8.21

**Thirteenth week.**

Material covered: Chapter 8 sections 3 to 5.

Exercises:8.32, 8.42

Problems for chapter 8: 5, 14