Math491 – Probability I
Fall 2018

Instructor: Elizabeth Meckes

Office: Yost 208

Phone: 368-5015

Email: ese3 [at] cwru.edu

Office Hours: T 1-2:15, F 10-11:15

Textbook:

Probability and Measure, 3e by Patrick Billingsley

Course web page:

http://www.cwru.edu/artsci/math/esmeckes/math491/.

All course information (including the homework assignments!) is posted here.

Topics: We will cover most of chapters 1, 4, and 5 of the textbook in detail. Chapters 2 and 3 are foundational measure theory needed for the measure-theoretic development probability which follows. You will need to read chapter 2 on your own; I will cover chapter 3 in class, although not as thoroughly as chapters 1, 4, and 5. The topics covered in the first five chapters of the book are: an introduction to rigorous probability theory, general theory of measures, Lebesgue integration, random variables and expectations, and convergence of distributions.

Attendance/Reading:

You are expected to attend the lectures, take notes (some material may be covered in class that is not in the text), and read the text book, (it is certain that not all material will be discussed in class). This book is very thorough and well-written, and will be a valuable resource for the course.

Homework Problems:

As you presumably know by now, mathematics is not a spectator sport. The lectures and the book are there to get you started, but real understanding comes through working with the ideas, which is what homework is for. You are welcome to discuss the problems with each other or with me in office hours, although you must write up solutions on your own. All solutions must be typeset with LaTeX; if you need help getting started, please let me know.

I will post homework problems below as soon as we have covered enough material in order to do them. I strongly suggest doing the homework the same day as the corresponding lecture. Homework will be collected weekly.

Grading: There will be a final exam (worth 30% of the course grade) and weekly homework assignments (worth 70% of the course grade). Selected problems will be graded.

Assignments: Problems are numbered as n.m, with n being the section number and m the problem number. When a problem has an up arrow indicating that previous results are needed, you may use them without proof.

Section	Problems	Due date
1	1.2, 1.4, 1.6	9/5/18
2	2.13, 2.15	9/5/18
2	2.18, 2.19	9/10/18
3 4 5	3.11 4.14, 4.16 5.1	9/17/18
5 8	5.11, 5.12, 5.17 8.3, 8.8	9/24/18
8 14	8.20, 8.21 14.3, 14.5	10/1/18
16 18	16.8 18.1, 18.4, 18.6	10/8/18
18 20	18.20 20.5, 20.8, 20.13, 20.16	10/15/18
20 21	20.18 21.14	10/29/18
21 22 23	21.21 22.6 23.1, 23.2	11/5/18
23	23.3, 23.4, 23.5	11/12/18
23	23.6, 23.7, 24.1	11/19/18
24, clt	24.2, 24.3(a,b,c,d), additional problems: 1, 2	12/3/18