Instructor: Elizabeth Meckes
Office: Yost 208
Phone: 368-5015
Email: ese3 [at] cwru.edu
Office Hours: TBA
Textbook: Probability and Measure, 3e by Patrick Billingsley
Topics: We will cover most of chapters 1 -- 5 of the textbook. For some of the foundational measure theory (mostly in chapters 2 and 3), I will state results without proof in class. You are welcome (in fact, encouraged) to read the proofs in the book, but you will not be responsible for them on homework or the final. 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.
Grading: 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. There will be student presentations (worth 20% of the course grade), one final (worth 40%) and weekly homework assignments (worth 40%). Selected homework problems will be graded.
Presentations: Each student will be responsible for giving half of one of the lectures during the course of the term.
Homework Problems: Doing the homework problems is probably the single biggest factor in determining how much you get out of the course. If you are having trouble with the problems, please come ask for help; you will learn much more (and probably get a rather better grade) if you figure out all of the homework problems, possibly with help in office hours, than if you do them alone when you can and skip the ones you can't. Homework is weekly, due at the beginning of class on Wednesdays. Problems will be posted below; selected problems will be graded. You may discuss the homework with other students, however, you must write up solutions on your own.
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.