HOMEWORK

Homework is from the textbook by Durrett. Homework is due in class on Wednesdays. Please hand in the starred problems.

Homework 1: due Wednesday, October 15, 2014, at the beginning of class.
Exercises 1.1.1, *1.1.2, *1.1.3, 1.1.5, 1.1.6, 1.2.3, *A.1.1.
Hint for problem 1.1.3: any non-empty open set in Euclidean space can be represented as a countable union of "boxes" of the form given in Example 1.1.3. You should prove this fact before using it. To prove it, restrict to boxes where a_i, b_i are all rational; there are only countably many such boxes since the rationals are countable. Then show that any non-empty open set can be represented as a countable union of such boxes.
Hint for problem 1.2.3: consider how many places the distribution function has a jump of size greater than 1/n, for n=1,2, ....
Solutions to starred problems on homework 1 are here. You will need a password given out in class in order to access these solutions.

Homework 2: click here to see homework 2 which is due on Wednesday, October 22, 2014, in class.
Solutions to starred problems on homework 2 are here.

Homework 3: Click here to see homework 3 which is due on Wednesday, October 29, 2014, in class.
Solutions to starred problems on homework 3 will be available here starting on October 30. As usual, you will need the username and password given out in class to access these.

Homework 4: Click here to see homework 4, which is due on Wednesday, November 5, 2014, in class. Solutions to starred problems are here. As usual, you will need the username and password given out in class to access these.

Homework 5, due in class on Wednesday, November 12, 2014: Problems 2.1.3, 2.1.4, 2.1.9, *2.1.10, 2.1.12, *2.3.12,*2.3.13, 2.3.18(ii) from Durrett. For a sketch of solutions to starred problems on homework 5, click here.

Homework 6, due in class on Wednesday, November 19, 2014: Problems 1.4.1, 1.4.3, 1.4.4, *1.5.1, *1.5.4, 1.5.6, *1.5.7, 1.5.9, 1.5.10 from Durrett. For a sketch of solutions to starred problems on homework 6, click here.

Homework 7, due in class on Monday, November 24, 2014: Problems 1.6.1, 1.6.2, 1.6.5, *1.6.6, *1.6.12, 1.6.16 from Durrett.
For a sketch of solutions to starred problems on homework 7, click here. There will be no homework due in the week of December 1-5 as there is a midterm on Wednesday, December 3 of that week.

MIDTERM There will be a midterm on Wednesday, December 3, 2014 in class. It will test the material covered in lectures and in related readings from the book through Monday, November 24 and in homework assignments 1-7. Please bring your student ID, a blue book or two, and pens/pencils to write with. No books or notes are allowed. You may not bring a calculator -- you will not need one. Make sure to justify your answers (credit will not be given for "inspired'' answers). Remember that part of each problem is to set it up and to arrive at the answer by a progression of logical steps. Please start each problem on a new page, write legibly, and put your name on your blue book.
There will be a review session given by the TA at 1-2pm on Tuesday, December 2 in AP&M 7421.
Solutions to the midterm are available here.

Homework 8, due in class on Wednesday, December 10, 2014: Click here to see the homework assignment.