Copy of the Fall 2010 Midterm.

Justin prepared a list of topics that have been covered so far in the course and which form the subject matter for the midterm.

## Prelimnary Instructions:

"On the midterm, you will have one multi-part question that just requires you to state either definintions, theorems, or facts. The other questions are problems that require you to demonstrated an honest knowledge of the results and techniques of the course material. These are "proofs" but all but one follow the patterns of proof that we have used in class on one (or more!) occasions.

"There are no "hard" calculations required --- if you understand the material covered so far and you don't somehow confuse yourself. You may well "finish" the exam in half of the time available. In this case, I encourage you to loook back over your work and make sure everything is water tight.

"As promised, here are the

instructions for the midterm:

- Read all of the instructions.
- When the time is up, stop working and hand in your blue book (or blue

books) ---without exception or delay.- If a problem X is not done, write "Problem X was not done" in the blue

book.- Be careful to avoid any embarrassing situations. Keep your paper out of

the eyesight of others and keep your eyes away from the work area of others.- Write clearly. Check your work.
- If you have more than one blue book number them "1 of 3", "2 of 3", etc.
- Be sure that your blue books have your printed name and your signature.
- Notation: 1_A or 1(A) are both used to denote the indicator function of the

event A, i.e. a random variable that equals 1 for omega in A and equals

zero otherwise.- Generic Question: "Can I use ...". Generic Answer: "You can use ANY

result that has been proved in class and ANY result from real analysis."- Generic Advice:
Do not get stuck! If you don't have an idea for a

problem, or if your idea is not working, go to another problem."The Midterm also has a final paragraph of advice:

"Check your work. Did you use the hypotheses? At any place did

you accidentally assume more that was given? For each of the problems (except the first) you can give a 100% correct proof on about one-half of one blue book page --- certainly one blue book page should suce. If there is some technical issue that is bothering you, it probably should not --- perhaps you need another plan. If you are worried about a technical point, you can make a note about what is worrying you and then return to that point later if you have time." "