115A MATH - Midterm One Advice
Paul Skoufranis
October 9, 2011
The following is my advice for the rst midterm in MATH 115A.
1. You should know all of the denitions given in this course. This is due to the fact that you cannot
solve a problem relating to an object you do not understand.
2. You should know the statements of all the results proven in lecture or on assignments. This is due to
the fact that you cannot solve a problem if you do not have the proper tools.
3. You should understand all of the proofs given in class and be able to recreate them on the midterm.
This does not mean you should go out and memorize all of the proofs. You should go and understand
the main idea, trick, and technique of each proof. Most techniques can be repeated or are useful in
other problems.
4. If you are asked to prove something from lecture, you should try to give the proof done in lecture and
cannot use material after the proof given in lecture. If you are asked to prove something new, anything
from class is fair game.
5. Manage your time during the test. When proving result a on the midterm, you should include as much
detail as you deem necessary. If you are unsure whether to go into more detail, leave it and come back
to the problem if you have time.
6. You should try to have an intuition about how to approach problems. This is the most dicult thing
to do in this course and, if you can do this, you should most denitely succeed. When trying to solve
a problem, you should think about what you are given and what the givens imply, think about what
you are trying to do and how you could do it, think about what techniques we have and which might
be useful, and think about which tools (i.e. results and theorems) you have and how they might be
applied.
7. Do not give up on a problem. Most problems in this course do not involve an absurdly dicult trick
and can be solved by reasoning using the denitions and results done in class.
8. Get a good night sleep the night before the midterm. If you are too tired to think because you crammed
all night, the cramming with not be eective and you will not be able to think critically.