Mistakes to avoid

Over the years we've had many good students perform poorly on the Comps because they made the following mistakes. Don't make them yourself!

  1. Don't take the Comp before you've finished the second semester graduate class if the class spans two semesters (Algebra, Complex Analysis, Functional Analysis, Real Analysis, Topology). Lots of people think that since the Comp primarily covers first semester material, it should be taken as soon as that semester is finished. In reality, during the second semester you reinforce and apply what you learned in the first semester. Concepts that were new and confusing at the end of the first semester will be easy and natural by the end of the second.
  2. Do study for BOTH exams well in advance. Remember that you take them on two consecutive weekends. Some people put off studying for the second Comp until after the first, giving themselves one week to study for the second. That's not nearly enough time.
  3. Don't take the Comps once before you're ready, just to get the feel for them. You only get two chances. If you burn the first one without serious studying, you're putting yourself under tremendous pressure for the second.
  4. Don't assume the Comp will be like the final of the relevant grad class. First, the Comp is usually harder. Second, the topics may vary a little. Check out the subject specific help for specifics.
  5. Do work through old Comps... Problems occasionally get repeated, and broad methods and themes often get repeated. Also, sometimes you are asked to prove classic theorems, so it may be worth memorizing proofs of these, as long as you understand what you are memorizing.
  6. ... but don't expect to pass on memorization. Although problems occasionally get repeated verbatim, more often the writers create new problems requiring you to apply the same basic principles in slightly different situations. It is pretty easy for a grader to tell when a student is regurgitating a verbatim answer to the wrong problem, and you don't get much credit for it. If you don't understand what you're memorizing, you're in trouble. To test your understanding, try modifying the parameters of the problem a little, or ask yourself to what other situations the same principles would apply.
  7. Do talk to other students or professors about the Comps. Don't study in complete isolation. The more you work problems and check your solutions with other students and professors, the better.
  8. Do answer as many problems as you're allowed to, even if some of your answers are incomplete. On the Algebra Comp, for example, you normally choose six problems. If you only answer five, you're throwing away points. A partial answer on the sixth is better than nothing. If you're worried about looking foolish, you can always write a note: "I recognize that this answers Part X, but not Part Y, of the problem." (Of course, don't write garbage just to get points -- the graders will distinguish between irrelevant rambling and steps that contribute to a correct solution.)