I'm currently an undergrad in maths and I wanted to know how those who have completed their degrees handled their test preparation. That is, how did you study and how did you manage the anxiety if there was any? As much as I prepare I find myself still feeling unprepared. Any advice is much appreciated.


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The professor should make the exam such that it is easy for anyone who is comfortable with the main definitions and theorems, and who has worked through several problems about how various definitions relate to one another and how the theorems can be applied in various ways. Unfortunately sometimes we yield to the temptation to make the problems too "interesting" (i.e. tricky) but if you are familiar with the main definitions and theorems discussed in the course then probably this means that you are already in better shape than the majority of the students, so you have little to worry about assuming a reasonable grade distribution.

As far as how to understand the basic concepts, I think that the best (and perhaps only) way is to expend a significant effort making sure that you understand everything you see, read, and write in the class. For some example, this usually means looking up unfamiliar terms sooner rather than later. It also means working on your homework solutions until you know that they are correct, and also know why they are correct. (Getting good grades on homework sometimes just means that the TA is lazy, in which case you may have to be extra careful not to delude yourself.)

Recognizing whether or not you understand something is difficult to explain how to do, so it is not often taught directly, but I think it is one of the most important skills a math student can have. It often helps to talk to other students in the class, both asking and answering questions about the subject, like "is this statement true, and why or why not?" This helps both parties, so you shouldn't be shy about asking people questions, and you should also signal to other people that you are interested in answering questions that are deeper than "what did you get for number 4?"

As far as reducing anxiety, here are some things that help me:

  • Consume only the usual amount of caffeine.
  • If the exam is in the morning, wake up at an hour that gives you just enough time to eat breakfast and maybe briefly review an outline, but not enough time to worry.
  • You're not going to learn much in the 24 hours or so before the exam, so it's probably best to use this time to maintain your health (or to cram for exams in other fields that are more amenable to cramming.)
  • $\begingroup$ +1 for Getting good grades on homework sometimes just means that the TA is lazy, in which case you may have to be extra careful not to delude yourself. $\endgroup$ – Dave L. Renfro Mar 18 '13 at 14:00
  • $\begingroup$ I don’t agree with your first sentence. I think that a good exam should have questions ranging from a few that everyone who’s even half-awake ought to get up through those that good but unspectacular students ought to get to one or two that give the truly exceptional student a chance to show off. I routinely expected a top score around $80$ or $85$% in most upper-division classes, with a median around $50$ or a bit better. (Of course I also told my students as much beforehand, though they didn’t always believe me.) $\endgroup$ – Brian M. Scott Mar 18 '13 at 16:40
  • $\begingroup$ @Brian I agree that a median of 50% score is a good goal, especially in upper division classes. In my (limited) experience this is consistent with making the problems easy for anyone who is comfortable with the main definitions and theorems (not "easy, period.") $\endgroup$ – Trevor Wilson Mar 18 '13 at 16:46

I do not have a degree in mathematics, but here is my advice.

If you know precisely what (types of) questions are likely to be on a given test, its probably a good idea to practice solving those questions and mastering them.

If you do not know the questions in advance, then you need to understand the fundamentals (especially definitions and key theorems) from the lectures. If you really understand these fundamentals, the thought of new (unexpected) questions should not produce anxiety since you will have the feeling that you are on top of the material.

Mathematics is an apriori science. For example, once a child has mastered addition of natural numbers, they do not have to worry that someone will make them add a large number of a fruit that they have never seen before. They understand that the size of the numbers, and the properties of the things being added are in a sense irrelevant. Mathematics and philosophy are a bit unique in this way. Studying mathematics should give you confidence that you will be able to solve new problems without really being prepared for them. That is the power of mathematics: you don't have to know everything in advance.

Finally, it is easier said than done, but study instead of getting anxious. I am rarely anxious when actually doing something (something besides worrying).


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