This is not a math problem per se, but I figured it wouldn't hurt asking for some advice in here, since a large part of the community consists of students.

I've recently taken several courses in mathematics out of general curiosity, and typically my experience has been as follows: I have no problem understanding the material and completing the assignments well, but I struggle finishing exams in time. When I solve assignments I usually take 1-3 hours or so per problem (say there are 5 problems per assignment, usually), taking my time to figure things out and check everything is correct. This strategy works well...for assignments, but not in exams, where time limit is a problem. I oftentimes struggle to figure out how to solve the problem set in an exam in the given amount of time.

So I suppose my question is, what are some tips for increasing my problem solving 'speed', or tips for taking math exams at college level?

The obvious bit of advice is, I suppose, practice, practice, practice. I got this down. But are there perhaps less obvious pieces of advice?

There just seems to be a discrepancy between understanding the material well, and being able to come up with a proof quickly, which I can't quite bridge...

  • $\begingroup$ For reference, the courses I took and struggled with were: infinitesimal calculus III (which translates to 'multivariable calculus' around these parts) and linear algebra II (inner product, some more matrix transformation tidbits, and other niceties). $\endgroup$ – ro44 Jul 5 '12 at 17:10

Well, I would suggest that you try to improve your ability to concentrate. How can you do this? Well, pratice blocking out all thoughts except for the problem that you are working on. This will reduce the amount of time you need to solve a given problem. But, it takes pratice. Anouther tip for taking proofy tests is that most professors will have questions that can be solved using techniques similar to the ones used on assignments and in proofs of theorems. So, it would definitly help to familiarize yourself with these ideas. Whenever you solve a proble, always ask: what did I learn from it? What technique, trick, idea can you glean from it? When you study, try to prove the book's theorems yourself.

  • $\begingroup$ Mhm, there is good advice here, although most of it I already know. I suppose one of my problems is that, though I can glean a lot of tricks to solve a particular 'class' of problems, usually my exams would contain problems that do not obviously belong to a specific 'class'... if that makes sense. I suppose with more practice I should learn about more 'classes' of problems and be able to identify them more easily. Concentration is certainly a problem I have; I can't concentrate when there's even a little bit of noise around, which is a shame. Thanks for your feedback, anyhows. $\endgroup$ – ro44 Jul 5 '12 at 18:22
  • $\begingroup$ @ro44: Have you tried ear-plugs? I’ve had a few students who used them for just that reason. $\endgroup$ – Brian M. Scott Jul 5 '12 at 19:02

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