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Quick question with starting math?

  1. Jun 2, 2013 #1
    So I have only started gaining an interest in seriously pursuing a math/physics career in the past year. Before, I have only been "good" at these two subjects and understood them relatively easily. I just thought about doing engineering and never actually had a serious interest in doing them. With regards to physics, I'm mostly ahead of others now since I have been self studying more advanced topics in the past year such as advanced EM and general relativity and the like.

    However, with math, even though I am mostly at the top of my math classes and took multivar calc/diff eqn in the past year, I don't think I'm good at math at all. I never did any competition-based math and only did it a little in freshman year of high school. Now, I only recently gained an interest in math and started doing math team again this year in senior year. Having done no practice at all, I only did slightly above average at competitions like NYSML and ARML. However, I'm mostly behind others who have much more experience and practice regularly. Even though I think I can pick up stuff easily and have a talent in these two fields, I'm slightly behind with regards to math. I will be attending college next year.

    1) Having only recently gained an interest in these two subjects, how would I catch up with others with regards to math and competition-based math since I intend on taking the putnam?

    2) Also, I did not attend a lot of math camps either, am I missing out on a lot? How would I catch up with those that have been doing this kind of problem solving math stuff 6 years more than me that usually come at the top of those regional math competitions?

    thanks.
     
  2. jcsd
  3. Jun 2, 2013 #2
    1) I believe it is possible to ace the putnam with only a solid understanding of basic college math (but obviously those questions are still immensely difficult). So know your algebra, discrete math (set theory and such), calculus, diff eq and linear algebra. I would also recommend taking some of the practice exams for the putnam available online.

    2) No. You can learn and become good at math entirely on your own.
     
  4. Jun 3, 2013 #3
    What's the importance of being good at competition amth and stuff liek ARMl and NYSMl then.
     
  5. Jun 3, 2013 #4

    verty

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    What I can suggest doing is learning/knowing EVERYTHING in the undergrad math syllabus, including number theory (especially those Fermat and Euler theorems) and probability. Looking at the Putnam questions (I looked at the 1992 paper), all the questions look difficult, and solving 5 of the 12 should get you into the top 100 according to the competition website, that means 1 hour per question which should be enough time if one knows EVERYTHING about the topic.

    It is my belief that questions at this level of difficulty cannot be solved in multiple ways, one needs to hit on the solution strategy within a reasonable amount of time, 15 minutes say. One's initial probing of the question should be to eliminate as soon as possible any less efficient solution strategy or idea at a way to solve the question.

    This is the first hurdle, to learn all this in a short time when other competitors have a head start. If you have the knowledge, practice makes perfect but this can only work, I believe, when one has available all the tools. One idea for practice is past papers from less demanding competitions.

    I see there are volumes for sale of past papers with solutions. I think relying on given solutions is a mistake because learning from a solution will give one only a superficial understanding of the subject matter. Solutions are for when you already know how to solve the problem but there may be a quicker/safer method.

    To be perfectly honest, this Putnam competition looks insanely difficult. To be in the top 2-3% of entrants and get that top 100 place, for only a mention in a magazine and a pat on the back, means that this is only for the math geniuses.
     
  6. Jun 3, 2013 #5
    Would I be at disadvantage because I don't have much experience with math team kind of stuff in the past years even though I am good with real math?
     
  7. Jun 4, 2013 #6

    verty

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    I think you won't be at a disadvantage in team events if you get some practice at them, but for individual events where there are no distractions, it shouldn't matter. I found team events to be more difficult because a team mate will say something like "I've got it, you do this and this and this is the answer", and it isn't your way of thinking, so now you weigh the odds, is it likely your team mate is correct? Is it the type of question they are good at? Should you cut your losses or have them be annoyed because you don't trust their answer? And the dynamics are wrong; you have one or two strong people and the rest don't enjoy themselves.

    But it would be a useful way to measure one's progress, to be in a team like that. I can see a use for it.
     
  8. Jun 4, 2013 #7
    I mean competition math is a lot different from real math. I have done some. I'm just not ridiculously good at it though. I was just asking because I don't know if I should practice with it because I don't think there are any math competitions beyond high school other than the putnam.
     
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