How well does high school competition math predict success in college math?

Colleges and Universities A-Z Massachusetts Institute of Technology
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<p>I lived in a rural area for most of my life and had never been introduced to the AMC and competition math until last year as a junior when I moved to a large city. I took the AMC 12 and did pretty terribly. I've been working on preparing for the AMC 12 this year, but I can't say I like competition math that much.</p>

<p>I've been considering a math major in college. I love math and am fairly good (790 SAT, 800 IIC - and yes, I realize these aren't indicators of success in college) but haven't really had exposure to math beyond what has been taught in school.</p>

<p>Is it necessary to do well in competition math to do well in college math?
What is needed to succeed as a math major in college? Thanks!</p>

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<p>Oh and I’m not applying to MIT (never took a science subject test). I just figured there would be more mathematically inclined people here.</p>

<p>I’m applying to other top schools (was recently deferred from Harvard)</p>

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<p>Success in competition math is not necessary to succeed as a math major. However, mathematical maturity while not absolutely necessary does help a lot. Doing math competitions is one way of gaining mathematical maturity but not the only one. I think learning to read and write proofs is probably more important so I would suggest you try that. </p>

<p>The above only applies to serious pure math majors. Many students start off with an interest in pure math but quickly realize when they take difficult theoretical classes that they would rather do applied math or some other major.</p>

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<p>Perhaps Terence Tao’s blog will help:</p>

<p>[Does</a> one have to be a genius to do maths? What’s new](<a href=“http://terrytao.■■■■■■■■■■■■■/career-advice/does-one-have-to-be-a-genius-to-do-maths/]Does”>Does one have to be a genius to do maths? | What's new)</p>

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<p>You should be able to write proofs. It might also be helpful to learn how to program in at least one language, and learn how to use mathematica or R before you have to.</p>

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<p>I don’t think being able to write proofs before coming to MIT is necessary to be a math major, though it would be very helpful. There are at least a few courses designed to be someone’s first introduction to proofs, including an “Introduction to Proofs” class that’s offered over IAP.</p>

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<p>Not a math major - but, I also came from a rural area, hadn’t heard of the AMC until senior year, took it, and didn’t blow anyone’s socks off. I only took one math class at MIT, but it went pretty well.</p>

<p>Lots of kids from suburban/city areas who take these tests and do well have been on the math competition circuit for years. The context they come from is a lot different, and just because you couldn’t “compete” with them on these tests at the end of your high school career doesn’t mean you won’t be competitive in college math classes or as a math major.</p>

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<p>It’s worth noting that the very best high school math students have a large advantage over everyone else in math (much more than what occurs in other majors).</p>

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<p>The more experience you have with high level, rigorous math, the more assured you are that you can handle it when you see it in college. That’s the simple and obvious answer. </p>

<p>At the very least, you should be crushing your math classes in high school, particularly if it’s a regular high school. You should be getting in the 98-100 range easily.</p>

<p>As for what it means that you didn’t do well on the AMC12, that’s hard to say. If you know algebra and geometry from traditional textbooks, it should be possible to score around 100.</p>

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<p>Competition math isn’t directly correlated with college math. An extremely strong math competition scorer is unlikely, if basically interested in college math, to be bad at it, I’d guess. Creativity in problem-solving, and strong skills of observation, seem to help a lot in acing difficult competitions, and these will also help in college math.</p>

<p>What’s crucially different about college math is, as with any major, you’re charged with the task of <em>learning</em> a lot. If you’re not interested in absorbing the details of what you’re learning carefully, you won’t perform as well at it. This is the main reason I’ve seen people with high mathematical talent not really do that exceptionally well in college math. </p>

<p>A person’s ability is one thing, but the complexity of the subject is quite another – it needs to be broken down steadily and digested, which takes effort and interest along with aptitude. </p>

<p>If you can read and write proofs when you come in, you’re pretty well-equipped, like people are saying, and if you can’t develop this ability tremendously, at least try to develop it a little. It feels a little less disheartening. </p>

<p>It’s kind of like, one can succeed at an intro CS course at a strong school without ever programming before, but since the course will probably not focus mainly on programming, and they’ll expect you to pick that up quickly, it’s best to not be totally unfamiliar coming in, even if mostly so.</p>

<p>Ah and I thought I’d add - what is “mathematical maturity” … </p>

<p>It can mean different things for different levels. I think a few things to say:</p>

<ul>
<li><p>mathematical reading/writing is different from English. It has its own language, patterns, etc. I tend to write with more English than just pure symbolic writing, and that’s just my taste. However, the barrier in translating stuff to mathematical jargon is tough at the start.
Writing/reading proofs here is mostly what I mean.</p></li>
<li><p>Recognizing the subtleties behind a definition or fact. Why is it surprising? What makes it true? What is at work? Why did they define it this way rather than that way?
Of course to some extent, this goes back to the first point. </p></li>
<li><p>Being able to guess based on how mathematical reasoning is written on paper, what techniques they’re employing, and/or what the approach is. A basic example being how in a basic analysis course, they subtract this from that and that from this, and show some kind of convergence. It’ll be a bunch of formal lines. But there’s something going on there.</p></li>
</ul>

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<p>Part of the difference between contest math and advanced college math is that in college math you learn the big picture. </p>

<p>Some of the math team tricks, for instance, are derived from number theory. For me, it is harder to pick up these tricks during math team practices because they are divorced from the larger theory. The OP probably wouldn’t encounter these math tricks unless he got the solutions to the AMC12/USAMO. If you are the same way, you may do better in college math than in these contests.</p>