<p>Hmm, the only thing I know about math research is that I know it exists :P</p>
<p>I've been thinking about doing some research (because I'm genuinely interested in math, the only science I'm interested in is computer science, which I think makes a great combo with math), but I'm not able to see what research you could do with math. If anyone's done math research, care to explain the type of research you've done and how much math knowledge it required?</p>
<p>I know some graduate students in math that do mathematical research. It's way over my head for sure. I finished college calc, differential equations, linear algebra, quantum mechanics... and I have no idea what they even do, I just see a bunch of equations with symbols that I don't know.</p>
<p>Well I guess I can rule out math research then... lol.</p>
<p>I actually did one on Geometry and planar rotation of objects. I submitted it to Siemens and Intel, but didn't make it into Semis. bleh. o__o</p>
<p>Anyways, I actually got the idea from reading a book and collaborating with a math teacher that I knew from a Taiwanese school. The concept is simple: suppose I have a sofa of any shape, any dimensions. Since I don't like where the sofa is sitting at right now, I want to move it to the adjacent location to where it is right now. However, the sofa is too heavy for me to lift, so is there a generalized way of rotating the sofa (on one of its legs) so that it moves into the adjacent location to the current location after an unlimited number of moves? The dimension and the shape of the sofa obviously makes a difference, so for which shapes (and dimensions) does it work? For which shapes (and dimensions) doesn't?</p>
<p>I used polar coordinates, number theory, and a bit of linear algebra in my 20-page research paper (it was about 25 pages, but had to shorten it for competitions). There were around 20 proofs in all (with math, proofs are very important - they are basically the bulk of your paper). </p>
<p>I like math, so I didn't think it was too much of a hassle. Besides, it gave me an excellent chance to learn LaTeX! =p </p>
<p>My research is actually more "elementary" compared to some of the projects I've seen at competitions. Just know that it's usually quite hard to win at competitions with a math project unless your's is really theoretical (ok, I'm generalizing), and REALLY logical and well-organized. (in other words, I think it's harder to win with a math project, compared to one in biology, for example).</p>
<p>Well that sounds a little more do-able :)</p>
<p>How long did your project take to do? I want to do one for Intel and Siemens as well, so I think I should start studying advanced mathematics now so I'll be able to do a project with a decent amount of time.</p>
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I think it's harder to win with a math project, compared to one in biology, for example
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I disagree. Not many people do math, so it's really impressive if you have a math project. There are a crap load of bio/chem projects.</p>
<p>^ I think math projects only win if the content is quite theoretical and organized. At least in the fairs that I've been at, the bio/chem projects seem to have more competition, but it's generally more "interesting" than 20 pages of proofs in a math project, and the judges are partial to "interesting" projects.</p>
<p>Oh - that project took me about a year from the very beginning to having the final draft.</p>
<p>Basically "Applied mathematics": you use your quantitative knowledge and reasoning skills to some field, usually something like physics, programming, economic theory or statistics.</p>
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I think math projects only win if the content is quite theoretical and organized.
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</p>
<p>Okay, I re-read that and I think it sounds quite ambiguous. What I meant was that a lot of the math papers that I see winning these competitions are 1) highly abstract mathematics, like discovering a collorary to a famous theorem, for example; and 2) mathematics with a very interesting connection to another field, like mentioned above (for example, like using math in demographics, economics, or the three major sciences).</p>
<p>
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I think math projects only win if the content is quite theoretical and organized.
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Depends on what you mean by "win". I thought my friend's math paper that received regional finalist was pretty pathetic. There were very few proofs and not very well organized. Oh, and it was written in MS World, wth?? (change the h to an f) But that was in 2005, when the competition was probably less intense. The 1st place math projects from past two years were just crazy, but they probably received quite a bit of help from their mentors. I mean, if Viscardi could write that paper by completely himself, I'm sure he would've made MOP a couple times. But nevertheless, those two people are very intelligent.</p>