<p>As to research- yes of course, I plan to get started on that as soon as possible. </p>
<p>I tried to do it with a professor at SUNY-Buffalo (for cosmology), but since it is so theoretical, it is mostly him teaching me the things he teaches in his courses (but one on one!). It’s very nice.</p>
<p>Well, you really can’t get out of coursework until you’re at a pretty advanced level, which is why research at the high school level really isn’t taken seriously. The most you can do is read stuff up by yourself.</p>
<p>Depends on the mentor…DS’s mentor basically took him through a graduate-level course one-on-one (DS had already covered the undergraduate level work self-study) and then turned him loose. So far, so good. :)</p>
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<p>tu160m, the more I read your posts the more I wonder if you are trying to puff yourself up for the sake of looking good in front of a crowd, or if you are truly one of the special few individuals who are in a league of their own and just sound pompous because they don’t realize their own greatness and treat it as something ordinary.</p>
<p>The reason I say this is because no respectable professor on this earth will say “I’d love to get your work published,” and I have never, ever heard any professor, particularly in math and science, use such language. Professors, grad students, undergrads, and high-schoolers all go through the same process. They submit a manuscript to a journal, the journal sends it out for peer review, if the reviews are positive the paper gets published. If a professors offers to “get your work published” by tacking their name to your work, then you are dealing with an ethically challenged person and should stay away. If your work is truly publishable, 99% of the professors out there will offer to mentor you through the publication process, without tacking their name to your work. Sure, having the name of a professor attached can help get reviewers to treat the work more seriously, but if you are going to do that then you better make sure that you are working with someone who will do so if and only if they have made substantial contributions to the work. Reading the manuscript is not a substantial contribution.</p>
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Another statement that does not fully make sense. If it is truly a simple pattern, any old desktop should be able to crank through at least a billion possibilities in a week, you should be able to program it yourself without the need for a supercomputer.</p>
<p>katia11,</p>
<p>You probably won’t see the Cantor set used to its full extent (one of the most beautiful things about the Cantor set is that although it is uncountable, it is a null set) at Chicago because physics majors (usually) don’t take honors analysis (or any other class that introduces measure theory). If you want to see this stuff, though, of course it is possible. </p>
<p>tu160m,</p>
<p>most high school teachers don’t publish, so they may not have any idea what they are talking about. then again, you may not have any idea what you are talking about: overreaching (and building up your “paper”) may end up biting you in the arse. That said, the best of luck to you.</p>
<p>“null set”… god, I always hated that terminology. A “null set” is a set with no elements, dammit.</p>
<p>Well, I already told you I work with a professor. I am basically under his tutelage. So, his name is going to be on the paper no matter what. I am not publishing this on my own. So, this isn’t completely a case of me finding something completely remarkable while reading Paul Halmos or something. I have also talked to other professors who consider my paper interesting enough to get published. Once again, I told you I have the work done and the paper not written, so I can’t tell you if my conjecture is right. From the professors I’ve talked to, I need a supercomputer. The pattern in my result is simple but the commands for sets, operations, and variations are harder to write and more complex. The professors I’m talking to are not high school teachers, they are professors at Universities.</p>
<p>Also, this shows up on nowhere on my college apps coz its not done, so i’m not just writing something to puff things up.</p>
<p>tu160m,</p>
<p>sounds interesting and best of luck with the paper and finding the computing power. </p>
<p>Althought the paper is not done yet … if the unthinkable should occur and you are waitlisted at a favorite school, that would be a nice card to play if it has been accepted for publication somewhere by spring.</p>
<p>Also - you might consider asking one of the profs you are working with for an additional rec. If your applications are already submitted, you might send along as additional information when you submit your midterm grades.</p>
<p>phuriku,</p>
<p>that’s funny, I always preferred calling the set with no elements the empty set. It is less vague, imho.</p>
<p>I was considering that, are we allowed to send in more recs even though the admissions deadline is gone? I didn’t want to send it in and annoy them with extra paperwork.</p>
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<p>Perhaps. I find the constant ambiguity in mathematical “definitions” obnoxious. I can think of 5 definitions off of the top of my head that can be defined in multiple ways. It’s the same thing for names of theorems - how many theorems are named the “Lebesgue Theorem”? Even names that would seem to be very specific, such as the Riesz-Fischer Theorem, are different theorems depending on the source. We need some kind of committee that would officially determine definitions and names of theorems. (I must admit that definitions that are equivalent, such as the multiple defs for compactness, don’t bother me as much.)</p>
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<p>I wouldn’t send in any extra recs unless they’re really strong and lend something to your application that previous recs wouldn’t have.</p>
<p>Ok. Thank you.</p>
<p>“Another statement that does not fully make sense. If it is truly a simple pattern, any old desktop should be able to crank through at least a billion possibilities in a week, you should be able to program it yourself without the need for a supercomputer.”</p>
<p>You’ve never worked on any kind of question that had a non-trivial amount of computational complexity, have you? Go write a simple program to find the first sign change of pi(x)-li(x), and please be quiet until it finishes.</p>
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<p>Yeah, I hear you. Euler is even more problematic than Lebesgue.</p>
<p>The biggest problem is when mathematicians can’t even agree on equivalent definitions for something (e.g. rings a.k.a rings with unity a.k.a associative rings).</p>
<p>Multiple equivalent definitions are usually very interesting, as they link 2 often completely different ways of thinking of something (e.g. Heine-Borel or construction of R by Cauchy sequences and construction of R by Dedekind cuts.)</p>
<p>well I’m certainly amazed, and grateful. I hadn’t checked the site in a few days, and I come back to 3 pages of replies to my question, most of which has veered slightly off-topic.</p>
<p>I’m working on incorporating the idea behind Cantor sets into the essay so others can understand it but thanks for all the advice guys.</p>