<p>If I were to mention Cantor sets and the concept of aleph null and so on without really explaining the idea of infinity behind it in my essay, would the admissions committee follow what I’m saying?</p>
<p>I’d give it a shot. The basis of one of my essays was the prime number theorem, and I have another friend who went quite in depth with vector calculus and linear algebra and was still admitted. I think the concepts you mentioned are fairly well-known among students at UChicago (even non-math majors), so I don’t see why the admissions committee shouldn’t also have knowledge of them.</p>
<p>and if they don’t know what you’re talking about, they’ll probably look it up. My own essays had a few throw-ins and cultural references that were potentially obscure, but everything was wikipedia-able.</p>
<p>But, of course, remember that writing a self-evident essay is the best.</p>
<p>Not always.</p>
<p>Most likely in this case, considering that adcoms spend, in average, no more than 5 minutes reading applicants’ essays.</p>
<p>Just curious, what did you write about Cantor sets and aleph-null? I’m currently publishing a paper on finite set topology, so I had to study a lot of this stuff.</p>
<p>In high school and publishing a paper on finite set topology? Is this some kind of unofficial publication or something, or something for your high school? I can’t imagine a reason why you would have a need to do such a thing otherwise…</p>
<p>I don’t know how you could link the concepts of the Cantor set and aleph-null. The Cantor set does NOT have aleph-null cardinality, despite having measure zero (which makes it very useful for counterexamples).</p>
<p>In the middle of the last century, my very-successful law school applications involved a plain-English explanation of a complicated, technical concept from my main field of study (which was NOT anything like law). Doing something like that can be really powerful. Spouting a lot of jargon that a reader without technical competence can’t follow isn’t necessarily fatal, but it is taking a pretty big risk. First off, you need your adcom reader to be your advocate, and that can take him/her out of the game a bit. Second, although they will undoubtedly show it to someone who will understand the jargon, if that person’s reaction is “B.S. artist” you are probably dead. If that person’s reaction is positive but not “this is the best!”, you may be in trouble, because the adcom won’t be able to communicate enthusiasm.</p>
<p>Uhhhhhh. . . Chicago is my number one choice. I think I’m pretty smart.</p>
<p>I’ve never heard of such things in my life.
And someone is publishing a paper on them?</p>
<p>I’m . . . . . . very scared! </p>
<p>on the other hand. . . I put footnotes on my favorite things “essay” to clarify things a bit.</p>
<p>I’m just interested in Set Theory. It’s really not that hard. If you are doing well enough to apply to Chicago, you shouldn’t have any trouble understanding its basics. That being said, it can get really, really messy, its just that I’m not working with the metamathematics/logic parts of it. </p>
<p>I’m basically working on an algorithm for determining patterns in subset topology for a given finite group.</p>
<p>wow…i guess that alot of people use math huh…i used fermats last theorem as the basis for mine</p>
<p>I wrote about a couple of Cantor’s weirder cardinality proofs in my essay, as well as Goedel’s incompleteness theorem. Try to avoid jargon and incoherence, like JHS said. Do not write about a theorem without first understanding - either informally or formally - a proof of it. Better yet, try your own proof; maybe you’ll gain some insight for your essay.</p>
<p>tu1650m – Do you have a preprint of your paper? Where’s it being published?</p>
<p>I think that one of perks of working for admissions at UChicago is that you get to read interesting essays - and it sounds as if they may be brushing up on their math. Your essay is for the intelligent layman - and you can assume a reasonable level of competence. If you think of Stephen G. Gould’s or Carl Sagan’s writing, they explain themselves very well without a blort of equations. If you can also manage this - you will have demonstrated your understanding of the concepts, as well as your ability to express them.</p>
<p>Katia11 -
You are pretty smart. Chicago attracts some really brilliant mathematics types - but not everybody is. You will be fine.</p>
<p>Okay, guys, don’t flip out. There are certainly people that understand set theory that come to UofC, but I’m a current UofC student who has no idea what Cantor sets are, and I’m going to try to avoid them. Nooooot a prerequisite for application.</p>
<p>Esoteric and obscure for its own sake? Then no. But if the concepts are used and explained (if necessary) in a cogent, logical and meaningful way, then yes. Let someone intelligent – but less versed in advanced mathematical concepts – read it, and see what they think. And Katia11, no worries! Everyone has their area of expertise; you undoubtedly have yours, too, and the University of Chicago values them all.</p>
<p>Well. . . I’m “only” in Ap Calculus now, and we’re doing various things. I think math is interesting and all (which is good, because I want to major in physics), but I just do school math. </p>
<p>If I eventually want to know all these things. . . can I find out at Chicago? </p>
<p>Did you guys study this on your own, or are you in really advanced math courses?</p>
<p>I’m in AP Calculus too. So, no advanced courses for me. But, I have a professor I work with. And, I don’t have a paper written yet (I have all the work done), but a couple of professors told me they’d love to get my work published. That’s important because I’m basically writing a conjecture which, as far as I can see, has to be proven through exhaustion, ie with a supercomputer running the algorithm through as many possibilities as possible until it hits a snag. Plus, what I’m working on isn’t really groundbreaking, just a random little pattern that I found, so don’t get intimidated, its not a big deal.</p>
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<p>Of course you can.</p>
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<p>They all learned it on their own - trust me. You don’t need the Cantor set until real analysis (and even then, it’s not really NEEDED until graduate analysis… Rudin introduces it as an example of a perfect set in which there exists no intervals, but this is hardly necessary), and practically no high school in the world teaches this. At a point in your life, no matter who you are (but especially as a physicist), you’re probably going to have to start doing independent research, though. Some people (like the math people here) already know this, but most people matriculating into Chicago have probably yet to learn it.</p>