Top Math Grad Schools - What seems to make the cut?

Graduate School
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<p>I have had a fair bit of conversation about this, so I'm aware of the basics - i.e., I realize the grad school game is different from the undergrad game, realize teacher recommendations are huge, research is good, and such things. </p>

<p>For math grad school, I've heard lots of things about the likes of Princeton and the other really elite schools. What seems to make the cut?? There are a very, very few people enrolled each year, right. So is it usually one really famous professor who makes it...is it papers...is it just being exposed to exceptionally serious math and showing promise as a sophisticated mind?</p>

<p>I have it from a Berkeley grad student or two themselves that papers aren't that common in the pure math world for undergraduates, unless they're not really pure math papers. Even the most brilliant professors kind of say what one can do in undergrad in terms of research is heavily limited - even for advanced undergraduates.</p>

<p>WHAT MAKES THE CUT? Is it ULTIMATELy random to a degree like undergrad admissions? I hope not! I have some years, so please comment.</p>

2

<p>I'd say there definitely is some randomness, though you will certainly find that the very top tier of candidates get accepted just about everywhere. I've even heard of Putnam champions being recruited from some very impressive schools. </p>

<p>I disagree with your grad students who claimed that publishing is not common. It is, in fact, very common for math students to attend one or two REUs, often resulting in publications. Whether or not those papers are likely to be pure I couldn't say. I'm only applying to Biostat schools, but I've published 2 papers, one in *Graphs and Combinatorics<a href="would%20you%20call%20that%20pure?">/I</a>.</p>

<p>So anyway, if you want to go to a really top school, here's what I think you should do. Accomplishing at least half of the list will probably make you a reasonable candidate. </p>

<ol>
<li>Attend 2 REUs and do a good enough job to get a recommendation from your adviser. Ideally the REU would be in your chosen field.</li>
<li>Publish. Try to make it into a decent journal; the Online Journal of Mumbojumbo won't help your application that much. </li>
<li>Take graduate level classes in the field you're applying to. Even better--TA those classes.</li>
<li>Take (and make A's in!) all of the following classes:
-2 semesters of real analysis
-2 semesters of algebra
-differential geometry
-topology
-probability
-complex analysis (not as important, but still nice)
-as many more as you can stand</li>
<li>Make at least a 20 on the Putnam. Higher is always better, though. </li>
<li>Complete an independent research project. A thesis, at minimum. </li>
<li>Get to know the professors who are writing your recs very, very well. Make sure they think you are just swell. A two-sentence rec from a fields medalist is nothing to sneeze at, but it is not going to get you in.</li>
</ol>

<p>Good luck!</p>

3

<p>My friend at Berkeley math more or less followed rezpane's model to get in, minus enrolling graduate courses and published work. He was basically the top student in the math department at his well-respected LAC, did the Budapest Semesters in Math program, took as many difficult math courses as he could schedule including the ones listed above, very good in-major grades, two REUs (no publications from those yet but I think one is in the works), senior thesis, respectable Putnam scores (though not top 100 in any year). Berkeley might be basically the best math program you can get into without being insanely exceptional, though.</p>

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<p>Budapest is definitely a good call as well. And it's a lot of fun. </p>

<p>Publishing takes so long that it's probably just as good to say that your papers are under review (that's where mine are, and have been for a couple of months). </p>

<p>I agree that the harvard, princeton, etc. class of graduate schools require something truly exceptional. It's not enough to be a good math student, you have to be pretty spectacular. If completing that list I wrote sounds completely impossible, then Princeton is probably not the best place for you. </p>

<p>Also, it is probably not a great idea to go to the best grad school you can get into. The last thing you want is to be the worst student and fail your exams. Also, most of the top programs (including Stanford, Berkeley, etc) are populated with fantastic foreign students who come into the program with basically the equivalent of a Masters already. Unless you are Terence Towe, these students are going to dominate you. I personally think it's better to go somewhere where you are more middle of the pack, even if that means graduating from a less prestigious institution. At grad school you're going to want to work closely with a good researcher, and get lots of publications under your belt. This is a lot easier to do when you aren't struggling just to stay afloat. </p>

<p>My advice--shoot for Princeton, if you think you could make it, but don't go there.</p>

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<p>"Berkeley might be basically the best math program you can get into without being insanely exceptional, though."</p>

<p>But there's still the problem of staying in the program. Berkeley has a reputation for accepting more people than they ultimately plan on keeping and trying to weed them out with difficult/competitive qualifying exams. I don't even know if anybody from my school the past few years has even bothered applying there because of this.</p>

<p>Also, having research (let alone a publication) can be a very good thing, but isn't always necessary. My friend last year got waitlisted at MIT, and accepted to Chicago and maybe one other top 15 school without having any research experience (they ultimately ended up doing Econ somewhere else).</p>

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<p>Hi all, thanks for your comments (I'm of course open to more). </p>

<p>"I disagree with your grad students who claimed that publishing is not common. It is, in fact, very common for math students to attend one or two REUs, often resulting in publications."</p>

<p>I must've phrased this poorly. The grad student didn't claim publishing is itself not common, but publishing in the abstract, pure math sense does seem logically uncommon. For instance, if I want to go study algebraic geometry, it is ridiculously uncommon for an undergrad to get far enough in our program to realistically survive our algebraic geometry course at Berkeley. The grad course, I mean. I think the grad student and my professors meant that it's very hard to publish in really, really pure abstract math! I mean heck, that's the kind of stuff the professors are struggling with at their own lofty level! </p>

<p>I am taking advantage of the Berkeley grad department currently (somewhat early), and that is I think one of my strongest points, given the department is already well reputed. The thing is, I am finding it tough to think of publishing in the areas of math I am currently leaning towards. One of which is algebraic geometry. I expect to get to some very serious stuff by my junior year, but I'm unsure where to go if I want to conduct independent projects, and such (the idea of which definitely interests me) if I want to keep it to my area of interest. After all, I'm not being THAT specific, i.e. so and so specific area of so and so specific subject, etc. I am just not a Putnam type, though I think I'm a fairly dedicated math student otherwise.</p>

<p>With these more subtle considerations, I hope for more comments, expanding on rezpane's post. I understand what I have to do in terms of coursework, and have a plan, but much less of one for the independent work area. </p>

<p>Thanks again for your kind advice.</p>

7

<p>Well actually rezpane, I guess you did know what I meant =] - yeah, pure math in the sense of analysis, algebra, topology and geometry, at the level of the courses they do in college. </p>

<p>Are my options very limited in this case? This is my main concern when posting above. I have heard of REU's, but I know for a fact that my interests are hard to match. This summer, I am planning on doing some sort of reading course in a topic of my choice. </p>

<p>I feel like I'll end up learning lots and lots and lots, but don't want to be lacking in this independent project area, and have that be the reason I don't get into the programs of my choice.</p>

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<p>If you're worried about the research portion of your application begin weak--then do some research! There are several options--you could act as a research assistant to a professor who is close to your area, complete a senior thesis, get a masters first, or apply to an REU (I highly recommend this, it can be a great experience, and there are certain to be some projects in algebraic geometry, or close to it). </p>

<p>It doesn't matter so much if the research is not the purest of pure, or even particularly close to your chosen field (biostats and combinatorics? not even close). I think the most important part about doing research is just being able to say on your application, "I have done research and I liked it. I promise I won't drop out of your program after 4 years of being paid for not finishing my dissertation." The programs you apply to need to know you are not only capable of learning mathematics, but generating it.</p>

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<p>How uncommon is "ridiculously uncommon" ? I think each year at Michigan there's about 2 undergrads taking graduate level algebraic geometry, and a few more that are qualified but either aren't interested or can't fit it into their schedule.</p>

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<p>Why does it even matter if you get into one of the super duper mega excellent top schools, or if you just get into a pretty good school? Almost every single person I know who has been in a math PhD program has found it to be difficult and stressful, and so I don't see any reason to put any <em>more</em> stress on yourself to arbitrarily get into one of the top three programs. The only people I know who are applying to such top schools are only doing so because they're so far along in their research already and they know a particular professor who they're dying to work with. If that's not the case for you, relax a little bit. And even if it is, there's plenty of time to stress out later in life.</p>

<p>I may be a bit cynical, having gone to grad school and then left, but I'm saying this more from what I've observed than what I experienced myself.</p>

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<p>It's important because starting with grad school, the tendency is to fall down the tiers as you move on. There's a lot of openings for graduate students, not very many for post-docs, and very few for tenure-track positions.</p>

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<p>Rezpane - thanks, I'll keep in mind that I don't HAVE to keep it related to my most immediate interests. I guess it'd be most ideal if any research work I did is, since you know....after having studies all this math which I like a ton, working with it in a research setting sounds really fun! </p>

<p>Emengee - well, I'm not aiming just for prestige, there are some professors I would rather like to end up working with. Some of the best schools in the stuff I'm interested in also happen to be some of the best schools in general =]. The point of this thread was that I think I'll have a strong application in terms of LEARNING math, to put it as rezpane did, and I have some time, so I think it'd be shame not to get into the best schools I can because I didn't show a grad school I can do something which I (hopefully!!!!) can do. I am actually a staunch believer that grinding mathematics is an awful thing to do, and it's important to have fun doing it. I'd like to have the best application I can, because that likely means more options for grad school, and more options can't hurt!</p>

<p>Dilsky - well, quite uncommon in the sense that usually the undergrads who venture to take grad algebraic geometry at Berkeley are the kinds who end making it to Princeton and Harvard for grad! That's what happened last year at least. I mean, the point is those who take it often are pretty serious mathematicians, and find it really really hard themselves to process. Berkeley's course is a really technical course on scheme theory, and jumps into that stuff whether or not you have exposure to more classic algebraic geometry. Not all our grad courses are anywhere near this intensity, and this one just happens to have that reputation.</p>

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<p>Rezpane - thanks, I'll keep in mind that I don't HAVE to keep it related to my most immediate interests. I guess it'd be most ideal if any research work I did is, since you know....after having studies all this math which I like a ton, working with it in a research setting sounds really fun! </p>

<p>Emengee - well, I'm not aiming just for prestige, there are some professors I would rather like to end up working with. Some of the best schools in the stuff I'm interested in also happen to be some of the best schools in general =]. The point of this thread was that I think I'll have a strong application in terms of LEARNING math, to put it as rezpane did, and I have some time, so I think it'd be shame not to get into the best schools I can because I didn't show a grad school I can do something which I (hopefully!!!!) can do. I am actually a staunch believer that grinding mathematics is an awful thing to do, and it's important to have fun doing it. I'd like to have the best application I can, because that likely means more options for grad school, and more options can't hurt!</p>

<p>Dilsky - well, quite uncommon in the sense that usually the undergrads who venture to take grad algebraic geometry at Berkeley are the kinds who end making it to Princeton and Harvard for grad! That's what happened last year at least. I mean, the point is those who take it often are pretty serious mathematicians, and find it really really hard themselves to process. Berkeley's course is a really technical course on scheme theory, and jumps into that stuff whether or not you have exposure to more classic algebraic geometry. Not all our grad courses are anywhere near this intensity, and this one just happens to have that reputation.</p>

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<p>And what dilsky said about math careers =] I mean, if I really DO want to research math forever, I might as well give myself the best shot I can!</p>

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<p>How long are REU's and briefly how do they work? How're you initiated into the research mindset?</p>

<p>Thanks again!</p>

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<p>You should really talk to your professors about this, send then an email outliving your interests and ask them what you should do to achieve this end.</p>

<p>On another note, I always like to ask this to people who only care about getting into top schools. Is your goal to be a mathematician or is your goal to attend Harvard or MIT? If you are that unsatisfied with going to a 30-50 ranked school, then are you really willing to do what it takes to be a mathematician?</p>

<p>Do focus on learning the material and talk to your professors more. They will let you know about any opportunities available at your school and abroad.</p>

<p>You pretty much know by your 2nd or 3rd year if you are Harvard or MIT material as a lot of those that get accepted have an insane application. I knew someone who got into Harvard and they once took 6 grad courses in a semester at a big time undergrad uni and got A's in all of them and did extra material.</p>

<p>Again, is your goal getting into a top notch grad or getting into a grad school that fits you? Everyone clamors to get into Harvard and MIT, but do you know how insane it is there? Some of students don't even take the mandatory grad courses because they already took a full 2 year sequence of grad courses as an undergrad. Harvard takes 10-12 students, MIT takes around 12-15, Stanford around the same. I mean to get into the top 5, you have to be in the top 50 in THE WORLD as an undergrad as you also compete with students from Europe and China and other countries. If you aren't even the top student at your school, really, what are your chances at the top 5?</p>

<p>I'm not trying to "crush a dream" as so many melodramatic people put it, but this is reality. Look for schools that have well known advisers in the field you want to pursue. Why do you even want to go to Harvard or MIT? Who is there that specifically interests you? Is it just because of the name?</p>

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<p>OK, first off, I don't think people who've taken a million grad courses are necessarily "more amazing," and way above the level of people who didn't. Part of the deal is they probably had more time, decided they want to study math earlier.</p>

<p>I go to UCB, and have taken only graduate courses last semester, and am in my second year. I certainly don't consider myself super brilliant, just a very enthusiastic student who will likely have a good application for top schools. I think people who're in the "overall prestige mode" will automatically drop out of mathematics, and won't develop Harvard/MIT caliber applications anyway. But you shouldn't be so cynical when someone asks for advice about top schools! I'm for one thing just asking about research opportunities, with a rather specific concern (if you read all my posts in this thread). </p>

<p>I have it FROM one of my favorite professors at Berkeley that I should attend top schools if I can. It's a rough world in pure math academia, and going to a top school and seeing some of those minds at work, I think, can really push one to do his/her utmost to produce good work! I know lots of celebrities from Harvard and PRinceton, I'm less knowledgeable about MIT, but I do know a bunch at Stanford, and of course, much more than a ton of great faculty at Berkeley whom I'd love to work with.</p>

<p>I'm thankful that you're bent on destroying pretenses of "prestige and grandeur" but I'll assure you that I don't have such delusions. I have heard it from old and wise professors that aiming for a top school isn't all about vanity or delusions, and is a good goal. Plus, if anything, it's just one way to motivate oneself to do some quality work as an undergrad. </p>

<p>My simple point - I think I have some very nice strengths to my application, and don't want it thrown out for lacking research experience, and want to find out the BEST WAY for me personally to enjoy the research experience. To those who wish to post more in this thread, I humbly request that you keep it to advice, not attacks on my attitude as a mathematician; read my posts clarifying my attitude before you attack, please, thanks!</p>

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<p>I think the attitude of "LOAD UP ON INSANE COURSES" is pretty immature anyway. I try to plan my semesters so I get to material I'd really like to see, and take challenging material upon myself, because that should naturally be exciting. </p>

<p>Hate to write so much about myself, but I'm hoping these few posts of mine will do something to encourage further posters to keep it to constructive advice, for which I am thankful.</p>

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<p>Re: the research thing--To be honest, this is the kind of advice you should be looking for from a good adviser. If your adviser isn't able or doesn't have the time to offer you insightful advice on this topic, then you really need to change advisers, asap. </p>

<p>I'll just make one more point--the professor who told you that you should go to a top school if you can get into one is expressing one view. It is a fairly common opinion but by no means the final word on the topic. My own adviser feels very, very strongly that you should not go to the best school you can get into. Getting a job will actually be HARDER if you were at a top school and barely staying alive, than if you were a star at a weaker school, building a great CV. You've mentioned how much you want to enjoy your studies--this indicates to me that you will not be very happy at one of those insanely difficult top-tier programs.</p>

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<p>Geez I'm just trying to get into Rutgers or UCSD, what do you think constitutes a good application for those maybe second tier schools?</p>