<p>Shortlist of stats:</p>
<p>4.0 GPA
Attend tier 3 no-name university
REU at Cornell in physics - no rec letter
REU at UCLA in math - 1 rec letter
2 other undergrad research experiences at my own institution - 2 rec letters - 1 publication
Assume near-perfect score on math subject gre</p>
<p>Here are schools:</p>
<p>UC Berkeley
MIT
Caltech
Stanford
UT
Yale
Cornell
Princeton
Harvard
UCLA
Purdue</p>
<p>Is this aiming too high? Do I need more safeties?</p>
<p>Your list seems a little top heavy, but you will probably get into at least one of them. If you know what area of math you’re interested in, then talk to your professors, they’ll be able to tell you if any of the departments you’re considering applying to are good for you.</p>
<p>Hey Deathly, have you taken the math GRE yet? If so, can you clue me in to what kind of diff. eq. questions were on there?</p>
<p>Also, how did you prepare for it?</p>
<p>ETS practice test and princeton text are only resources I know of. Diff eq’s from what I’ve seen were basic - seperable, exact, linear w/ constant coefficients…</p>
<p>So would you say the princeton text was a good prep?</p>
<p>I would say the princeton text was a good prep but it did not cover all the material you need. Plus, real questions were a little bit more difficult than those questions on the princeton text. </p>
<p>My advise is to focus on what you have already learned and what you are good at. You don’t need to answer all the questions to get a perfect score. However, saying that, I assume you have a solid understanding and mastery in calc, real analysis, topology, complex analysis, abstract algebra. If you do, knowing differential equations, numerical analysis, graph theory, etc. will be minor. I didn’t know any of those and I didn’t answer any of those questions (except for the most basic ones) and I still did pretty well in the exam.</p>
<p>My 2 cents, coming from a beginning graduate student in math who’s just been through the application process herself:</p>
<p>I agree with broken_symlink that your list is too top-heavy. Even the Ivies make their top students apply to several graduate programs outside of the top 20 and as someone not from a top university, you will need that safety net even more. </p>
<p>My current understanding of the admission process is that the two most important factors are your math background and your letters of recommendation. Successful applicants to the top 10 programs usually have a solid 2 year’s worth of graduate coursework under their belt. (That is, a foundation in graduate-level algebra/analysis/topology and additional coursework in a narrower specialty like representation theory or low-dimensional topology.) Of course it’s not surprising that the content of your letters of recommendations is important, but it also seems to matter who they are from. The top math graduate programs seem to swap students among each other and you might be at a very significant disadvantage if your professors have no relationships at the schools you are applying to.</p>
<p>As a concrete example, 18 of the 21 American admits to the math PhD program at MIT this past year had their undergraduate degree from a top 20 math program. The remaining 3 were from Duke, the University of Illinois at Urbana Champaign, and Bryn Mawr College (though practically an undergraduate at the University of Pennsylvania) - all very strong universities too!!!</p>
<p>Out of the graduate programs I visited, MIT, Princeton and Stanford seemed very exclusive and prestige-oriented. Berkeley, Michigan, Austin, Columbia and Cornell were more open to bright students from “normal” universities, though most of their accepted students still had some graduate-level training as undergraduates. Penn accepts a lot of students from liberal arts colleges, where graduate courses are not commonly available.</p>
<p>Hope this helps.</p>
<p>P.S. Applying to PhD programs is not about getting into the most prestigious program but rather finding the best adviser for your interests. The top programs usually have a high concentration of good advisers, but not every program is strong in every discipline. Conversely, there are some fantastic and famous advisers at less prestigious programs. Work with your undergraduate advisers to find graduate programs which will meet your academic needs; don’t just take the x most prestigious ones.</p>
<p>To add another datapoint, I was speaking from someone who finished PhD at Stanford in recent years. He said about 2/3 came from “good” schools. Contrary to your experience.</p>
<p>Also, in response to “Successful applicants to the top 10 programs usually have a solid 2 year’s worth of graduate coursework under their belt.” If you could find anybody reputable saying this, I would be surprised. Noone does this. Maybe 4 grad courses at max. Maybe if you consider Rudin to be graduate coursework…</p>
<p>And PhD programs are about most presitigous program. UCLA might be better ranked than Harvard/MIT in applied math, but which is more competitive? Which is getting better people? Not UCLA.</p>
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<p>Err… how would you know this? This is a very undergrad-ish perspective. Probably it’s not terribly accurate.</p>
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<p>No, they’re not. They’re about finding the best fit with an advisor to pursue research that fits your interests.</p>
<p>“Prestige” as defined by USNWR rankings, like it always is on CC, is utterly meaningless in graduate studies. Different universities have different strengths and weaknesses depending on what the program’s professors are researching. No single university is “best” at everything, or remotely close to it.</p>
<p>
I don’t know what the norm was a couple of years ago but it does seem to be the norm now. On the East Coast, you can find freshmen in graduate math courses these days. (I even know two high school students taking graduate math courses at Penn right now.) When I did an REU after my sophomore year, all 20-something students in the program had taken a few graduate courses already and they all still had 1-3 years to graduation. And places like Princeton and MIT have their graduate programs set up in a way that makes it practically impossible to start out with a year of analysis/algebra/topology.</p>
<p>Maybe the sentence in question would be more accurate with “top 10” replaced by “top 5” but I do stand by my assertion.</p>
<p>Even outside the top 10, it’s fairly common for undergrads to take graduate courses. At my undergrad school, about five students took 4 or more graduate math courses before graduating.</p>