Princeton vs MIT for Pure Mathematics

Colleges and Universities A-Z Massachusetts Institute of Technology
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<p>I have offers from these two, and need to decide by the deadline, which is rapidly approaching. I attended MIT's CPW, and plan to visit Princeton next weekend.</p>

<p>In terms of academics (math and the general ed requirements), social life and the undergraduate experience, which one would prepare me better for graduate school?</p>

<p>I'm going to ignore costs, as I am more concerned about the things listed above, but Princeton gave me a really nice package. Total family contribution is 20,000. Haven't heard back from MIT yet, but I doubt it'll be close.</p>

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<p>So I know a few people who’ve experienced these schools – former mathematics undergrads from both who attend Berkeley for graduate school, and conversely, Berkeley undergrads who either attend or plan to attend these for grad…while I of course haven’t attended either myself. </p>

<p>The main impression I gather is that MIT is a broader department, and that it tends to cater to a broader variety of tastes. The fact that MIT is also known for engineering and CS may create a broader mix of students taking math classes. At least for graduate school, Princeton’s atmosphere in mathematics is one that really reeks of intensity, or if you will a “hardcore” mentality – that can be a good thing or a turn off, and of course it may or may not carry over to the undergrads. The Princeton former undergrad I talked to said there was a fairly small number of math students.</p>

<p>Honestly, as far as graduate school, worry not about which school will prepare you well – worry about which school fits your taste, so you can make the leap to be prepared for mathematics graduate studies, as it’s no joke – have to be slow and steady. Both of these schools shower you with the best, but as I said, it’s no joke to be able to take advantage of it and actually prepare for graduate school. The burden is on you, not the school, so you have to be happy with where you’re going.</p>

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<p>I am planning to do pure math, and though the general impression is that MIT has an applied slant, I found lots of pure math guys during CPW and they were really hardcore math guys. I enjoyed that. Being able to mingle with other enthusiastic pure math guys.</p>

<p>I’m sure that may be more prevalent at Princeton then based on what you have stated about Princeton’s math department.</p>

<p>Both schools require a certain amount of general education requirements. Which school in your opinion, would allow me to take more math classes?</p>

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<p>^That’s not really a matter of opinion, is it? :)</p>

<p>MIT requires 17 courses, some of which you may already have credit for (single- and multivariable calculus, two semesters of physics), and some of which will also be required for a major in math (a laboratory class, two restricted electives in science). There’s no limit to the number of courses you can take per semester after freshman year, and you can begin taking upper-level and graduate courses whenever you feel you’re prepared to do so.</p>

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<p>I think except for 8 HASSes, 1 chem class, 1 bio class, and 2 physics classes, you can take all Math Classes at MIT. so it’s like 12 classes out of 8*4=32 (assuming you’re taking mininum amount of classes each semester) </p>

<p>I don’t know how the class requirements work at Princeton though</p>

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<p>I don’t know the answer to your question, Derivate, but this is a simple matter of checking their websites – I’m sure you can find out what the graduation requirements are. Or hopefully someone who’s done them will pick them out for you.</p>

<p>The things I can tell you about relate more to the actual mathematics departments, less to do with the overall undergraduate schools…which of course people who actually go to them could say more about.</p>

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<p>Well, I think the accurate way to phrase it is that MIT’s department is broader as I said. That means there will be people with somewhat more varied interests. Which sort of makes sense, right…MIT is a pretty technical school and you can imagine people getting interested in mathematics for a variety of reasons. Whereas at Princeton, I’ll bet the people into anything math-related is very specific, and perhaps more self-selecting, so the culture may reflect that in the department. I should note that by broader, I ALSO mean with regards to what fields of mathematics the faculty seem to be concentrated in.</p>

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<p>MIT has a ton of classes. The list of science/math/engineering classes is like half the size of a phone book. It may have more applied classes that are applied than Princeton, but you don’t have to take them. There are a lot of theoretical classes too. </p>

<p>In fact, for the lower level math and physics classes, MIT typically offers two versions: the super-theoretical version and the standard version. </p>

<p>Don’t be concerned about the lab requirement. If I remember correctly, you can take care of it during IAP or with a programming UROP or something (if it’s registered as a class.) </p>

<p>MIT may have a more applied atmosphere, but in terms of classes, your math classes can all be highly theoretical. </p>

<p>If your a theoretical math major, you probably won’t have trouble placing out of most of the GIR’s. </p>

<p>Echoing what mathboy said, go wherever you feel more comfortable.</p>

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<p>MIT strikes me as having more different kinds of classes. Then again, for pure math, there are several fundamentals that you have to learn very well, and the attitude of squeezing in “more classes” is not something I ever favor. I think if you mean by “more math classes,” which school will let you take fewer extraneous classes, that’s a better question :D</p>

<p>Let me explain this a little more. In math, when you go on to study independent topics in graduate school, it will be most helpful if you have a very good impression of how the foundational things actually fit into a broader picture, what sorts of techniques recur, etc. Taking more of different kinds of classes is in some ways nice if you’re just a machine that likes tons of problem-solving, but ultimately, what you will need for the future is a thorough appreciation for fundamental things. In other words, you’re learning how mathematicians think. Taking the fundamentals and understanding why they are so fundamental is a fairly big job by itself.</p>

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<p>Great post, mathboy. Couldn’t agree more.</p>

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<p>There’s plenty of pure math majors here, and if you happen to take 18.701/18.702 (Algebra sequence), or 18.100B/C (analysis) you freshman year, you will meet lots of them. The thing though, is that at MIT, a lot of non-major majors (or math double majors) will also enroll in theoretical math classes (the algebra sequence is pretty popular among physics majors). I don’t see that as a turn off, since those people are also extremely smart.</p>

<p>What I notice are: there are 2 separate path/directions for math courses at MIT (applied vs. Theoretical). There tends to be a version for each type of class (18.04= applied complex variables, 18.112= Complex analysis), and if you follow the theoretical track, you pretty much don’t have to take a single applied math class, and you can get to grad level course work pretty soon (although I don’t see why you would do so, there are plenty of challenging math classes at the undergrad level). Theoretical math classes will involve a very high ratio of pset/lecture time: as in 10hrs for a pset/3 hrs of lecture. Some of my friends spend 10-15 hrs on hard math psets, and those math classes are really intense because you are probably enrolling with people who did USAMO, math research in high school etc… But they are also very helpful too!</p>

<p>Also, one plus is at MIT, a larger part of the campus will be able to understand the “pure” math culture: we crack math jokes all the time, and we understand a lot more the burden of proof etc… You might not have such a concentrated population of math-science people at Princeton.</p>

<p>On the number of classes: MIT is extremely liberal in letting students whatever they want. If you want to take 5-6 math classes every semester, go ahead. I know some people who take 6-8 classes every semester. However, as mathboy said, with pure math, quality is much, much more important than quantity. You will find out that to really understand what is going on, you will have to sit down for hours digesting proofs, and arguments until they become innate, until you can write your own versions of the proofs etc… The time commitment is very large for the “theoretical” math classes here, even for people with lots of math experience. The smartest people I know still spend anywhere between 4-8 hrs on Analysis/Algebra psets.</p>

<p>As far as the quality of the course work offered at Princeton and MIT, I’m pretty sure they are similar. There are not 50000 ways you can learn rigorous math, and the books used for both institutions for theoretical math should be pretty similar (Rudin for Analysis, etc…) You shouldn’t worry about the quality of pure math courses at either institutions, they probably don’t differ that much.</p>

<p>So to summarize, the plusses I’ve seen for MIT are:

  • More freedom to play around with your schedule/academic liberty.
  • more choice if you happen to decide to go applied instead or CS (lots of USAMO people I know thought they liked pure math until they hit 18.701).
  • Solid and diverse curriculum for theoretical math track.
  • More math/science centered student body (if you ever go to Random hall, you’ll know what I’m talking about: there are dozens of math books lying around in the lounge).</p>
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<p>I think another question you should be asking is how the classes are structured. For instance, UChicago, an absolutely terrific school for being an undergrad in pure mathematics, is very exam-centric, and notorious for trying to be especially hard about class. While math is hard at any top notch school, there are schools with a more relaxed attitude about how they run classes. There are classes that cater to people whose goal is to learn the subject well in the most efficient, perhaps least painful way [without compromising on quality] possible, and there are classes whose purpose is to challenge those with an aptitude for problem-solving.</p>

<p>Noteworthy but extreme example of the latter is Harvard’s Math 55, known for absolutely insane problem sets. </p>

<p>How the classes are structured is a huge factor, because again, the stuff is no joke to absorb, and if you feel you’re being hosed under pressure and that’s not your style, you may just find you complete problem sets but learn and absorb less. </p>

<p>I don’t know how the schools compare in this regard, but this is certainly a useful point to figure out from those who can tell you, now that some people have posted about the difference in culture.</p>

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<p>faraday, this is a good point</p>

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<p>[William</a> Lowell Putnam Mathematical Competition - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition]William”>William Lowell Putnam Mathematical Competition - Wikipedia)</p>

<p>The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students of the United States and Canada, awarding scholarships and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools. The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, who was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.</p>

<p>The following table lists teams that finished in the top five since 1990 (as of 2009[update] competition):</p>

<p>Top Five Team (s)
19 Harvard<br>
**14 MIT<br>
13 Princeton **
12 Duke<br>
8 Waterloo<br>
7 Caltech<br>
6 Stanford<br>
4 Toronto<br>
3 Cornell, Washington U in StL<br>
2 Chicago, UC Berkeley, Harvey Mudd, University of Michigan, Yale<br>
1 Miami University</p>

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<p>**Undergraduate Mathematics Majors from last year’s Graduating Class **</p>

<p>Harvard = 83 students
Princeton = 35
MIT = 90</p>

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<p>Would fewer math majors be a good or bad thing?</p>

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<p>^ It depends on what you want:</p>

<p>Do you want to hang out with STEM majors and be able to talk about math without being considered nerdy?</p>

<p>OR</p>

<p>Do you want to hang out with humanities majors and talk about history and poetry?</p>

<p>NB: these are generalizations especially since MIT has a great humanities program.</p>

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<p>Derivate - </p>

<p>FWIW, the former Princeton undergrad I knew said the number doing math at Princeton is usually very small. </p>

<p>The thing about it being very small is that the math majors at that sort of school probably take a lot of classes together and bond closely. Take into account that usually people take more classes in the areas of math they like, and you get a small group you’ll probably get to know very well. You might have to get more overspecialized for that to happen at MIT.</p>