<p>Title says it all. How good is Caltech for a math major?</p>
<p>i’m gonna go ahead and say best in the nation… possibly the world</p>
<p>Alot of people say that about their college, but what sets Caltech apart from HPYMS etc.</p>
<p>I wouldn’t go as far as littlemikey4, but we do have a strong math program. </p>
<p>What sets Caltech apart? All the schools are different, and they will all offer you an excellent education. We are small, so it is somewhat easy for students to get involved with research. We also have a very rigorous core (including lots of physics), which other schools don’t have. But the biggest thing you should look at is the student culture, and where you think you fit in the best. For some people, it’s definitely Caltech, and for other people, it isn’t.</p>
<p><a href=“http://talk.collegeconfidential.com/california-institute-technology/577759-why-caltech-different-open-letter.html[/url]”>http://talk.collegeconfidential.com/california-institute-technology/577759-why-caltech-different-open-letter.html</a></p>
<p>i don’t go to caltech (only aspire to) but the general consensus seems to be that for math and sciences you’ll have a very hard time beating Caltech or MIT</p>
<p>^^ I don’t go to Caltech either, but have done a relatively good bit of homework on different schools’ math programs. I think while I wouldn’t say that one can beat MIT or Caltech, depending on one’s likes, there are schools easily as good for math. This may not necessarily be true for engineering – there may be fewer such terrific ones. But the main thing is that some Ivy League schools like Harvard and Princeton suddenly are on the the radar when you’re talking about math, and they’re really awesome. </p>
<p>So calling the department the best in the world is more than a little strange way to put it. </p>
<p>Realistically I would say that for a student coming in to major in math, the least of your concern should be whether Caltech will have enough for you to do in math, and rather the focus should be on what kind of school it is, and how it fits you. The comment about a rigorous core is for instance key. </p>
<p>For math, honestly I don’t even think HYPSM is any longer close to a canonical list. Yale for instance is a great school, but my personal view is that there would be schools where there is simply more math going on in the various different subfields. MIT, while with a strong math program, has a student body with plenty of applied interests, as friends of mine have confirmed. UChicago and UMichigan will enter the list for sure. UChicago is quite hardcore from what I hear. But might I add, each of these math programs are very different. There is something more to seeing if a school fits you than just visiting and seeing how you like the general feel – the academics can be structured incredibly differently, and this is mainly what I think shouldn’t be underestimated when making a decision. </p>
<p>One little tidbit. If I take a look at where some of the best mathematicians in the world even got their undergraduate degrees, the list is hugely varied. Whereas somehow in a given subfield, they all tend to have obtained graduate degrees from roughly 3 suspect schools. </p>
<p>I’m not sure how much of this you did and didn’t know, but I think it’s worth saying for anyone considering coming in as a math major.</p>
<p>good post, you’ve obviously done your homework about these things… just curious, in your opinion what is the top school for undergrad math in the nation… also what are the 3 grad schools?</p>
<p>^ ya I am curious too.</p>
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<p>Pretty sure the gist of his post was that there are plenty of great schools you can go for undergrad and that the particular school only matters at the grad school level. At that point, <em>it depends on the subfield you’re interested in</em>.</p>
<p>Yes, ThisCouldBeHeavn got what I was saying. It’s not 3 particular schools, I meant to say that depending on the field of interest, top researchers in that field may come from relatively less diverse graduate backgrounds.</p>
<p>I don’t think there is a top school realistically for the undergraduate years, and it depends largely on goals. People going into math have various goals, particularly because math is a very foundational type subject. Those who want to research theory learn more theory, and others supplement it with things like engineering. So it really depends on your personal goals. Obviously for those of the latter type, certainly MIT and Caltech are wonderful because you’ll find like-minded folk.</p>
<p>You basically have to somehow figure out what the math student body at these schools is interested in, and while I could throw out some stereotypes, I think I’ll abstain.</p>
<p>However, I will say this: a professor I know did comment he thinks Cambridge is really unbeaten in terms of undergraduate math education. I’m talking about the place outside of the U.S. of course.</p>
<p>I applied to Cambridge for math, but man it is almost impossible to get in…</p>
<p>“I don’t think there is a top school realistically for the undergraduate years, and it depends largely on goals.”
I’d say this depends less on goals (given that you want to be a mathematician) than on the environment in which you would like to learn math (and at ~18 years old the latter may be easier to gauge than the former). Some things to consider could be…</p>
<p>a)Number of advanced courses offered. Among the top schools, this varies greatly is pretty weakly dependent on the size of the department. Some of the top departments offer surprisingly few special topics courses–if grad students want to learn subject X they organize a reading group or student seminar, and maybe invite speakers–something undergrads can’t readily do. One thing I loved about Caltech was that (since there are so few undergraduates to teach), they let post-docs teach graduate/special topics courses, so despite the department being quite small, it seemed (at least to an undergrad who doesn’t know much) that there were classes offered (at least every other year) in pretty much every area of math one would fancy. I’m now a grad student at UChicago, where (despite the much bigger department, lots of famous professors and lots of postdocs who will soon be famous professors), it feels like a lot fewer classes are offered. For example, there are (usually) no classes in algebraic geometry offered, despite the algebraic geometry group being one of the best in the world. </p>
<p>b)Methods of assesment/ style of courses. At Caltech most grades are based on HW assignments, so you got regular feedback to check whether you’re on the ball. On the other hand, a lot of people fell into the trap of spending so much time on homework that they had no time to think about the material (I often thought I would have learned more if I was given a textbook and some papers and allowed to just think for a month). At Cambridge, from what I understand, “grades” are based on yearly exams, and for the rest of the year students learn at their own pace, regularly meeting with supervisors to gauge their progress. In retrospect I probably could have learned more under the latter system.</p>
<p>c)Amount of red tape in the department. Some departments heavily regulate who is allowed to register for advanced courses, and heavily enforce prerequisites; some do not. At Caltech prerequisites are just guidelines and you can register for any course you feel prepared for–if in some area you feel you already know the material in the undergraduate sequence you can almost always argue to take the graduate version instead. At Chicago (for instance) it seems to be almost the opposite. For freshmen to take the highest level Real Analysis course they have to distinguish themselves on placement tests; students with poor grades in certain courses are sometimes prevented from registering in more advanced courses in the same area; non-math majors are not always allowed to take advanced math classes, etc.</p>
<p>The ability to get involved with “mathematical research” should probably not be a deciding factor for choosing schools: math is cheap, you can do research anywhere with internet access, and at any decent school there will be faculty willing to guide you through the process if you are interested; besides there are plenty of math REU’s around the country.</p>
<p>happyentropy, I have a math major at UChicago who talked his way directly into Analysis first year (was offered HA, decided to stay with IBL because he liked the approach better) despite placement test results. He has found the math and CS departmental advisors extraordinarily helpful with placement issues, and there are others on the Chicago CC threads who can also attest to their flexibility. There are also some current Chicago CC posters who know non-math majors taking some heavy-duty math courses.</p>
<p>Every top math department has its specialties; OTOH, there are ways to work around that should you like the school’s approach but are interested in other fields (at least for UG). S2 wanted Chicago’s grounding in tough, pure math, but his primary interest is in complexity theory and representation theory. The cross-pollination with the CS department works well, and he’ll get extra applied goodies through REUs and BSM. In some ways MIT’s math department may have been better in some ways, but Chicago offered things MIT didn’t.</p>
<p>There was a study a few years ago that ranked graduate departments in math, with the consensus being that MIT, Chicago, Berkeley, Stanford, Harvard and Princeton were in the top tier with a relatively equal ranking.</p>
<p>I’d just like to confirm that every one of happyentropy’s points is very important. I guess I alluded to the structure of program being important in a previous post, but those points expand on what I’d also say are important.</p>
<p>The Cambridge system sounds terrific, now you mention it.</p>
<p>Might I add that if Caltech assigns grueling homework, Chicago supposedly is very exam-centric. That can be good for some (it depends what actually is going to get you to learn something, and if you’d rather have a few exams to worry about instead).</p>
<p>The undergraduate year in math serve as a time for one to get background in what one is interested in, and different schools seem to have very different ways of giving the students this background.</p>
<p>CountingDown-I’m glad it worked for your son. I know some students here who had to (and failed) to jump through insurmountable hoops to take classes they wanted. (eg cs majors whose math background was deemed insufficient to take a class in logical model theory, who had to take the same class as “independent study” instead). The problem with the “advising” system being in place is that sometimes you have to follow their advice. Personally I was glad to be treated as an adult when choosing what courses to take…(on the other hand those who were looking for guidance at Caltech were often not able to find it or given explicitly bad advice–a friend of mine was told by his “advisor” that unless he took at least three math classes a term he would not get into grad school. You had to figure things out by talking to your peers or going with the flow).
I will mention that many students at Caltech and MIT take more graduate math classes as undergrads (I took
28–in retrospect many of them were so over my head I didn’t get anything out of them…as in didn’t understand a single word) than are OFFERED at Chicago (this is of course not reflected in any rankings since grad students don’t choose departments based on course offerings). OTOH Chicago makes up for it with the directed reading program which allows students to study any subject in math they want with grad student mentors, and is probably as good approximation as any to what grad school is really like. </p>
<p>So the environments in the math departments are very different (and have nothing to do with the research interests of the faculty, or even the specific course requirements for the major, which are not that different), some may prefer one over the other, and such a choice will not affect your chances of becoming an awesome mathematician except by affecting your motivation to become one.
(Of course if you’re choosing between Caltech, MIT, Cambridge, Chicago etc the differences in math departments shouldn’t be your principal criterion…)</p>
<p>Re:exams: I loved not having many exams in college (I NEVER had an in-class test) but definitely got more out of classes with more exams rather than more homework. Having exams encourages professors to teach a well-defined chunk of material and students know what they are getting out of the course–if instead students are given impossible homework problems every week…after a week of working on them they still might not learn anything except math is hard. I like Chicago’s approach here better…</p>
<p>I tend to find that the best approach for me is for there to be homework that is not more or less challenging than the material at hand warrants. One needs to grapple at close range many times to really get something out of it, and weekly or biweekly problems tend to be a nice way to learn the stuff efficiently, so as to be able to research it later. A very famous professor at my school even said that hard homework tends to defeat the point – usually one is trying to learn the material so that one can use it later in research. Why not be doing research instead?? An occasional very hard problem can be a good exercise to get things together, though. I personally dislike exams, just because I concentrate much better when I decide when I want to do it.</p>
<p>As for flexibility, I anticipate many schools offer plenty of it – Caltech, MIT, Stanford, etc. I’m not explicitly 100% certain, but have a strong feeling. I can see some preferring the close advising system, but I definitely prefer having total freedom.</p>
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<p>I guess I would like to put in a word in defense of the Chicago system. Yes, it is true that most students don’t take graduate courses until their 4th year (although each year, about 5-10 3rd years do take graduate courses), but I have to give my opinion that from what I’ve seen, Chicago’s honors undergraduate courses seem to be about equivalent to the graduate courses at peer institutions.</p>
<p>For instance, many (by which I mean ~5-10 or so) MIT first-year math majors opt to take 18.125: Measure Theory and Integration ([MIT</a> OpenCourseWare | Mathematics | 18.125 Measure and Integration, Fall 2003 | Home](<a href=“http://ocw.mit.edu/OcwWeb/Mathematics/18-125Fall2003/CourseHome/index.htm]MIT”>http://ocw.mit.edu/OcwWeb/Mathematics/18-125Fall2003/CourseHome/index.htm)), which is a graduate course. Although it is technically a graduate course, the course content resembles very closely that of Honors Analysis at Chicago, which is an undergraduate course taken by about 5-7 first-years and 10-12 second years each year. 18.125 covers the first 3 chapters of Rudin in the first semester, and in Honors Analysis, the first quarter covers Chapters 1-6 of Royden. The former is slightly more abstract (using abstract measure theory instead of just Lebesgue measure theory, although the presented proofs don’t differ by much), but the latter covers more material (for instance, a more rigorous theory of differentiation and the (abstract) fundamental theorem of calculus). I have compared problem sets from both classes, and I see no tangible distinction.</p>
<p>Chicago’s Graduate Analysis class, on the other hand, is significantly more advanced and covers about 5x more material than 18.125. It covers the first 9 chapters of Rudin, along with the professor’s (rather long, I might add) notes on rigorous probability theory. So although yes, Chicago’s undergrads take fewer graduate courses, it seems that the undergraduate honors courses are just as rigorous, and that Chicago’s ‘beginning’ graduate courses are about equivalent to other schools’ more advanced graduate courses (which most incoming graduate students probably start out from anyway).</p>
<p>It is true that Chicago’s DRP program is rather popular, although I’m not sure if it would have too much of an effect if Chicago’s undergrads didn’t take classes as equally challenging as the graduate courses presented elsewhere. More of the esoteric topics of mathematics require a sophisticated understanding of abstract concepts, and so I don’t think the DRP program would be as effective without the strong undergrad program in place.</p>
<p>One little point that I found helpful to think about myself was what I really wanted out of classes. Depending on this, I may or may not want exceptionally rigorous courses. I guess I tend to prefer a relaxed atmosphere, and find that my understanding at the end is just as formidable as (if not sometimes more so than) someone who slaved through a rigorous course, because learning math is an ongoing process, and things tend to solidify as you keep seeing them over and over in various settings. A professor told me that this is his style, yet many others have said that highly rigorous course offerings help them master material very well. </p>
<p>And seriously, I wouldn’t worry about rigor of program when thinking about schools like Caltech or Chicago, I’d worry about the style of instruction and things like that. I think one thing to take from happyentropy’s post is that some schools offer more topics courses, and this has little to do with how big the department is. This could be nice, though reading about them in a reading group could be fun too. Depends on style. I’m sure phuriku is right and that Chicago’s classes are very rigorous; in fact, I know a professor who I think got his undergraduate and graduate degrees at Chicago, and funnily enough, he runs extremely ridiculously heavy workload courses.</p>