Caltech for MIT rejects?

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pisforphysics
But why the 37% yield rate? Where are the Caltech's admits going?

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I think this is the explaination

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by Not too old
Virtually all admits to Caltech were in the "possible" pool at all the other top colleges and might have been accepted with a different non-academic hook.

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<p>Note that not all Caltech's admits going to MIT. Some might chose to go HYPS especially those in east coast. Actually the 37% yield at Caltech just proves that Caltech has stronger overall student body, at least at acadimic level.</p>

<p>I was admitted EA to both Caltech and MIT this year.</p>

<p>Caltech continues to be an important top choice for me. </p>

<p>Being in dire need of financial aid, this factor will make a
big difference on where I choose to go eventually.</p>

<p>I also know enough MIT students from my high school to know that
if they are hacking it, I should clearly be able to survive. I do not
know any Caltech students at this point to draw a similar
comforting thought.</p>

<p>:)</p>

<p>"Actually the 37% yield at Caltech just proves that Caltech has stronger overall student body, at least at acadimic level."</p>

<p>That doesn't make any sense at all. I think by virtue of the cross-admit data, it's extremely hard to draw the conclusion that Caltech students are "on average smarter" than MIT students. In fact, it looks a little like Caltech fails on some level to retain its top admits (the ones that also are admitted to MIT), since many are choosing instead to go to MIT. I do, however, believe that Caltech on average has more qualified applicants, which would account for the differences in acceptance rates. I do believe that the minimum level of technical competency of its graduates is higher. I also believe that the culture is one that places more emphasis on smarts and hard work, so perhaps that encourages students to pursue and attempt things that they would not at other institutions, and perhaps to an outsider has an effect on the perceived intelligence of the student body. </p>

<p>I don't at all believe, however, that a Caltech education is necessarily more "rigorous" or (?) "better" than an MIT education. MIT allows you more freedom, so that you could avoid the more rigorous classes if you really liked, but if your nature is avoiding challenges, you probably won't benefit from the "superior" education at Caltech even if you were there. I'm also beginning to be disillusioned slightly by the falling minimum standards at MIT, but I defend staunchly its rigor against Caltech if the accurate comparisons are made. Apples to apples, a wave mechanics course at MIT is as rigorous as one at Caltech. Quantum mechanics. Laboratory physics. Orgo. Statistical Mechanics. Combinatorics. You'd be hard pressed to prove otherwise. Our faculty is not second to Caltech's.</p>

<p>I really think the student bodies are comparable when you look within the same major between the two institutions. Which makes sense of you think about how many applicants and admits they share. And that's the end of the usefulness of these comparisons. I don't believe there is any value comparing the intelligence of an architecture major with that of a math major.</p>

<p>EDIT: To respond to the OP, the "Caltech, because not everyone gets into MIT" t-shirt is a joke. It'd be just as ludicrous comparing the quality of the Harvard and Yale student bodies.</p>

<p>pebbles -- I was obviously being provocative, but I think if you made everyone take a good IQ test, the average at Caltech would be higher at MIT. Totally a personal judgment based on (not completely trivial) experience with both schools. That's all I meant by smarter.</p>

<p>Of course, IQ may be meaningless, and of course Caltech selects more heavily on IQ than MIT does. I'm not saying that these things should make your decision. Just stating what I think is true.</p>

<p>As for "better education", I'll stick by that. Brown has some good physics classes too. So, for that matter, does Rutgers (in New Jersey). By your logic, the education at Rutgers is as good as MIT, comparing apples to apples. But that's wrong. </p>

<p>The reason is one you understand already. At Caltech, you're cooking a denser sauce. Everyone around is doing what, at other schools (including MIT), only the most hardcore kids do. Does that push the most hardcore kids at Caltech to be even better? You betcha. </p>

<p>At MIT, you cook in a dense sauce, but less dense. People who have written a real mathematical proof in their lives (excluding two-column geometry proofs) probably form a minority at MIT, but they definitely form the full population at Caltech. Is that worth something? I think yes (and I am right!). But of course I invite everyone to disagree :)</p>

<h2>Ben Golub: "As for "better education", I'll stick by that. Brown has some good physics classes too. So, for that matter, does Rutgers (in New Jersey). By your logic, the education at Rutgers is as good as MIT, comparing apples to apples. But that's wrong. "</h2>

<p>As you probably know, I'm no MIT cheerleader unlike some others on the MIT board. However, I think you are totally wrong in saying that Caltech:MIT is like MIT:Rutgers or even that Caltech is more rigorous than MIT. I don't think Caltech is any harder or more rigorous, with the exception of the <em>intro</em> math and physics classes. And as I said before, you can take the theoretical version if you desire it. The upper level classes in math or physics are theoretical--if you can't adjust, then you're toast. Same goes for the engineering classes--if you took the less theoretical classes because you aren't great at physics + math, you are going to have serious problems. The profs don't care which version you took.</p>

<p>Frankly, it's hard for me to imagine that Caltech engineering is as difficult or rigorous as MIT. I mean, is there an equivalent to the year long "Unified" sequence for Aerospace engineering? And the ability to write proofs well is really not what can make engineering difficult. </p>

<p>I came into MIT having taken number theory and abstract algebra, a theoretical version of multi-variable calculus, and a topics in real analysis class taught by the coach of the U.S. math team. Like you, I have a theoretical bent. However, I don't think that writing mathematical proofs is really that vital to performance in most engineering disciplines. Even if it is, does it matter if differential equations is presented in that way? I don't think so. It's important to be smart enough to do it that way, but unnecessary to actually do it. </p>

<p>I think you are vastly underestimating the quality, rigor, and difficulty of MIT's curriculum.</p>

<p>To address the OP, even a poor cross-admit yield between Caltech and MIT does not mean that Caltech students were MIT rejects. In the old days (before M. Jones f-d everything up), Caltech students were roughly a smaller subset of MIT admits due to the difference in size. Caltech's class size is 200 whereas MIT's is 1000. Let's imagine Caltech and MIT both admit a set of 500 students and 300 choose MIT. In that scenario, MIT would have won the cross-admit duel but every Caltech student would have been accepted at MIT. And the other 500-1000 students MIT accepts would have been Caltech rejects. (Note: the admitted class sizes are larger than the final class size due to losses in yield.)</p>

<p>collegealum -- I don't think you understood what I was saying. I agree that the upper level physics and engineering classes at MIT are as hard as anywhere. Let's say, just for the sake of argument, harder than at Caltech. My point is only that the OVERALL culture at Caltech is more intense, and that tide lifts all boats. </p>

<p>Basically, my theory is that people compare themselves to others in three ways -- they compare with the big world, with their school, and with their major. Caltech and MIT students are pretty much identical in the first and third comparisons. They both look the same relative to the big world, and a Caltech student looking at his peers in his major at Caltech probably feels about the same as an MIT student looking at his peers in his major at MIT. That's the point you're making.</p>

<p>What I'm saying is that a theoretical Caltech student relative to his SCHOOL feels very different from a theoretical MIT student relative to his school. At Caltech, if you know proofs or quantum mechanics, you're average. At MIT, that makes you somewhat unusual. And I claim the more hardcore overall student body at Caltech makes everyone more ambitious.</p>

<p>My theory may apply only to people like me. Maybe a small personal story will make my point more clearly. I had a choice of some Econ PhD programs and picked a very small, very theory (and math) heavy program at the Stanford GSB over the much more traditional program at MIT. At MIT, I would be labeled as a "theorist" and would have felt like I had an automatic advantage in theory courses due to my math background. In my program, at least 75% of my class has studied algebraic geometry! (This is an economics program!) That makes it impossible for me to relax and feel like that experience makes me special. I have to work still harder to do something interesting and distinguish myself. That is roughly the way I think, that Caltech compares to MIT (on a different scale).</p>

<p>This basically comes down to whether you think students look mostly at their major when evaluating their overall hardcoreness or at their school. Depending on the model, your view of my "harder" claim will vary.</p>

<p>What do you think of math at MIT vs. Caltech? People comment a lot about physics, and while I love physics(!), I want to major in math. Specifically departmental-wise, would you say there is much of a difference? I do notice that MIT appears on "top 5" lists for math, while Caltech doesn't but that might be more graduate school. Any comments?</p>

<p>(sorry to use this thread to ask my own questions; I will be making the choice between caltech and MIT and, living nearer to MIT, I know a lot more about the culture/students/academics/atmosphere at MIT than I do at caltech, so I find threads like these helpful!) (thanks Ben Golub for your comments, btw. rather illuminating and well-stated)</p>

<p>Ben: One thing I see that you're overlooking in your social theory is the relative size of the two institutions. You seem to put a lot of importance on overall peer influence on a campus level, but I have to dispute that you are overestimating its effect at MIT. At 4 times the size of Caltech, the number of MIT undergraduates in CS is alone equal to an entire Caltech class. When MIT students feel the need to compare themselves with others, especially in the larger departments-- math, cs, mech E, bio, and to some extent physics-- they really need to look no further than their classmates within their major. I'm confident in this from personal experience. I don't think I've ever tried to measure up to the work of a management or economics or music major. We have so little academically in common. Perhaps the commonality of experience is what leads Caltech students to think more on a campus-wide scale, but that's neither here nor there since that mentality is not reflected at MIT. Rather, I am saying that in the same way Caltech students look to all of their classmates as their peers and competitors, MIT students look to only those classmates within their major.</p>

<p>You made a point that confidence, or pride, tends to lead to academic underachievement. By which I mean not achieving to the greatest of one's potential. Personally, I've always suffered from the opposite affliction. I have this really deep rooted tendency to believe that I'm really not at all intellectually capable of competing on this level and really I've just gotten here through luck and hard work. Often, I find it hard to motivate myself to really take advantage of the opportunities on this campus because I'm afraid of my own mediocrity. I think maybe the opposite (of your claim) is true for some. If I were head and shoulders above the rest I would want to stay there by working really hard. If I really believed I had a talent others did not I would use it to my full advantage. Maybe it's a wash in the end, because some are one way (such as yourself) and others are the opposite.</p>

<p>@lalaloo6:
Schools considered Top tier for theoretical math are (not in particular order): Harvard, MIT, U of Chicago, Princeton and UC Berkeley. Caltech is almost there. Caltech certainly has the same quality compared to these 5 schools in math. The only reason that Caltech is not among that 5 is its size. A friend had posdoc training in math from Caltech and had easy time in finding an academic job, in future promotion through academic ranks and grant funding.
MIT math department is bigger. MIT last year had 1/3 share of the top 75 scorers in Putman competition. Caltech had 6. If you adjust the size of student bodies, Caltech and MIT are comparable in last year's Putnam competition.</p>

<p>One could argue, however, that if one is a math major, there are other schools in the universe of top-notch programs than Caltech and MIT. It's possible to do the math degree in a liberal arts environment (i.e., H/P/UChicago/Stanford, among the top tier math programs) or via the engineering school route. For a a student who wants to hang around with folks who consider the humanities more than a necessary evil, or who wants to expand one's horizons in the humanities before embarking on a math/theoretical graduate program, some of those other schools can outweigh the advantages of a Caltech/MIT.</p>

<p>Not sure that this would work as well in other majors, but it is something that has been considered long and hard by the theoretical person at our house. </p>

<p>Flame-proof suit on!</p>

<p>The most prestigious and probably overall best undergrad math programs in the country are Harvard and MIT, in terms of (a weighted average of) student and teaching quality. I would say that Caltech and Princeton tie for second (but it's not a terribly close second), and then you have Chicago and Stanford. These are, incidentally, ranked roughly according to their success at enrolling IMO and Putnam types, as well as the success rates of getting people into top notch math graduate programs.</p>

<p>I would rank the departments quite differently at the graduate level. There, it looks more like Harvard/Princeton > Chicago/Berkeley/MIT > Stanford, Caltech, Columbia, NYU.</p>

<p>Caltech is a small department and while the research scholars it has are among the top in the world, it does not cover all fields as well as the bigger departments. This hurts more at the graduate level than undergrad. At the undergrad level, there is excellent teaching and unequaled support for undergraduate research, and that makes it a great place to go, assuming you like the rest of Caltech. But the overall peer group is probably a bit stronger at the Cambridge schools... once again, depending on your preferences, this could be good or bad.</p>

<p>pebbles. That was a very thoughtful and reasonable post. I find nothing to disagree with in it. Caltech students probably do have more of an esprit de corps as a school than MIT students just due to size considerations, and this can be a plus or minus depending on one's intellectual (and non-intellectual) personality. I would say as a result there's somewhat more intellectual interaction outside one's major at Caltech, and there are some fringe benefits like the fact that the management professors can talk about the heat equation if they want to and nobody blinks an eye. But you pointed out the virtues of the MIT system well.</p>

<p>I think the Caltech system is harder and more academically motivating for some types of people, and MIT for others, and hopefully this back-and-forth has given people some information to decide which system they prefer.</p>

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People who have written a real mathematical proof in their lives (excluding two-column geometry proofs) probably form a minority at MIT,

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<p>Ben, what? I know a lot of people who go to MIT and they ALL definitely knew how to write REAL proofs before they graduated high school. A minority? More like a majority. Out of the USAMOers and MOPers I know, all but 1 chose MIT (and a minority HYP) over Caltech. By your reasoning, I would say MIT has a much stronger student body than caltech (even though I am not claiming that). I think you are really inaccurately downplaying the scientific knowledge of the "average" MIT student. Have you spent time on campus?</p>

<p>:) amb3r, I've spent a fair amount of time at MIT and you are simply wrong about this.</p>

<p>Your claim that most MOPpers chose MIT, even if true, does not imply that most MITers know how to write proofs. I assume this point of logic does not need further explication.</p>

<p>You know a biased sample of MIT-ers. (Maybe you know many of them through MOP?) Go on campus (don't go to Random), poke a random person, and ask if he or she knows how to prove that differentiable functions are continuous. Do this 10 times and you will agree with me (...and maybe get your share of quizzical looks, too.) You will also note that no current MIT students posting here will disagree with me about what the outcome of this experiment will be.</p>

<p>(The question is taken from a standard Math 1 problem set at Caltech.)</p>

<p>I'm a current MIT student and I'll disagree with Ben if anybody offers me food..</p>

<p>I agree with Ben that you'll be a bit hard-pressed to find a non-math major at MIT who can do a proof (well). Even the Analysis courses at MIT are barely proof-based (and it seems like some of the problems on OCW hint that this Analysis class is more of an "introduction to proofs" class than it is an actual analysis course, which in turn hints that most of the people taking Analysis haven't been introduced to proofs before). At Chicago, everyone (yes, everyone) has to know how to do delta-epsilon proofs. It's emphasized even in the lowest classes, and calculus is a part of the Core so it's unavoidable. MIT's general education pure mathematics requirements seem to be very lenient, and if a school like Chicago (with many humanities/social science students) can have such strict requirements, why can't MIT?</p>

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The most prestigious and probably overall best undergrad math programs in the country are Harvard and MIT, in terms of (a weighted average of) student and teaching quality. I would say that Caltech and Princeton tie for second (but it's not a terribly close second), and then you have Chicago and Stanford. These are, incidentally, ranked roughly according to their success at enrolling IMO and Putnam types, as well as the success rates of getting people into top notch math graduate programs.

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<p>Admittedly, MIT has an oustanding student body (specifically pointing toward the top math majors) and an excellent staff, but I don't think the difficulty of its courses even approach those of Harvard, Princeton, or Chicago. You'll have to reach into MIT graduate courses to even touch Honors Analysis at Chicago or Math 55 at Harvard. If I had to rank each program with respect to the three crucial areas, I would do it in this way:</p>

<p>Staff: MIT/Harvard/Princeton > Stanford/Chicago > Caltech
Courses (Undergraduate): Chicago/Harvard > Princeton > Caltech > MIT/Stanford
Student Body (considering only the top math majors): MIT/Harvard > Princeton > Chicago/Caltech > Stanford.</p>

<p>How to rank them generally would then be up to the individual, as different people look for different things. Personally, I value course content the most and staff the least (of course, we're only considering undergrad here).</p>

<p>I don't understand why you're ranking according to IMO/Putnam types. The USAMO students in Honors Analysis seem to be inferior at times to the students who stick with research mathematics. Also, where are you getting stats for graduate admissions?</p>

<p>lol at epsilon-delta proofs...</p>

<p>btw, i encountered the proof Ben mentioned when I was 15, and I was not a math major nor did I qualify for USAMO. It is an incredibly easy proof.</p>

<p>18.100B "barely" proof based -- another favorite statement.</p>

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18.100B "barely" proof based -- another favorite statement.

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<p>Most of the proofs in that course are short and don't require much thinking. Thus, the "barely".</p>

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At Chicago, everyone (yes, everyone) has to know how to do delta-epsilon proofs.

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Uh, epsilon-delta proofs are covered in introductory high school calculus classes.</p>