<p>Look, I took the theoretical physics option (8.012, 8.022) with the Kolenkow and Purcell and it didn't compare to the difficulty of the engineering classes. Also, it by-and-large didn't help you. I suspect MIT's engineering emphasis is the reason for the existence of the regular track. Not everyone wants to see that much theory. And even those that had a strong theoretical bent and background don't necessarily want to see it--rather, they may want to learn how to program robots in 6.270 or something like that.</p>
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Uh, epsilon-delta proofs are covered in introductory high school calculus classes.
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<p>Actually, no they aren't. You might get a glance at one or two, but unless you had an exceptionally good teacher, you've never done them. Plus, I'm not arguing that no one at MIT covers epsilon-proofs. I'm saying that if everyone at a humanities/social science school can do delta-epsilon proofs, MIT should get with the program and require a little bit more pure mathematics.</p>
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Uh, epsilon-delta proofs are covered in introductory high school calculus classes...
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What?</p>
<p>Yes, MIT math has a lower minimum bar than other schools, but many students start taking graduate classes in their sophomore or even freshman year - there is no real divide between the two in terms of what you can sign up for (other than what you want); On the other hand you can definitely find graduated math majors that can't write a real proof. The actual requirement is 'take 8 math classes'. Finally, Math 55 is an extremely controversial course at Harvard.</p>
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Uh, epsilon-delta proofs are covered in introductory high school calculus classes.
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Actually, no they aren't.You might get a glance at one or two, but unless you had an exceptionally good teacher, you've never done them.
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</p>
<p>I did them in my sophomore year, and so does everyone in my school, since epsilon delta proofs are done in the first month of a required math class here. I always thought all intro highschool Calculus classes covered them. They're only elaborations on the definition of a limit... not quite "undergraduate material", so I don't know why you would choose that particular topic to show the rigor of Chicago. E-D proofs aren't really "real proofs" in any case, because they are all essentially variations on the same one proof (only a step above the 2 column honors geometry proof). Anyway, the topic of this thread was caltech vs. mit..</p>
<p>Perhaps MIT's math program is more welcoming than those at other schools. Remember, the degree requirement is 'take 8 math classes'. Now go look through the entire curriculum at the wide range and array of courses available.</p>
<p>amb3r: 'epsilon-delta proofs' are much more difficult to grasp than 'limits'</p>
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Yes, I have in my sophomore year, and so has everyone in my school
<p>Two midterms. One at the beginning of third week, one at the beginning of seventh week. Admittedly, the first homework wasn't a fair representation (as the other homeworks seem to be 2-4 pages in length), but even so, 55 and HA's problem sets are ~10 pages long and can take as long as 60 hours to complete. Are there any courses at MIT like this? I don't think there are at Caltech either, I'm just making conversation.</p>
<p>I've dwelt too long on my opinion of MIT and have avoided the subject of Caltech almost entirely, though, so I'll comment a bit on Caltech next time.</p>
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Yes, I have in my sophomore year, and so has everyone in my school, since it's done in the first month of a required basic math class. I always thought all intro highschool Calculus classes covered them. They're only elaborations on the definition of a limit... not quite "undergraduate material", so I don't know why you would choose that particular topic to show the rigor of Chicago. Anyway, the topic of this thread was caltech vs. mit..
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<p>I've explained this point already. Read up.</p>
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Now go look through the entire curriculum at the wide range and array of courses available.
<p>phuruiku:"Our engineering program is probably the best in the country. It is, however, very competitive to get in. I have a few friends majoring in biomedical engineering, and most of them got into other top schools like MIT but decided to come here because of our school's great reputation for engineering."</p>
<p>phuriku: The best pure math majors at MIT immediately start taking many graduate level and upper graduate level math classes each term, skipping the entire undergraduate curriculum. Others take easier/more applied classes according to what interests them. Chicago has a very constrained core curriculum.</p>
<p>Note that this flexibility does not apply to other departments (for instance Aero/Astro eng. majors have practically their entire curriculum plotted out for them); in general each department emphasizes a method of teaching that attempts to mesh with the faculty and the learning styles of the students.</p>
<p>They don't put all the courses on OCW. The (mostly) undergraduate course bulletin is an inch thick. </p>
<p>BTW, I don't have a lot of experience with the math department at MIT, although I doubt at very many elite schools (read, any school other than Caltech and MIT) you are even required to take multivariable calculus. So I don't even agree that the bar is lower in terms of mathematical skill for the general graduate. Still, you haven't looked at any of the other majors. </p>
<p>There is no school that approaches the rigor and difficulty of the Unified sequence in aero-astro, for instance.</p>
<p>I don't really want to get involved in the debate about the relative merit of various top schools, but I would like to make two quick comments:</p>
<p>Phuriku, I'm a bit surprised that you would cite UChic as having the best engineering program in the country. When I applied to colleges as an engineering major, UChicago wasn't even on my radar, and I haven't heard anything since to change my mind. What evidence do you have to support this claim?</p>
<p>amb3r: I certainly never saw delta-epsilon proofs before coming to Caltech. Nor did any of my friends who went to school in my area. </p>
<p>Now I'd like to get this thread somewhat back on track by adding some comments on the OP.</p>
<p>I honestly feel that one of the biggest reasons our yield is low is because of the prestige issue. I knew a lot of people who chose to go to schools that weren't considered excellent in their intended majors but had a good amount of overall prestige--for example, I know two EE majors at Duke. Duke may not be horrible for EE, but it's certainly not on the level of Caltech/Stanford/MIT or even Berkeley/Carnegie Mellon. In the case of MIT vs. Caltech, I see the academic offerings as on par with each other for the most part, with one field or another having advantages here or there at a particular school. That being said, most of the people who live in my neighborhood have no idea what Caltech is. They are convinced that I attend Cal Poly. For a student who is prestige-minded, I could see favoring MIT over Caltech by default (I certainly favored MIT over Caltech until I visited the two schools). </p>
<p>I think a lot of the problem is our PR issues. There is a lot of amazing research going on at Caltech, but for some reason it never seems to get into the mainstream media. I don't understand or know why this is, but I'm hoping we can change it. As a EE, it's a bit annoying for me sometimes to read magazines and see something about innovation coming out of MIT when I personally know we're doing something cooler/better/more interesting at Caltech.</p>
<p>Edit:</p>
<p>Ah, I see. No Engineering at UChic. That would certainly explain why it wasn't on my radar, lol.</p>
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phuruiku:"Our engineering program is probably the best in the country. It is, however, very competitive to get in. I have a few friends majoring in biomedical engineering, and most of them got into other top schools like MIT but decided to come here because of our school's great reputation for engineering."</p>
<p>more good stuff...
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<p>I believe you pulled that from this thread:</p>
<p>(Go ahead. Click. Testimonials are there for why Chicago is the best for engineering.)</p>
<p>The University of Chicago has the best engineering program in the nation. Hands down. Anyone who thinks otherwise has pathetic judgment. MIT and Caltech don't even come close.</p>
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Still, you haven't looked at any of the other majors.
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<p>I'm looking at the basic foundations of each college (the Core, if you will). Not specific majors. I got sidetracked. (Hey, you assisted, so don't blame me!) :)</p>
<p>phuruiku:"Don't listen to him. Chicago's engineering is great; gbh875 is just bitter that he wasn't accepted into the program. Go back to your pathetic MIT engineering program, gbh875, you'll never be good enough for Chicago's."</p>
<p>UChicago Engineering is like dividing by zero--if it could be defined, it would be both greater and less than every program in the country, at the same time.</p>
<p>The tears of UChicago engineers cure cancer--too bad they never cry.</p>
<p>You are full of lies. The tale of the nonexistence of Chicago's engineering department is a ploy by those rejected to distract future applicants while simultaneously boosting one's own school's reputation. Unfortunately, the prestige of the CSE (Chicago School of Engineering) outweighs any of your pathetic efforts.</p>
I don't think you've accounted for the vast differences in size between schools with this comment. Remember that if MIT has 5 times the number of students that Caltech does, Caltech needs to win only 20% of the cross-admits to have a percentage of cross-admits equal to that MIT has in their class.</p>