<p>Does anyone know what Caltech ranks in each engineering field? Especially BioMedical, Aeronautical and Computer Science??</p>
<p>I don't have any information about the ranking of caltech's engineer program, but I can tell it should be one of the best in world.</p>
<p>Basically, the top 20 schools are about the same, depends on individuals.</p>
<p>They're ranked 0.5 in everything. What's it matter really? Rankings are all junk anyway.</p>
<p>By the way, we have no undergraduate program in Biomedical engineering. There's a grad program in BioE but not Biomed E as far as i know.</p>
<p>In Aeronautical Engineering, the "top three" recognized by academia and industry are Caltech, MIT, and Stanford. It would be silly to say that any one of these three is better than another. A good GPA and some strong recommendation letters from any of these three will get you anywhere in Aeronautics you might want to go.</p>
<p>But what about Computer Science?</p>
<p>In Computer Science, both MIT and Stanford are ranked above Caltech. Caltech is roughly #10 in these fields, MIT, Stanford, and Carnegie Mellon are 1,2 and 3 in some order. Caltech's CS program is very strong in theoretical branches but the traditional CS major will probably be happier at MIT or Stanford, unless there is some other great reason for going to Caltech. The faculty and research at Caltech in CS are superb, but the other programs are broader and probably will satisfy a bigger range of people.</p>
<p>Hmm. I guess that might be just right for me. A strong and happy CS course.</p>
<p>Just curious, what is the theoretical computer science? How ''theoretical'' can it be, compare to subjects like physics and cosmology?</p>
<p>Theoretical computer science concerns itself with finding mathematically proved answers to questions such as these:</p>
<ol>
<li><p>Suppose three people all want to find out the sum of their salaries, but nobody wants to reveal his salary to anybody else, and there is no trusted third party. Can they do this? How? Can they do it over the phone?</p></li>
<li><p>Does there exist an algorithm to check whether a number n is prime, such that the running time of the algorithm can be bounded by P(n), were P is a polynomial?</p></li>
<li><p>Is there a computer program which takes a computer program as an input and tells you whether it stops running or goes into an infinite loop?</p></li>
<li><p>What is the most efficient way to search for a word in a big, unorganized database? </p></li>
<li><p>Suppose you and I want to communicate securely (in code) but we have no way to exchange a password securely. Can we do this? How?</p></li>
</ol>
<p>All of these questions belong to what is now considered theoretical computer science. Moreover, the tools used in this discipline are at least as mathematical as those used in physics. Indeed, the typical paper in theoretical physics contains fewer real proofs and more sketchy arguments than the typical paper in CS. That is, probably only pure mathematics is more rigorous than theoretical computer science. For an example of a recent (famous) result which answers #2, see <a href="http://www.math.princeton.edu/%7Eannals/issues/2004/Sept2004/Agrawal.pdf%5B/url%5D">http://www.math.princeton.edu/~annals/issues/2004/Sept2004/Agrawal.pdf</a> (published in the most prestigious mathematical journal) and keep in mind that this is considered a fairly "easy" argument in this field, at least to read.</p>
<p>that's pretty interesting!
however, what kind of field of work is that useful for, other than research purposes?</p>
<p>can you elaborate on EE and mechE at caltech too? I am fairly interested in those majors right now.</p>
<p>The applications of 1, 4, and 5 are fairly obvious, I would say. It is important in many situations to be able to do computations with data without sharing it. Think of the five largest energy companies wanting to find out whether their current best solar energy panels are above or below average, without revealing how good they individually are to their competitors. Such an algorithm would help (and is an easy generalization of the n=3 case). Google spends a huge amount of time doing 4. Number 5 is the basis of virtually all secure corporate, military, and diplomatic communication throughout the world.</p>
<p>EE and MechE at Caltech are great. (Some other Techers in those fields should probably chime in.) The EE research here tends to be more innovative than mainstream -- e.g. DNA circuits, microfluidics, etc. -- so it's important to browse the department websites and see if the research and professors at Caltech interest you. In the fields where it is doing research, Caltech is top notch. MIT and Stanford have broader and more traditional programs (i.e. they have groups in every area whereas Caltech focuses intensely on somewhat fewer) but both MechE and EE at Caltech are top 5.</p>
<p>Interesting! But I still think that theoretical CE is not really ''theoretical'' because, from those examples you gave me, those researches are not suggesting a new general theory, they are solving problems exist in their field. (Except number 2, it is the kind of Math questions I love! I do not want to look at the website right now because I want to do some brainstorm first =P)</p>
<p>However, I am pretty surprised that Ben said typical paper in theoretical physics contains fewer proofs. I know a lot of physics theories are like: ''it is the way it is''. (Since it would be too abstract to truely prove a theory, like Einstein's special relativity, no one has proved it yet; or even ''F=ma'' is pretty abstract in high energy and quantum level, there are 2 definitions of ''mass'' and we dont know which is ''right'': this results in our inability to predict/ calculate ''mass'' at certain level) But, nowadays I can see physicists are trying to integrate different branches of physics together, like there is a department in Cambridge called ''particle cosmology'', I think such combination of branches will make Physics becomes more and more rigorous, especially in both ''math proofs'' and ''sketchy arguments''.</p>
<p>Anyways, I could be wrong, I am only a high school kid, maybe my opinions will change in few month later =P</p>
<p>Ben Golub: thank you for your very informative answer.
I have another question >.< What's double majoring at Caltech like? Almost impossible?</p>
<p>Hi Kit4hk,</p>
<p>Sorry I wasn't very clear. Of course I am not expecting physics to "prove" the fundamental postulates of any theory. That is impossible. But most theoretical papers are not introducing a new theory. They are claiming, for example, that some previously baffling phenomenon actually fits neatly into a certain framework -- e.g. that we can deduce this effect from Maxwell's equations or these two quantum postulates. At that point the argument is purely mathematical. Does A imply B? Even in very high level physics, people answer these questions by using series expansions whose convergence is poorly understood, making roundoff assumptions that aren't justified, etc. etc. Most mathematicians consider this non-rigorous, but physics has a different standard.</p>
<p>As for this statement,
[quote]
Interesting! But I still think that theoretical CE is not really ''theoretical'' because, from those examples you gave me, those researches are not suggesting a new general theory, they are solving problems exist in their field.
[/quote]
</p>
<p>I would respectfully have to disagree with you ;). The big general theory that CS is trying to create is a theory of "what can conceivably be computed" and "what are the theoretical limits on artificial intelligence" and even "what theorems can in principle be proved (by people or machines)". If that's not general enough for you, I don't know what is! :). Of course when you look at particular questions, they seem more specialized. But if you ask a physicist what he does, he usually won't start by saying he is trying to understand the structure of the universe. He will probably say that he is studying whether neutrino spin in ferromagnetic environments is well explained by QED, which wouldn't sound very "big" or "theoretical" by the standards you gave, either.</p>
<p>[Sorry for trying to convince you -- I just think the theoretical CS questions are very beautiful and deep!]</p>
<p>rainynight,</p>
<p>Double-majoring is very doable if you do it in "complementary" fields, like (commonly) math and economics. You can take many courses which satisfy a requirement for both at once. Another reasonably complementary combination would be applied math and a mathematical type of engineering. Many people double major in any science/engineering and one of the humanities, since the requirements for general education humanities courses are almost enough to get a major. So if you pick wisely, double majors are doable, though still not easy.</p>
<p>Some combinations have requirements that, for one reason or another, don't mesh very well, like math and physics (a little surprisingly). So you have to have an incredible capacity for work to do both and even the smartest and most capable people I know who have done this would probably not recommend it to their past selves.</p>
<p>If you come to Caltech and are considering a double major, talk to upperclassmen who seem to be academically similar to yourself and see whether the combination you are considering is one of the feasible ones.</p>
<p>Well, thanks Ben. I think I get your point, I mean it. I used to think CS is ''only'' artificial intelligence, and it is not a new branch of science (most of its theories are based on Math). Anyways, I can see the difference now. It is interesting to use mathematics to manage data in computers, also it could be very challenging too. I can see its beauty now, even though I am not interested in it at this moment.</p>
<p>About the physics proof, I always believe physics is more a philosophy than a science. However, math is the language of physics, isn't it? Do you think everything in physics is mathematically explainable? Why do they hold a different standard of justifying research paper?</p>
<p>[Don't worry for trying to convince me, I enjoy it as long as it is respectful =)]</p>
<p>
[quote]
Do you think everything in physics is mathematically explainable? Why do they hold a different standard of justifying research paper?
[/quote]
</p>
<p>Interesting question. I think the goal of physics is to state some fundamental assumptions ("laws") from which as much as possible of the universe's behaviors should be derivable in a purely mathematical way. For example, Maxwell's equations do this basically perfectly for classical E&M. And, in the ideal, the derivations of phenomena from laws should be mathematically rigorous, without hand waving.</p>
<p>I think in practice the standard is not as high because there is still a huge amount to be done so physicists do what will "probably work", leaving the rigorous details to mathematicians 50 years later. :)</p>
<p>maxwell's equations!!!!!</p>
<p>LOL reminds me of the t-shirt
"god said <insert maxwell's="" equation=""> and then there was light"</insert></p>