It is the time of year in the US that high school students have found out what schools have accepted them and now have to decide where to spend the next four years. Maybe because I am of that age, but I find myself talking more to students and parents about what school they should choose.
So let's assume you are a high school student who knows they will eventually want to get a Ph.D. in computational complexity or perhaps some other math-related topic. Where to go to school? Depends much on your personality and your choices.
The Elites (examples: Princeton, Harvard, Stanford, Yale): Many rich kids who feel entitled so you can get good grades without working hard. But you can also take advantage of great professors and some challenging courses and research opportunities if you are up to the challenge.
Intense Schools (MIT, Caltech, U. Chicago): Here you have to work hard for your grades against other very strong students in challenging courses. You won't have a better math/science education anywhere else but these schools won't give you as broad a social experience.
Broad Private Schools (Cornell, Northwestern): Here I have biases having gone to Cornell undergrad and now teach at Northwestern. Fine math and science programs not quite as strong as the above but more than made up by experiencing an undergraduate life with smart students across a wide spectrum of disciplines. Many a theorist got their start as a Cornell undergrad.
Liberal Arts Schools (Williams, Wesleyan, Harvey Mudd): You don't get the large research programs but instead have very good profs who focus on undergrad teaching. This is the easiest way to get involved in research as an undergrad.
Big State Schools (Illinois, U. California, Michigan, Wisconsin): You get a real mix of students from athletes to partiers to really smart kids looking to save a few dollars. You can certainly get a great math and science education. But you'll have to work hard when many of your fellow students may not be.
General advice: Doesn't really matter that much where you go, as long as you work hard you will succeed. Above all enjoy your undergrad days for they will be the best times of your life.
I went to a BIG STATE SCHOOL
ReplyDelete(SUNY Stonybrook) and I teach at one now (Univ of MD at College Park).
If you have a serious interest in a topic (for this audience likely Math or CS)
1) Take Grad courses there
2) Do research there
Both are quite possible.
Also, if they have some sort of University Honors Program, thats a plus.
I wonder which undergrad school produces the most theorists. My guess would be Cornell...
ReplyDeleteMy guess for the undergrad school which produces the most theorists - the Indian Institutes of Technology.
ReplyDeleteAgree that big state schools offer some intriguing opportunities, including in undergrad research. Think about it this way: if you had a choice to go to an Ivy and went to a state school, that means you should be one of the best students in the state school. You will find that a lot of professors are eager to work with you, while at Harvard you would be one of many.
ReplyDeleteThe downside is that you need to take the initiative at the state schools, and that some strong students get lost in the field and end up with an average record or worse.
So, maybe, if your kid is very determined, send them to a state school with strong research. If they are more likely to blend into the crowd, send them to a top school where the crowd is stronger.
The privates are not lumped together; why are the publics lumped as a single "big state schools" category?
ReplyDeleteAlso, that really smart kid who chooses his/her state's flagship public university over an expensive private school may very well save more than "a few dollars". There are a lot of cases where a strong applicant may get a full ride to their state school but little or no financial aid from the private school(s) of his/her choice. That $200,000+ difference in tuition and fees could mean a lifetime of debt for a prospective theorist who may or may not find suitable employment even after getting a Ph.D. in a theoretical area.
Advice for American youngsters: study abroad if you can, even if for one semester only. I went to UCSD last year (as an undergrad) for two quarters and ended up quite disappointed with the poor level of Math courses for undergrads and with the poor level/knowledge of Math majors.
ReplyDeleteMy professors back in Chile tell me that UCLA or Berkeley are not much better, even when you follow the Honors Program. Other Mathematics and Engineering students from my country report similar experiences when going to the US: (ridiculously) easy classes and plenty of spare time.
Put some effort into learning Spanish, French or German, handpick a university and go study abroad to see what "difficult classes" really means, especially if you're interested in theoretical Mathematics and/or Computer Science. I'd be happy to elaborate if somebody asks me, but I won't do it here in a comment.
^This helps to explain why so many more strong mathematicians and computer scientists come out of south american universities than American universities.
ReplyDelete@Anonymous: WIN
ReplyDelete(the fact that the classes feel easier sometimes is very related to the fact that the professors actually tend to know what they are speaking about)
I'm missing the irony, although I do sense a lot of prejudice.
ReplyDeleteBy the way, Mathematicians and Computer Scientists come from Grad Schools, not undergrad programs. I knew an undergrad program of a very prestigious university in the US and it sucked. I have nothing to say against grad programs in the US, because I know them to be good in general.
I still fail to understand. Do you think that the undergraduates who come out of MIT, Stanford, Carnegie Mellon, Harvard, Princeton, Caltech, etc. are not prepared for graduate school? But many of them go to graduate school (Many more than from any university in Chile). How do you explain this?
ReplyDeleteAlso, the graduate courses and undergraduate courses at these universities are taught by the same faculty members. Do these people (who teach at strong graduate programs) lower their standards so much at the undergraduate level that the level of discourse falls from world-class to sub-par?
When I went to Harvard as an undergraduate, I was told repeatedly that I would be one of many. This could not have been further from the truth!
ReplyDeleteThree professors reached out to me to get me involved in theoretical computer science. I was asked to be a teaching fellow by Harry Lewis for the introductory computer science class. I taught the class three years in a row and got to see lots of him, teach the subject to students, and work with the other teaching fellows that were also excited about theoretical computer science. I was asked if I wanted to apply for a summer research funding by Salil Vadhan, and was even reminded when the deadline was fast approaching. I was asked to do an independent study by David Parkes to turn a final project into a paper, and was a teaching fellow for his class one semester. He even funded me to go to a conference and present our work.
I cannot say whether my experience was typical, but it was great. I wish I could say that the initiative was mine, but in all three of the above cases, it was not.
@Anonymous 7: [Citation needed.]
ReplyDeleteI said I didn't want to elaborate, but...
ReplyDeleteDo you think that the undergraduates who come out of MIT, Stanford, Carnegie Mellon, Harvard, Princeton, Caltech, etc. are not prepared for graduate school?
That's way too general to be answered with one word. The answer depends on many factors, for example: where are they going to do graduate studies? Did they follow the honors program? Are they hard-working? And so on. Most students all over the world are not ready for grad school, and that's perfectly normal.
But many of them go to graduate school (Many more than from any university in Chile). How do you explain this? It's pointless to compare quantities, but here are three reasons: more people, more universities, and more funding/grants for grad school. Also, the difficulty. I have known good students who had to leave the university because it was too difficult, and I know they would've done fine in many universities in the US.
Also, the graduate courses and undergraduate courses at these universities are taught by the same faculty members. Do these people (who teach at strong graduate programs) lower their standards so much at the undergraduate level that the level of discourse falls from world-class to sub-par? Yes they do. At UCSD, our TA for the algebra class (who had finished his Math major at the same university a year before) used to tell us how difficult his first year of grad school was for him, because he wasn't used to the difficulty of lectures (i.e. the level of abstraction) and the workload. Yet many of his classmates who were coming from other countries also studied for 4 years before going on to grad school, but didn't have the same problems coping with grad school life. The professor for that class was Australian, and he told me how much more difficult was undergraduate algebra for him than for his students when we talked about this.
The whole experience also taught me not to blindly believe in rankings. University rankings take into account stuff like number of publications and Nobel prizes. This favors bigger universities simply because they have more people and resources (also more influence). None of these reasons has any implication or relation with respect to teaching quality and, in particular, course difficulty, which was my original point.
Harvey Mudd is not a liberal arts school; it's more of an intense technical school. However, it's one of the Claremont Colleges, including Pomona, which *is* a liberal arts school. Mudd students take classes at the other schools, and vice versa. These schools are great for getting to know the faculty, and have opportunities for undergraduate research, or anyway did in ancient times.
ReplyDeleteI disagree with the assertion that difficult courses yield better students, without explaining what "difficult" and "better" mean.
ReplyDeleteThere's a part in Feynman's memoirs about this student from south America who on the surface seemed to know a lot of physics, but who could not "think" at all. (John Sidles help me out here..)
Same goes with Math. "Abstract" does not mean better. For example, I can teach linear algebra from Herstein's book "topics in algebra," without a single appeal to geometry. And it would be a lovely and challenging course. But what will an undergrad learn from it, even if s/he aces it? Nothing.
I disagree with the assertion that difficult courses yield better students Can't find the assertion in the discussion...
ReplyDeleteSame goes with Math. "Abstract" does not mean better. It doesn't mean worse either.
I can teach linear algebra from Herstein's book "topics in algebra," without a single appeal to geometry. And it would be a lovely and challenging course. But what will an undergrad learn from it, even if s/he aces it? Nothing. That would speak really badly of the teacher or of the grading system. Not being able to "use" what you learn in "real" situations doesn't mean you can't use that knowledge at all. This is particularly true for Mathematics, since a lot of the research is done in a purely theoretical level, where "we found an application" usually means "there is a relation between this abstract area and this other one" For example, see how many "applications" group theory has; the topic's abstract enough, but you wouldn't say students learn nothing, would you?
"World education rankings: which country does best at reading, maths and science?"
ReplyDeletehttp://www.guardian.co.uk/news/datablog/2010/dec/07/world-education-rankings-maths-science-reading
So how do the Chilean students cope with such difficult courses once they get to college?
You have to put numbers in context: most high school students won't go to college here, because access to education is expensive and we have a lot of economic differences between social classes. Besides, of those who go to university, only a small group will go to a really good one, and of those, only a tiny little group will study Mathematics.
ReplyDeleteYour question is like saying that most Americans are overweight and then wondering how can the US have good results at international sports competitions. Athletes are a few exceptions, outliers, and so are math students. Most math students can cope with courses because they are brighter than the average John Doe.
For the record, only a small number of students who chooses a Math degree/major finishes it (no more than 20% in my university, I'd say). The rest leaves in the first two years because they fail too many courses and/or realize that's not what they want.
***
By the way, I appeared to have touched some kind of (patriotic) nerve with my original message, and this discussion is becoming obnoxious, trollish, and full of prejudice and nonsensical arguments. I wonder how many of the anonymous have actually been in other countries and known first-hand how other universities work.
I disagree with the premise of this post: How in the world could you possibly know that you want to study complexity theory as a senior in high school?! When I entered school, I planned to major in chemical engineering, majored in something else, and now work in computer science.
ReplyDeleteMy advice would be to try lots of different things to find out what you like. At some schools, you are locked in to a major than can be very hard to change, or the school may not offer a wide choice of (good) departments. Look at the whole picture, not through the narrow lens of a computational complexity blog.
@Janoma I cannot speak for the others, but I'm not surprised that several people seem annoyed at your remarks. I don't resent that you think Americans should try to study overseas (a fresh perspective is always beneficial), but I do take issue with your implication that one cannot find challenging courses at an undergraduate program in the US. In fact, I know this implication to be false from personal experience.
ReplyDeleteThe quality of undergraduate programs varies significantly based on the department, the faculty, the university culture, etc. Indeed, I've found a significant difference in the level of the coursework at different universities that I have attended. While I'm sorry to hear that your experiences were not positive, I suggest that you should increase your sample size before making sweeping generalizations.
Anonymous requests: "There's a part in Feynman's memoirs about this student from south America who on the surface seemed to know a lot of physics, but who could not "think" at all. (John Sidles help me out here..)"
ReplyDelete-----------------------
A Google Books search for the phrase "Their knowledge is so fragile!" finds anonymous' remembered passage as an episode on pages 36-7 of Surely You're Joking, Mr. Feynman. A longer excerpt is:
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"They didn't put two and two together. They didn't even know what they 'knew'. I don't know what's the matter with people. They don't learn by understanding; they learn by some other way---by rote or something. Their knowledge is so fragile!"
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This theme arises in contexts that span pretty much all STEM disciplines. In particular, The March 2011 issue of Notices of the AMS has an article by Mark Saul titled "More Than a System: What We Can Learn from the International Mathematical Olympiad". The article includes excellent interviews with practicing mathematicians like Tim Gowers, Terry Tao. A sample quote from this article:
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“IMO problems are like animals in a zoo. Mathematical research is like studying animals in
the wild.”
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The transition from dealing with "zoo animals" to dealing with "wild animals" is similarly challenging in every profession: science, math, engineering, medicine, business ... and politics especially.
Every student has to decide for themselves whether, when, and how to manage this zoo-to-wild transition. Lance's post rightly emphasizes that this transition can occur at any school, and that there is no one path to accomplishing it.
Not only individual students, but also entire disciplines, nations (and even planetary civilizations), are challenged to accomplish this (immensely difficult) zoo-to-wild transition. Historical overviews of this planetary-scale, centuries-old, and still on-going process include (from most accessible to most scholarly), Richard Holmes' The Age of Wonder: The Romantic Generation and the Discovery of the Beauty and Terror of Science, Patrick O'Brian's Joseph Banks: A Life, and Jonathan Israel's A Revolution of the Mind: Radical Enlightenment and the Intellectual Origins of Modern Democracy.
For individual students, the aspect of these challenges that is most nearly subject to one's individual control, is maintaining a personal aequanimitas ... that's what medical students are taught, at any rate! :)
Best wishes are extended to every student who is grappling with the intoxicating challenges of "zoo-to-wild" transitions, whether personal, institutional, or global!
ReplyDeleteBy the way, I appeared to have touched some kind of (patriotic) nerve with my original message, and this discussion is becoming obnoxious, trollish, and full of prejudice and nonsensical arguments. I wonder how many of the anonymous have actually been in other countries and known first-hand how other universities work.
Some of the responses are indeeed rude, but your posts aren't much better. You studied for six months at UCSD and pronounce judgment on all US universities, when the US has a much more diverse university system than most other countries. Furthermore, you act like the best way to judge undergraduate courses is by their difficulty and failure rate. This comes across as some combination of ignorance and trolling.
The general philosophy at US universities is that if the undergrad courses are easy, try taking grad courses or doing research. There generally isn't a detailed, set curriculum that students must follow, so there's plenty of flexibility to find challenging courses. You can also use this flexibility to find not so challenging courses if you prefer, and some students do. Graduating from a US university is generally not difficult - anybody who can get admitted to Harvard can easily graduate (even people who were admitted primarily for athletic or fundraising reasons) - so if your standard of comparison is how difficult it is to graduate, you will be disappointed.
You could judge programs according to how much you could learn if you tried, how much the average student learns by default, and how little you could learn if you tried (and still graduate with reasonable grades). By the first standard, many US universities do very well. By the second, some of the top schools do. By the third, very few do (maybe Caltech forces everyone to learn a lot or drop out?).
Janoma is fairly ignorant.
ReplyDeleteWhere does he think International Math Olympiad gold medalists study?
Which country does he think has the largest pool of Mathematically gifted kids (per PISA) after China? In terms of proportions of Mathematically gifted kids, USA is about 10 times the Chilean fraction.
More here:
http://infoproc.blogspot.com/2006/12/more-caltech-bragging-rights-patents.html
"Caltech leads with about 50% of all undergrads going on to earn a doctorate."
More on trivial American education here:
http://infoproc.blogspot.com/2009/05/vernon-smith-at-caltech.html
Nobel Laureate in Economics, Vernon Smith, on Caltech:
"I was majoring in physics, but switched to electrical engineering, which was in the same division (Mathematics, Physics and EE) as a senior. In this way I did not have to take the dreaded "Smyth's course," required for physics majors, but not EE, and received my BS on schedule in 1949. At the time I relished the unbending facts and mathematics of physics/engineering. "
The first thing to which one has to adapt is the fact that no matter how high people might sample in the right tail of the distribution for "intelligence," ... that sample is still normally distributed in performing on the materials in the Caltech curriculum. The second thing you learn, if you were reared with my naive background, is the incredible arrogance that develops in conjunction with the acquisition of what you ultimately come to realize is a really very, very small bit of knowledge compared with our vast human ignorance. ... the difference between Harvard and Caltech: "At Harvard they believe they are the best in the world; at Caltech they know they are the best in the world."
I still see a lot of arrogance in the way Americans defend their beliefs (e.g. "at Caltech they know they are the best in the world"). Many IMO Gold Medallists study in the USA because it offers a wider variety of strong graduate programs than anywhere else in the world, not to mention that the money they will get for their beautiful minds is also considerably higher.
ReplyDeleteAnd the percentage of so called "gifted" kids has nothing to do with universities. The quality of primary and secondary education in Chile is shameful, unless you go to an expensive private school. Many gifted kids never have a real chance of developing their talents because even their teachers can't notice they're exceptional. Eventually, the kids themselves lose interest too.
Anyway, putting aside the fact that some people started arguing against my country and my country's educational system (which is lame) instead of going against my original point, I will restate my position, this time trying to be more specific: I believe that studying abroad is a refreshing, mind-opening, prejudice-shattering experience for the average American undergraduate student. In particular for Mathematics and Computer Science majors, a well-chosen university overseas will also present an interesting intellectual challenge, which might help, albeit little by little, eradicate some ugly prejudices against less developed countries and cultures..
"Where does he think International Math Olympiad gold medalists study?"
ReplyDeleteAnd where do you think fields medalists did their undergrads?
"And where do you think fields medalists did their undergrads?"
ReplyDeleteWhich country do you think has more of its undergraduate students win Fields medalists than the US?
"I believe that studying abroad is a refreshing, mind-opening, prejudice-shattering experience for the average American undergraduate student."
ReplyDeleteThe point of an education in Math/CS is not prejudice shattering except amongst the diversicrats that infest liberal arts academia.
Anonymous complains of "diversicrats that infest liberal arts academia"
ReplyDelete------------------------
LOL .... Charles Koch, is that you? :)
Hmmmm ... let's see what the Founders have to say. In The Federalist #10 we read:
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As long as the reason of man continues fallible, and he is at liberty to exercise it, different opinions will be formed. As long as the connection subsists between his reason and his self-love, his opinions and his passions will have a reciprocal influence on each other; and the former will be objects to which the latter will attach themselves. The diversity in the faculties of men, from which the rights of property originate, is not less an insuperable obstacle to a uniformity of interests. The protection of these faculties is the first object of government.
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The conclusion is inescapable: true conservatism worships at the alter of diversity; moreover, according to the Founders, "the first object of government" is to protect that diversity.
It's no surprise to find Mark Twain's celebrated character Pudd'nhead Wilson expressing the same respect for diversity in plainer terms:
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It were not best that we should all think alike; it is difference of opinion that makes horse races
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And so ... best wishes for happy horse-racing are hereby extended to liberals and conservatives alike! :)