arkleseizure

"If you are counting on your interest in math as any kind of a 'hook', then for it to be useful to gaining admission to the top math schools in the country, your record had better be exceptional, because you will be competing with the best high school math students in the country."

I'm not sure I agree. In my experience -- to be brutally honest -- only a few of the "best high school math students in the country" actually enjoy or take pleasure in math. Being really, really emphatic about your love for the subject -- and being able to wax philosophical about it, and bring up interesting books on the subject in an interview (Godel, Escher, Bach, anybody?), and having really strong recs from math people (preferably profs), and having some other interests too -- moves you away from comparison to people with great scores on math competitions and makes you a better subjective candidate.

phuriku

<tangent>

All real mathematicians I've talked to says that this book isn't that good. (By real, I mean they actually have their PhDs and know the content of the book quite well.)

I usually hear that this book tries too hard to be artsy and is not for people who actually want to learn. I asked my MVC prof last year (who has a PhD from NYU) and he says that there are some really good books for learning the incompleteness theorem et al, and this book is not one of them.

Personally, I like conversations comparing Apostol and Rudin more than I like books about mathematical philosophy such as the book previously mentioned. I did look through God Created the Integers by Stephen Hawking, however, and from what I saw, it looked pretty interesting.

</tangent>

As for your comment, arkleseizure, I think this applies to some schools but not all of them. It's certainly true for Chicago, but as for admission at the other top schools in math... probably not so much. Most top schools look at the objective much more than the subjective.

I also know a fair amount of people who are really interested in and love mathematics. Maybe it's just where you go to school?

Corbett

For undergraduate-level instruction in mathematics, one gauge not yet mentioned in this thread might be the list of AMA Haimo Award recipients for "extraordinarily successful" mathematics teaching. The school with the most Haimo Awards to date (four) appears to be Williams College, which is a LAC rather than a research university.

sherm.justin

Thanks again for all of the replies.

I am interested mainly in pure math, as opposed to applied math.

All of the colleges that I have listed, I have chosen for reasons other than their math programs. I wondered what the top college for math programs mostly just to see where these colleges fall into the scheme of things. Don't worry, I am not just looking for a list of the top math programs so I can apply to just those schools, and only because of their math programs.

My school's math program ends with AP Calc AB (which I took last year as a junior). This year, I am taking AP Calc BC as an Independent Study, along with the help of the Calc AB teacher, who is very capable to teach BC, however, there is just not the interest in my small school.

I think I answered all of the questions so far...if I missed one, or if you have more questions, just ask.

kotchian123

I would strongly recommend "pure math honors program" at University of Connecticut if you're into pure math. It is very selective and the instructors are great. The honors student body here is quite sharp.

For applied math, I would recommend Johns Hopkins University and Carnegie Mellon University. My brother will be attending JHU shortly. I am looking forward to applying to CMU graduate program in the near future.

I have visited and done a lot of research on these colleges but I'm sure there are many other wonderful colleges for math.

Slartibartfast94

I stumbled across this thread while looking for schools with solid undergraduate computer science and math programs. I am currently in my second year at the University of Connecticut, and I am not really sure what kotchian123 is talking about.

UConn's math program definitely has some advantages-- last year they implemented a new four semester advanced calculus sequence for incoming freshman who are seriously interested in pure mathematics. I am one of the first students in the sequence (entering the second half) and although there were five of us in the first semester, now there are only two students left. I have only had two math instructors so far and one of them was excellent, the other was somewhat below average. It is obviously a huge advantage to be in a class with less than five students, especially when the teacher is a serious researcher and cares about teaching.

That said, the course offerings at UConn in mathematics are pretty standard and the material in most courses is not terribly difficult. Advanced or honors courses offer more challenge, and you can take graduate courses if you wish, but it is not at the same level as, say, Princeton or Harvard. I actually transferred to UConn from Caltech last year, and I can tell you that what we covered in the first term (1/3 of a year) at Caltech we spent about a year covering at UConn. Of course, the experience was much more enjoyable and we learned the material far more in-depth than at Caltech. At Caltech I was in a lecture hall with 230 students and the professor was a somewhat eccentric genius named Barry Simon. Let me tell you undergrads, if your professor cannot teach, you will not give a damn how many Nobel Prizes, Fields Medals, or Turing Awards he has won over the years.

You should probably take what I have said about UConn's undergraduate program with a grain of salt because I am only in the second year, but I am not so sure that it is anything particularly special. There are some really cool things about it-- small class sizes, generally good professors, some interesting advanced course offerings. Oh, by the way, the majority of honors students at UConn are not 'quite sharp' by my estimation. In general I cannot tell the difference between ordinary UConn students and the honors students. But as we all know college is about much more than academics or having your major department ranked highest by US News and World Report.

I am actually looking to transfer and continue to pursue a double major in computer science and mathematics. I am mainly considering Carnegie-Mellon, but some of the others I will probably apply to are Stanford, Harvard, Brown, and Cornell. All are very good in computer science and/or mathematics for undergraduates.

rocketman08

Worldwide, Cambridge would be the most famous (for its history and rigor) mathematics course. Alumni include Newton ect.... enough said ;-)... but it is still just as famous today.

If you don't want to leave the US, then something like Princeton is probably the top American school...

kotchian123

slartibartfast94, I would disagree with you that honors student are not different from the regular ones at uconn. I have taken honors courses at uconn (in math and other subjects) and the student caliber is significantly higher. The instruction is more in-depth then regular courses and challenging. Try running a stat check in the honors student body at uconn and you'll find that most have ivy stats and chose uconn for 1)scholarships or 2)proximity/more pleasant teaching style

datalook

In terms of faculty reputation, in pure math, the best program is Princeton. Princeton is noted for winning most Fields medals in the world. It has most math professors selected into the national academy of sciences. After Princeton, Harvard, Berkeley, and MIT would be the next 3 best. Then after these 3 schools, Stanford, Chicago, NYU, and Yale will be about equal.

In statistics, Stanford and Berkeley are #1 and #2, followed by Harvard, Cornell, UNC, University of Washington, and Wisconsin.

For applied math, NYU, Stanford, MIT, Caltech, and Princeton would top the list.

ChicagoScholar

Where did you get these facts? I'm not saying you're wrong--I honestly don't know which school has the most Fields medalists--but I think you may be talking about the Institute for Advanced Study, which is NOT affiliated with Princeton University. A lot of the prestige associated with the Princeton math program actually comes from the IAS. Many people think, for example, that Goedel taught at Princeton, but he really only worked at the IAS.

ChicagoScholar

I looked around online and counted the number of Fields medalists associated with several top math departments, but I couldn't find any evidence that Princeton has the most Fields medalists. The following list is probably biased in Chicago's favor because I know exactly which of the winners were Chicago graduates. I'd be interested to see more accurate counts if anyone has them.

Institute for Advanced Study: 34
University of Chicago: at least 10
Princeton University: at least 8
Harvard University: at least 5
University of California, Berkeley: at least 5
MIT: at least 2

The IAS has an impressive record considering only 48 people have won the Fields medal. Of course you can't apply to the IAS for college, so it doesn't much matter!

powergrid1990

The Math at Cambridge is amazing. It's probably the most popular Math dept in the world.

In the US, I would say that it is still Harvard then the following schools:
Princeton, Berkeley, MIT, Caltech and Stanford.

ChicagoScholar

Here are all the names, in case anyone's interested.

Chicago: Efim Zelmanov, Stephen Smale, Andrei Okounkov, Lars Hörmander, Vladimir Drinfel'd, Charles Fefferman, John Thompson, André Weil, Elias M. Stein, Paul Cohen

Princeton: Charles Fefferman, Michael Freedman, John Milnor, Terence Tao, Edward Witten, Andrei Okounkov, Gerd Faltings, William Thurston

Harvard: Lars Ahlfors, Heisuke Hironaka, David Mumford, Curtis McMullen, Daniel Quillen

Berkeley: Stephen Smale, Vaughan Jones, William Thurston, Shing-Tung Yau, Richard Borcherds

MIT: Jesse Douglas, Daniel Quillen

powergrid1990

^ Harvard's Math is better than Chicago. Not even close.

ChicagoScholar

I recounted and it looks like Chicago and Princeton are tied for the lead with nine wins each. After that, Harvard has eight, Berkeley seven, and MIT two.

Chicago: Efim Zelmanov, Stephen Smale, Andrei Okounkov, Lars Hörmander, Vladimir Drinfel'd, Charles Fefferman, John Thompson, Elias M. Stein, Paul Cohen

Princeton: Charles Fefferman, Michael Freedman, John Milnor, Terence Tao, Edward Witten, Andrei Okounkov, Gerd Faltings, William Thurston, Curtis McMullen

Harvard: Lars Ahlfors, Heisuke Hironaka, David Mumford, Curtis McMullen, Daniel Quillen, Vladimir Voevodsky, Edward Witten, Shing-Tung Yau

Berkeley: Stephen Smale, Vaughan Jones, William Thurston, Shing-Tung Yau, Richard Borcherds, Curtis McMullen, Michael Freedman

MIT: Jesse Douglas, Daniel Quillen