<p>Yes, I think there are 77 undergraduate math majors at Princeton. If students do not declare their major until the end of their sophomore year, that would indicate approximately 30-something math majors per class/year.</p>
<p>PS, I took that figure from my notes as I am assisting a math applicant. But just to be accurate, I have gone back to my original source which is on Princeton’s own Math Department website which states:
<p>At Princeton, students declare their major (concentration) in April of sophomore year before registering for fall classes for their junior year.</p>
<p>But to answer the original question, other math programs in which you can make bombastic claims similar to the OP include those at CalTech, Chicago, Harvard, MIT, and Stanford. Of course, there are many other colleges with excellent math programs too, but these are the colleges that people seem to comment on the most. For example, there are numerous threads on CC about Harvard’s Math 55, or MIT’s Putnam performance.</p>
<p>Agree with warbrain. Princeton is one of the well regarded undergraduate math programs. But it is one of several that are highly regarded, including the ones that warbrain mentions.</p>
<p>Hi OP and other posters. Concur with the notations that MIT, Caltech and Harvard also offer top-calibre mathematics programs. Have you considered Trinity College, Cambridge as well? We have a young family friend from Australia who looked at MIT, Caltech, Harvard and Princeton for maths and is now commencing his third year at Cambridge (Trinity), where he has been doing exceptionally well. </p>
<p>As an aside, our friend did apply to a few, if not all of the four U.S. uni’s I’ve mentioned, but after being admitted to Trinity (in late December or early January), attempted to withdraw his U.S. applications prior to U.S. decisions being made. Each of the U.S. schools he applied to very definitely did not want this to happen, and evidently not so much because of our friend’s undoubted talents, but because, he was told, procedures for withdrawing applications don’t exist. (Perhaps others of you know differently, but I hadn’t heard of an extreme reluctance, if not outright refusal to permit withdrawing applications before and found it interesting.)</p>
<p>Also, have you looked at the syllabus for, say, Harvard’s Math 55 - or the relevant course content syllabi at any of the others? They might offer a guide of sorts in aspects of your thinking, too.</p>
<p>Good luck with your considerations, DoinSchool.</p>
<p>Thanks everyone for the great information in this thread. It looks like there are anywhere from 5 to MAYBE 10 truly “top” programs. harvard, princeton, caltech, chicago (honors analysis track) and some LAC’s. Myself? I will be more than happy if I can subsist in honors calc at chicago, unless I do very well in that course I will throw in my towel as a mathematician - although I do find the subject fascinating…wish me luck. I have a great deal of respect for people who excel at math. Now, I’m going to sign off for a bit before my inferiority complex kicks in from overexposure to collegeconfidential :D</p>
<p>Unless you have some verification that you are a super math genius (USAMO or something) I’d recommend you not pick your school based on which has the most prospective math majors give up. You never know, you could end up being among them. </p>
<p>Michigan doesn’t have as high a reputation as all the other schools mentioned here, but it has a very wide selection of math courses and almost all (including PHD level courses) are available to all students (including incoming freshmen) and have no enforced prerequisites. And in case you are merely “smart” and not “genius” it might give you a better experience since you won’t be the dumbest guy in all your classes.</p>
<p>What is really puzzling is why there are so few math majors at Princeton. It is certainly one of the top mathematics departments in the country and the world, yet for some reason far fewer undergraduates have primary math majors there than at what one would consider peer institutions of comparable size: Harvard (88 in the class of 2010, on a base about 33% larger than Princeton), Chicago (66, same size), MIT (107, same size), Stanford (50, about 33% larger), Brown (60, about 33% larger). </p>
<p>While the OP was clearly being fed a healthy dose of folklore from his friend, I wonder whether there isn’t something to the notion that there are real barriers at Princeton to advancing in math. And – unlike the OP, but I think like any rational adult – I would counsel kids to think hard before putting themselves in a situation like that, no matter how famous the faculty, and no matter how hot stuff the students think they are. </p>
<p>Of course, I hasten to add, there may not be any problem at Princeton at all beyond a plethora of other great options for mathy people – like the 55 operations research graduates in 2010. But do your research, and don’t accept folklore.</p>
<p>Another folklore suspicion: There’s a great reason why most top math programs DO NOT encourage freshmen to take analysis. Most of them don’t have a strong enough background in proof-based university-level mathematics yet. I think most top schools take a “boot camp” approach with all but a handful of very advanced students, asking them to re-learn calculus (and with it other math fundamentals) in a more systematic, theory-based way than they may have experienced before. There’s no shame in starting out like that, and the math departments do it because they think it produces stronger, better-prepared students. I know little or nothing about the math department at Princeton or the texture of math courses there, but I would be pretty surprised if it turned out to have an approach that was fundamentally at odds with what everyone else does.</p>
<p>The absence of a graduate program in math at St. Olaf means that highly advanced students in math (the ones who will take real analysis, abstract algebra, and the like as freshmen) will likely exhaust the math offerings there, even though it may be a good place for math majors starting from non-advanced or only “normally” advanced (up to a year) in math.</p>
<p>In some universities, students taking freshman and sophomore level math courses can choose honors courses with more theory and proofs than the regular courses, though the regular courses are accepted for math majors as they are for physics and engineering majors, and not all math majors choose the honors courses (and some may have transferred from community colleges). Of course, it is common for math majors to be one year advanced, having completed AP calculus in high school, starting off in regular or honors sophomore level math courses. After completing either regular or honors freshman and sophomore level math courses, math majors would then take real analysis, abstract algebra, etc…</p>
<p>Two year advanced freshmen would be those taking real analysis, abstract algebra, etc. as freshmen (having completed freshman calculus (probably in high school AP) and sophomore level math (probably in community college)). But these students are the top students in math, so they would be least likely to have trouble transitioning to the junior level math courses. (And these students tend to take graduate level math courses as undergraduates.)</p>
<p>One reason schools like Princeton may have fewer math majors is because many outstanding math students choose to major in engineering rather than math. Engineering seems more practical and lucrative (sorry to be so blunt or crass but there is a reality there) than pure math. Am I wrong here?</p>
<p>Princeton’s math major is pretty pure, but Princeton does have a certificate program (a minor) in Applied and Computational Mathematics (“PACM”), and of course there is always the Operations Research and Financial Engineering major.</p>
<p>And while it may make sense for many prospective math majors not to jump into Analysis in the first year, the fact is that given the intense competition and the caliber of students worldwide, if you want to get into a high-quality PhD program – say top 10 overall, and top 5 in your speciality, not just any ol’ PhD program – so that you have a shot at tenure eventually at a good university, you pretty much have to be good enough to start with Real Analysis in your freshman year. In fact, Harvard offers TWO specifically freshman courses that include Real Analysis, Math 25 and Math 55, at the Rudin level (plus Math 23, which is more like an “Honors Calculus” or “Vector Analysis” course in other colleges). It is quite common, in fact, among top math kids to have been exposed to Analysis in high schools already. Of course, we are not talking about most math majors here.</p>
<p>I think it actually makes very good sense to have a high attrition rate in a pure math program. Academic mathematics is a very demanding, and not particularly rewarding financially. For using the same talent, there is much to be said for switching into computer science, engineering, or finance. So Harvard may produce more nominal math majors than Princeton, but I suspect a bachelor’s degree is as far as it goes. The kids at these top schools are savvy; in their high-powered math departments, they get a flavor of graduate school math pretty early, and they switch out of math, whether they get the major or not. I think if Princeton is discouraging all but their tippy top students – those who have realistic chances of doing real significant research – from a math degree, so much the better!</p>
<p>So I know of a bunch of alumns of Harvard’s Math 55 – reputedly the most difficult undergraduate math course in the country – who ended up in economics, computer science, statistics, whatever. And one, Bill Gates, dropped out of college altogether.</p>
<p>Parent of a senior math major here who looked at the top programs and was accepted to a few (Chicago, MIT and Mudd were his top three acceptances).</p>
<p>My recollection is that Princeton weeds out more proportionally more prospective math majors than other top schools, though I’d need my other computer with my many links to find that source after all this time.</p>
<p>JHS pretty much beat me to my point, which was this:<br>
Analysis as a first year UG is VERY unusual. Honors Analysis and IBL Analysis at UChicago generally have only a few freshmen. S1 was one of two first years in his IBL course. Decided he liked that format better than HA.
Analysis is the killer course for most would-be math majors. It’s highly abstract and proof-driven, and a LOT of students get to that point and decide they prefer their math with numbers, thank you very much. S considers it a point of pride that he has not touched a calculator in college.
Success in math competitions does not = success as a math major. S didn’t do the big math competitions (though he did USAMTS for the proof practice and did USACO), but his HS offered college-paced courses through real analysis (i.e., BC Calc, MV, DiffEq, LinAlg and calc-based AP Stat) as one-semester courses. </p>
<p>MIT also has the 18C major – mathematics with computer science – HEAVILY theoretical. This is basically the path S1 carved for himself at Chicago and what he would have majored in at MIT.</p>
<p>If you want knot theory, St. Olaf’s is THE place to go. They also run the US end of Budapest Semesters in Mathematics. They know what rigorous math looks like. And everyone at Harvey Mudd takes eight semesters of math. Not for the faint of heart!</p>
<p>As many have stated, Princeton is only one of the top math programs in this country. You need to look at the total school when you consider colleges. My son finally declared his math major when he needed to for graduation. He did start with Honors math and physics sequences- theoretical instead of problem based and later made his choice. He was able to take several grad level courses at a top 20 school for math grad schools while an undergrad. This would not be possible at a college like St Olaf. He also added a comp sci major. The math field is brutally competitive as he discovered for grad apps. </p>
<p>Look at the infamous US News and World Reports rankings for math grad schools. Target schools among the top 20 or so for your reach/match and safety schools for undergrad math opportunites. Research schools among these for how they run their math departments for undergrads and the rest of the school environment. Look for an overall best fit. Of course, you may want the small liberal arts college atmosphere and would consider those schools. You may be one of those at the very top in math aptitude, but you are just as likely to be humbled by your peers (top math portion scores of the SAT and GRE are common). Decide how hard you want to work and what other interests you may have. Remember to live your life as well as passionately following your interests.</p>
<p>Remember- you may not get into the schools you apply to. We do not need to learn your credentials here. While you are doing college research you should take a look at the background of the professors and TA’s to see where they got their educations. Those Princeton professors most likely got their degrees from other schools.</p>
<p>Agree that doing well on the Putnam is not the indicator of being the best mathematician. Also- mathematics is a diverse field (as are most), each great mathematician is great in one area. You don’t specialize as an undergrad, you want exposure to many areas to find out what most intrigues you.</p>
<p>Just caught a link to the St Olaf site. Definetly NOT for us. Religion, a definite factor when choosing a college. Not for atheists (emphasis on JudeoChristain mythology as well). Consider the nonacademic factors when considerreing colleges.</p>
<p>"You can’t seriously think St. Olaf’s is anything close to Princeton in quality of math undergraduates or faculty? "</p>
<p>I can think that (because it is true) 1) they produce more math majors; 2) a higher percentage of the student body are math majors; 3) A higher percentage of the student body goes on to Ph.D.s in math.</p>
<p>The numbers are what the numbers are. You can interpret them as you please.</p>
<p>And to quote the above:</p>
<p>"If you want knot theory, St. Olaf’s is THE place to go. They also run the US end of Budapest Semesters in Mathematics. They know what rigorous math looks like. "</p>
<p>Good to know one doesn’t have to be wildly successful at math competitions in high school to do well as a math major in a selective school. Son’s only done AIME twice but never USAMO. Will study real analysis this year as a senior.</p>