<p>I’d like to second ucbalumnus’s point of view:</p>
<p>Advanced math students definitely hit a ceiling at LACs, even at strong colleges like Swarthmore and Haverford. (Been there, done that.) Swarthmore students have the added disadvantage that the college limits the number of courses that they can take in any given subject for the sake of a broad education. Horrible for grad school-bound math majors because grad schools are looking for advanced students with demonstrated dedication to their field.</p>
<p>I can also personally confirm that the top graduate programs in math are biased against liberal arts colleges. There are a few exceptions (most notably Berkeley and Chicago) but you won’t find a single liberal arts graduate (who didn’t take graduate courses at a bigger university) at Princeton or MIT or Stanford.</p>
<p>To be more explicit:</p>
<p>Beginning math majors at Penn with your son’s background would normally take undergraduate real analysis and abstract algebra in their first year, and then graduate math courses from their 2nd year onward. By the time they are done with college, they have usually completed the full first-year PhD math sequence and have gained - through advanced graduate courses, seminar attendance and supervised work with a faculty member - a good understanding of a current area of research.</p>
<p>The same student at a LAC would spend his whole college career dorksing around in undergraduate math courses. They might take one or two 1st year graduate-level courses that are offered as advanced undergraduate electives, do a reading course on another topic that might be taught to a first-year graduate student and do a summer research project that might be publishable in an undergraduate research journal (i.e. of no interest to the rest of the math community). </p>
<p>This may or may not be relevant to the OP’s son - OP did not say that he was interested in grad school in math in particular - but it’s something to keep in mind as he is weighing his options.</p>
<p>Still gotta mention Harvey Mudd, especially if graduate school is a goal. Mudd is excellent at preparing an sending students to grad school. And, as mentioned before, students have access to the great LACs next door.</p>
<p>The vast majority of math majors (at LACs or unis) will not go on to do PhDs in math. The top math grad programs are open to only the very top undergrads pursuing careers in academia. I know many very talented math majors who understand that they are not going to go that route. But there are obviously many other possibilities, including grad programs such as the MA in statistics that my son was encouraged to do (at Princeton).</p>
<p>I just want to say that I find this discussion fascinating (and revelatory).</p>
<p>My son’s still in early high school, but the advice he’s gotten from people who are sort of math mentors is to look at colleges with strong graduate programs in math. The advice is that his talent will then be recognized earlier and he’ll have more opportunities for research and advanced study. Assuming he doesn’t change his direction (and that’s still a possibility).</p>
<p>I used this list from the mathematical society:</p>
<p>Don’t rule out top schools’ need-based aid. </p>
<p>Caltech and Vanderbilt were exceedingly generous with need-based aid. Princeton was very generous. I understand Harvard and Stanford are very generous. Have you run calculators on all of these schools?</p>
<p>Also check out UTDallas McDermott Scholars program. It’s fantastic for the right kid.</p>
<p>And yes, with the exception of some LACs, your son might run out of math classes, depending on the LAC. That was a concern of my son’s (who ultimately chose MIT over Mudd, Princeton, Caltech, Vandy, Penn, and WUSTL, as well as UTD and Pitt).</p>
<p>Mudd is an awesome school but I think the merit scholarship is only 10K a year. They have another one for URM/first gen type students that’s full tuition.</p>
<p>b@r!um, thank you for weighing in. I was just reading some of your old posts about your UG -> grad experience. The first hand experience you have had is very valuable, indeed. I have no idea if S would want to pursue a PhD in math, although at this point he thinks he would like to go on to get a PhD in something. He loves math, and is very good at it, so I think he feels that it would be foolish not to complete an UG degree in it as one of his majors (as long as he still feels the same way after the proof based course he is currently taking). Thanks for pointing out Chicago as an option. He loved the school when he visited! I know their merit scholarships are highly competitive, so not counting on it being affordable if he gets accepted.</p>
<p>Thanks for the link, piesquared. Good info.</p>
<p>I’ve run NPC for several need only schools. It’s incredible the difference in net price from school to school! I was particularly surprised at the difference between Cal Tech and MIT (~10K)…and not so surprised at Cornell vs. Princeton (also ~10K).</p>
<p>If your son wants to do research in science or medicine with a PhD, not just, say, be a medical doctor (some people count that as STEM too), then the problem mentioned by several people on this thread about running out of courses in LACs is very real. His peers in the top graduate schools would indeed have taken real graduate courses in their upper years. And even when a LAC does offer advanced courses, you have to watch that because they are offered only in alternate years, collecting enough of them in four years can be really tricky.</p>
<p>Have you looked at Dartmouth? It is really a LAC, but does have graduate programs in several science departments, so the offerings and resources are more abundant at the advanced levels.</p>
<p>The funny part about this is the vast majority of STEM majors at Oberlin who go off for further education go into PhD programs to become research scientists…including topflight ones at elite universities like MIT and Harvard. </p>
<p>Not as many go into medical school even though I’ve heard from Med school Profs/doctors that their pre-med program prepares students well for med school. Main issue from what I’ve heard/gathered is due to student preference and campus culture.</p>
<p>This is the kicker, isn’t it. There is such a qualitative difference between calculus (including MVC) and diff eq vs Honors Analysis and other upper level mathematics that are completely proof based. And there’s no way to know whether one likes it, or is any good at it, until you get there and do it.</p>
<p>I held my breath as DS came up against that step. Fortunately, he sailed through much to my relief.</p>
<p>As an undergrad at UChicago, I had a friend who earned his MS in math (as an ‘oh by the way, you’ve fulfilled all the requirements for this’) at the end of his college junior year, but did not get his BA until the end of senior year as he had to fill all his Common Core requirements :D. He was a transfer from UCSB at the end of freshman year and his math profs from UCSB encouraged and facilitated his transfer to UChicago. They apparently felt strongly that he needed what Chicago could provide that they could not.</p>
<p>ihs - yes, I agree. It will be interesting to see what S thinks after this course. I’m happy that he has the opportunity to try it out now. Hopefully it will help him narrow down his major(s). He was also lucky to land a paid internship this summer working in a lab at a local company doing research (and playing with some really cool equipment!). He thought it would be a good chance to see if he likes research and lab work as much as he thinks he will. He is very fortunate to have these opportunities while still in HS.</p>
<p>The concerns about hitting ceilings at LACs appear to be most pronounced in math, rather than in other sciences. It is typically more difficult and less common for a student to become as extremely advanced in a non-math science than in math, and non-math science majors tend to have more core undergraduate requirements and labs which can make getting highly advanced in college in those majors (to the point of taking mainly graduate level courses as a sophomore or junior) less likely.</p>
<p>The main concerns against LACs among most STEM aspirants at my urban STEM-centered magnet was mainly the lack of a critical mass of hardcore STEM nerds like that at our HS and/or the fear of being mandated to take more reading/writing intensive courses in the humanities/social sciences(Mainly those who are relatively weak in those areas or who are already struggling at their academic limits. The ones without those issues didn’t care or enjoyed those courses alongside their STEM ones).</p>
<p>In short…it was much more campus culture/fit related.</p>
<p>I think that in most cases it is much better for someone planning to do a PhD in a STEM field to go to a research university. In my experience (Physics at a largest research university), kids at universities are able to take advanced courses more easily, can get involved in research sooner and to a much greater extent, and can meet faculty in their field who know people in the greater academic community (this helps a ton for recommendation letters). I am currently doing an REU at another research university after spending the past two summer at my home institution. There are not many other people in the program from universities and from my interactions with kids from smaller schools, it is very obvious that I will be at a much greater advantage applying to grad school because of a combination of my research experience, coursework (I will graduate with a masters and will have had 8 grad classes), and the mentorship and exposure I have had to professors in my field. It seems there is much less breadth of research opportunities for students at liberal arts colleges and it seems that most of it is geered towards completing a thesis and isn’t actually publishable. At a university, pretty much any project undertaken should have the potential to lead to a publication in a respected journal. Furthermore since professor’s at LACs are there to teach, they don’t have as many connections in the research community. They also do not know as much about the application process to grad school, so many of the students I have met at the REU don’t seem to have a clear strategy for their applications.</p>
<p>^^^Regarding the essay topic, one can always dream! I have an older thread where I asked about how to encourage competent but reluctant writers to suck it up and get it done (alright, I was much more PC about it, but that about sums up my S’s interest in writing for the sake of writing. Add to that the fact that he doesn’t like talking about himself and takes being humble about accomplishments to a whole new level and I am in for a stressful few months.).</p>