“Going to an LAC that doesn’t have a substantial math department means essentially entering into a tutoring relationship with a couple of faculty members.”
But I do think there are LACs, as many have mentioned here, that DO have robust math departments. St. Olaf has 15 Math professors, 25 at Williams, and even 11 at tiny Haverford (plus another 10 at Bryn Mawr). I’d consider those substantial.
Too many schools to go with just named ones here. Be prepared for both the pros and cons of a school of any size. Figure out priorities (actually, your son does this- it is his list). Remember that college is radically different than HS- eliminate peer pressure, for example.
Wesleyan is a LAC with its own graduate school in Math:
http://www.wesleyan.edu/mathcs/graduate/index.html
Caltech has maybe 900+ UGs, but many more grad students. I doubt your kid would run out of math courses.
My son is also a math/music kid who is looking for “bright kids who actually read and think”. Although he isn’t specifically looking for a LAC, I’ll share the schools we’ve looked at that you may interest you also. A little background, my son took Calc BC freshman year and has since completed Diff equations, Math Modelling, Number Theory, Intro to Analysis and will study Linear Algebra and Knot Theory this (senior year). His interest in music is Composition. The Music Comp has been one of the limiting factors in our search - most schools have a decent math program but trying to find a great math program and music comp is more challenging. I imagine it is similar to looking for a good math/opera program? In any case, below are the schools we looked at/are looking at:
Harvey Mudd - One of the first schools we visited, we thought son would love it but although the math department is certainly stellar, we didn’t like the dorms or the general concrete 60s style architecture. Plus, no music comp.
Pomona - Liked a lot, great academics, nice kids, beautiful campus and would’ve been on the final list but it doesn’t offer music comp.
Stanford - Great academics and music comp but son felt campus was “too big”, he’ll apply because of the academics but not sure it’s a great social fit.
St Olaf - Visited this summer and LOVED it. Great math, music and the people we met were so nice! Also, they offer great merit scholarship opportunities. Son will definitely be applying. The dry campus was a plus as son isn’t looking for a party school. The one drawback that stood out was the dorm rooms seemed very small compared to other schools.
Carleton - Visited and liked a lot, new beautiful arts/music center (Weitz Center for Creativity.), great academics, beautiful campus. Drawback was very little merit aid offered.
U Chicago - Fantastic math, strong music with lots of performance opportunities. Great internship opportunities and career support.
Other schools on the list which we plan to visit this October: Princeton, Yale, Amherst, Brandeis, and Brown.
You may also want to look at the interesting new dual degree between Harvard and Berklee School of Music.
Best of luck with your search!
Most students who major in math end up doing graduate study or working in related applied areas (you can see this in exit surveys from colleges), such as computer science, statistics, economics, finance or engineering. These students generally are served well by LACs, particularly if they combine math with another field of interest (which also will eliminate the problem of running out of math classes if they begin post-calculus).
However, students contemplating graduate study in math, with the goal of being a research mathematician (e.g. a prof at a research university), will be at a disadvantage attending LACs, even elite ones. The typical student entering a top math graduate program would come from (if they are from the US) a top private university or strong state flagship, would likely have started with sophomore/junior level math classes in college, taken honors classes, and finished with graduate level courses during their junior or senior year (in some cases they may start them even earlier). The research mathematician track is very competitive. Your son is likely only going to be on that track if he really loves math, and probably also only if he finds his math classes (even at a magnet school) not very challenging.
If that is the case, I’d recommend the usual elite private research universities (Ivies, MIT, Caltech, Duke, Chicago, CMU) and stronger flagship state universities (Michigan, Wisconsin, U C’s, etc…). Look for schools that have honors classes in math up through the advanced level (not just Honors Calculus, but at least Honors Analysis and Honors Algebra). These honors classes are designed for the relatively few students who are on the math grad school track. They are also small and taught by full time faculty (just as at an LAC). One somewhat less selective private school that provides these classes is U of Rochester.
The poster b@r!um went to Bryn Mawr, and ended up at an elite math grad school, but took grad level math classes at Penn as an undergrad – see the link below
http://talk.collegeconfidential.com/parents-forum/1414683-prestige-versus-cost-p7.html
Swarthmore also has advice which illustrates some of the difficulties students applying to math grad school from LACs might face:
http://www.swarthmore.edu/Documents/academics/math/grad_GRE/MathGradSchool.pdf
Here’s a link that will get you past the login requirements to see the math sections offered at the 5 undergraduate colleges in Claremont this semester (there are more than 100 this semester alone). I think it will work if you just choose “Mathematics” in the “Course Area” box and keep all the other options at their default: https://my.pomona.edu/ICS/Academics/Academics_Homepage.jnz?portlet=Claremont_Undergraduate_Course_Schedule&screen=Advanced+Course+Search&screenType=next
In case you’re curious…the National Science Foundation has conducted a survey of all earned doctorates annually since 1957. Among other questions, they query where one attended for his/her undergraduate degree. You can find the original data at: https://www.nsf.gov/statistics/srvydoctorates/.
Based upon this data, the top undergraduate feeder institutions for producing math and statistics PhDs (as a percentage of undergraduate enrollment) are (note that statistics is included in the mathematics data):
So…I don’t know that I would be worried about limiting factors/opportunities at places like Reed, Pomona, Swarthmore (etc), given that they are sending, proportionally, among the largest number of students to get math PhDs…no? And this data (from the NSF) directly contradicts what a poster commented earlier about LACs hurting students’ abilities to go on to get PhDs…
Here’s another list of schools that produce http://wp.stolaf.edu/ir-e/baccalaureate-origins-of-ph-d-s/
I think it’s a good place to start for any kid who’s looking for math, music, and a dynamic undergraduate LAC experience. I’d recommend looking at schools that produce PhDs in lots of disciplines – you want friends who are smart in all kinds of subjects, not just your own.
What would be more relevant in evaluating the suitability of the math program is percent of math-related majors going on to earn PhDs. It seems rather obvious that a STEM undergraduate school is going to have a higher fraction of the entire student body going on to math graduate school than would a school which offers a wide array of majors. Not that I think Cal Tech, Harvey Mudd, or MIT are bad schools but their numbers would be inflated by this methodology.
My comments earlier questioning the preparation in math at LACs only applies to a small number of extremely talented, motivated students who might be on the path to becoming professors in math at research/PhD granting universities. These institutions hire faculty with PhDs primarily from the top 10-20 (mainly 5-10) graduate programs (particularly in pure math; applied math is somewhat less competitive).
The NSF data that is publicly available doesn’t indicate the fraction of students who go on to these top 10-20 programs. Students in lower ranked programs generally don’t become primarily research mathematicians – they mostly teach in non-PhD granting institutions, or leave academic research.
Some schools (such as Grinnell) provide very detailed exit surveys. I’ve looked at these surveys in the past, and have noted that in some fields (Chemistry, e.g.) students end up in top PhD programs, but I generally didn’t note math graduates going to these programs. This is consistent with b@r!um’s comments.
Math is unique. There are wide ranges in how quickly students seem to learn it, so top students are generally only challenged when they are tracked together in honors classes. Even the most selective research universities (e.g. Harvard) provide these, but LACs are generally not large enough to separate students into different levels in math.
Also, math is the only field in which a significant number of students arrive accelerated enough to start at upper level classes, and therefore face the problem of exhausting the curriculum if there are not options to take graduate level classes.
However, many of those math sections are many sections of service courses like calculus 1 and calculus 2, rather than more advanced courses that math majors would take.
I guess I object to the stereotype that kids at top research universities are so much more competitive and so much more focused on resume building than kids at LACs. I know LACs are the darling of many posters on this site, but I would take seriously the issues raised by @comfrey. My STEMy kid had a math background comparable to your kid–she was not on as rigorous or advanced a math track as the most mathy kids at her school, but she did take a very rigorous physics class. She found the kids to be very collaborative–and some of these kids were also taking very advanced math and I have no doubt some will end up in top math PhD programs. And, also importantly, there is an entire classroom full of these great peers.
You may also want to look at the results of the Putnam competition as another indication of which schools have some extremely strong math students.
@comfrey: it’s not only math where students can exhaust the undergraduate curriculum before entering college. It’s (close to) possible in foreign languages. If a high school student has very advanced language & literature skills in (say) Chinese, then it becomes difficult to find an LAC with enough of a stand-alone curriculum to support four years of further study.
As far as modern languages go, at some point of advancement in study, a student should be looking at studying abroad to achieve fluency. There really is no substitute.
I would also speculate that there are very few high school programs providing a level of Chinese instruction that develop very advanced skills for a student not exposed through family or time spent in China.
To bring it back to a math discussion, college students can also further their curricular options by studying in Budapest. http://www.budapestsemesters.com
@doschicos. I agree completely. The case I have in mind is precisely that – a student who studied abroad in elementary & high school, then returned to the U.S. & took 4th & 5th year at the local college (as high as it goes). Now a senior, applying to college, finding few LAC options.
One thing to consider is that a high school level course (or even local college if its a directional or community) isn’t going to match up to a course level at a competitive rigorous college. Have you looked into Williams and Swarthmore?
@doschicos. I appreciate your help with this. The student took 4th & 5th-year language (literature/history classes, really) at a top-25 LAC & received top grades. They want to continue studying at this level & higher, but it’s looking like only universities can provide the depth of curriculum.
To bring it back to math, this same HS student has been taking LAC math courses (through Multivariable so far) and loves the LAC style of teaching (after sitting in on an “elite u” calculus course for comparison.)
If he intends to take more advanced (junior/senior/graduate level) math as a math major, most such courses will be taught in small faculty-led lecture/discussion sections even at large universities, so there is less difference in class format between LACs and large universities for these advanced math courses than for many other types of courses. (Although other discussions referenced here hint that some math PhD programs have a lesser regard for the content and rigor of such math courses at some or many LACs, a different aspect from class format.)
From what I have seen the kids at the top research universities in math are very collaborative. I agree with @mathyone on this issue