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[quote=Anonymous]The suggestion that one HAS to take math courses in graduate school to get into a competitive program is blatantly false.

First of all, the highest upper-level courses at elite LACs are already modeled after first or second year graduate level courses. Looking at the Mudd listing of courses, I see at least 20 courses that would resemble graduate level courses at a major research U, like UCLA: https://www.math.ucla.edu/grad/courses The courses demarcated as "graduate level" for Mudd seem to be the seminars listed at the end, but the bulk- the upper 75% or so- is just advanced math courses.

I'm part of the American Mathematical Association.  One of the coveted distinctions is "Exemplary Program or Achievement in a Mathematics Department", given to one school each year for excellence in math. 3 LACs have won out of 12 recipients- Harvey Mudd (the first recipient), Bryn Mawr, and Williams. Mudd is one of maybe 12 schools or so which has placed in the top 10 of Putnam (top undergrad math competition) or had a Morgan prize winner (top undergrad research0based distinction in Math). Williams has produced a Fields Medalist (the Noble Prize in math), and of the past 5 recipients of the Morgan Prize, 2 of them participated in Williams's summer math research opportunity (SMALL- it's considered one of the top 3 summer math opportunities for undergrads) and cited it as an important force for them. They were from MIT and Harvard, but think about it- if Williams' professors (who lead the program in full and mentor their own math students during the school year) have the ability to give transformative experiences to what are virtually the BEST math students in the nation, you seriously think that your precious child who took a few intro-level math courses at Blair is too good for them?

Here were the top 20 schools for producing Math PhDs on a size adjusted basis in order, based on the NSF: Mudd, Caltech (both far above the others), MIT, Carnegie Mellon, UChicago, Rice, Princeton, Swarthmore, Harvard, Reed, New Mexico Tech, Carleton, Williams, Bard, Haverford, Rose-Hulman, Pomona, RPI, Stanford, Amherst. That's 9 LACs. Math PhDs are so selective that common advice is to take as many advanced math courses as possible (while doing well) and to pursue research. The LACs in the top echelon know who they're competing against and what they need to do to prepare their students.

Let's be clear- not all LACs are built the same. Few will have the range of courses that the Claremonts or Williams have. At some good but not exceptional LACs, an advanced student can definitely run out. Even some top tier LACs not known for math, like Middlebury, can be limited- Middlebury only offered 24 mid and upper level math courses in 4 years. The net result is that these schools do poorly in math PhD production- Middlebury is not in the top 100 for production of Math PhDs. The central premise- do your research. Have your child see where he or she is, how robust the curriculum is, and how often courses are offered. Look up success in sending students to academia. Don't assume that only schools with an associated graduate program can prepare students well. The only time I'd say a student would inherently pick a school with a graduate program in is for someone placing in International Math Olympiad or USAMO, which is just 500 high school students in the US per class year.  In those circumstances, only 9 or so universities are recommended- MIT, UChicago, Princeton, Harvard, Stanford, Caltech, UCLA, UC Berkeley, Carnegie Mellon- and these students know this from the get-go.[/quote]

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