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[quote=Anonymous][quote=Anonymous]OP: thanks for all the feedback so far. Def a lot to think about:

- DC wants to do pure math (he has a lot of experience with proofs) and loves problem solving. Also a very advanced math student

- toured both schools and liked both schools. Comes from a small high school hence liked Williams

- def aware that CMU will have better/more challenging math classes for him. But concerned about the applied math focus (and the grind at CMU)

- thought at Williams he would get more research opportunities

planning to go to both admitted student days; and looking forward to Ivy day decisions.[/quote]

Hi OP,
Parent of pure math major who is currently in a top PhD program.

Re: your concern about CMU's applied math focus,  I don't think that's a meaningful issue for the undergrad curriculum. CMU has LOTS of pure math and theory courses for undergrads including real analysis, complex analysis, probability theory, combinatorics, topology, graph theory, set theory, model theory, etc.  Also important to know they can take graduate level classes. My son specifically chose a university with a graduate math department because he was interested in taking graduate level classes. He came in with a deep bench of mathematical knowledge and needed the additional rigor and breadth that graduate level courses would offer. He was also advised that for entry to the very top PhD programs in math, a transcript with some graduate level classes is almost expected (not true for all math PhD programs, but true for some of the top tier). To be fair, this is probably only a consideration for a small subset of math students, and knowing nothing about your son I only mention it in case he falls into that group. That would be one key difference between CMU and Williams.

I think the applied vs pure issue would be a bigger consideration if your son was applying for graduate school. CMU would not be the best place to get a phd in number theory, for example.  But IMO it's not something your kid needs to worry about for undergrad.  Have him take a look at the list of courses offered by the math department at both schools and compare.

The grind at CMU is real. But if your son decides to pursue a math curriculum in preparation for a PhD, some grind is to be expected. On the flip side, the kids who are truly mathematically gifted are not the same ones complaining about the grind. They are sort of in their own world of mathy paradise, lol.

I'm curious why you think he'd have more access to research at Williams.  There should be opportunities at either school. Understand that access to pure math research as an undergrad is hard to get, but REUs are one way to do so.  And Williams SMALL REU is excellent (not sure if they give any preference to their own?)  It is true that SLAC professors are typically more accessible to undergrads than profs at research institutions, but the flip side is the research institution has more research going on, not to mention graduate level coursework. [/quote]

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