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[quote=Anonymous][quote=Anonymous][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]
Go to CMU for sure. The math department isn’t that large there, but it’s very well staffed.

He’ll learn this in college, but the whole pure/applied split is a bit arbitrary and a lot of applied coursework relies fully on pure mathematics.

Because CMU’s math department is quite small and his options are much more widespread, there are a ton more research opportunities for a students

And now the frank part: Math isn’t easy. If he’s afraid of a challenge, good luck doing math at Williams or CMU. We know math majors at LACs who work like they’re in the navy. Those are the best students and they get into PhD programs- that is life.[/quote]

[b]Applied math is rather different from pure math, except at schools that don't have strong pure math departments.[/b] However, a high school student really has no idea whether they'd thrive in pure math or applied math. Pure math is arcane art.  Applied math PhDs often come from pure math undergrad, since undergrad pure math is a foundation for rigorous applied math and physics.
[/quote]
I'd say the exact opposite is true. It's very easy for me to unrigorously teach you statistical linear models, but a rigorous statistics department is obsessed with pure mathematics.[/quote]

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