<p>I am a very competent student in math- I have already completed most of the requirements for a math major on my own and through school; I am also a fair way through a minor in Physics.
I was accepted at Case Western with a very generous scholarship- but my question stands, is it worth it?
Does the Case Mathematics program stand up against better known schools like MIT and Princeton, will it let me advance in a way fitting to my ability and ambition, and will the students be of the intellectual calibre, in mathematics especially, to keep me interested?</p>
<p>Look up the classes that are offered and the professors on staff to see.</p>
<p>Of course they offer the classes I would expect, but that speaks nothing to the quality of the students, or the flexibility of the program. Most Math programs are filled up with people whose ultimate interest is in being teachers, and are usually not terribly good at “Real” math. I want to be at an institution with a reasonable number of students I can relate to and interact with at a reasonably high level, and I want to know if Case Western might be such an institution.</p>
<p>Wait and see if you get into MIT and Princeton before you worry about this. Lots of folks will be happy to give you advice on the financial tradeoffs in April.</p>
<p>Dummies don’t major in math anywhere, but especially not at engineering schools like CWRU, which do not tend to attract math-education types. In general, any university that offers a Ph.D. in pure math is going to have everything you need. If you are really way ahead of the other undergrads, you’ll just end up working with the grad students.</p>
<p>The short answer is no. I think looking at Math 321 and Math 322 will tell you all you need to know. </p>
<p>18.100B at MIT coveres almost the entirety of Math 321 and Math 322 in one semester. Case’s graduate versions 421 and 422 are basically the same slow courses with additional work. Lebesque doesn’t even show up until the follow on graduate course. </p>
<p>I think you’d be selling yourself short if you have a chance at MIT,Princeton or UChicago for math. You could potentially place right into UChicago’s Honors Analysis and be studying Lebesque integrals and measure theory 2nd quarter of Freshman year. </p>
<p>Some easier schools to get into with solid math departments and which may give you merit scholarships are Brandeis and Rochester. NYU is a great school for math, but they are kind of stingy with merit money. </p>
<p>For bigger schools consider Wisconsin, Michigan, and Ohio State. </p>
<p>Look for schools that have an “honors calculus sequence” that’s theoretical and uses Spivak or Apostol. You may already be beyond that, but schools that can fill classes like that are the kind of schools that cultivate fast-track mathematicians. </p>
<p>Just my opinion</p>