Chicago has been great for math for decades, and is one of the few places students can go if they are really into math and want to be part of a sizable math community that’s part of the university mainstream. It’s a very mathy place. Almost 10% of the students historically have carried a math major, often as a second major.
That said, having a Computational and Applied Math department and major is a very new thing for them. I think it just started last year. The department only has 6 grad students, vs. 93 in straight math.
Historically, they had an applied math track within the Math department, but it hardly differed from the straight math track, and I don’t believe it was very popular. I think it had a focus on biology/medical applications. They also had (and continue to have) a “Math with Concentration in Economics” track that was essentially an applied math track where all the people who plan to apply to economics PhD programs hang out. It’s much more focused on producing econ grad students than on students going into financial jobs. My sense is that people who wanted quanty jobs on Wall Street tended to major in economics and to take the math that was necessary for an economics major at Chicago – and maybe a little more than that – and that was more than fine.
The straight Math major (including its special concentrations) is still vastly more popular than the Computational and Applied Math major. There are about 350 math majors in years 2-4 (first years can’t declare a major), and 40 CAM majors. If you look at the equivalent statistics at Harvard, for instance, you will see a radically different distribution.
A current student will have to tell you about the internship market for CAM. Few if any of its majors have graduated yet. In general, students in math and economics at Chicago who do well and who want to work in finance or related fields are very successful.
It doesn’t make a whit of difference what major you put on your application, at least not for anything like math or econ. They don’t accept by major, and those majors are so popular there’s not a lot of difference between being interested in them and simply being interested in applying to Chicago. It might help you a little if you had a strong focus on Classical Greek, or Russian poetry, but your interest in math merely makes you part of the pack unless you are some kind of demonstrated prodigy.
You may also be interested in the new Business Economics major that will be introduced next year. I think it will have a finance track, among others. It seems actually to be a little less mathy than the regular economics major, and there is lots of opportunity to take classes at Booth or with Booth faculty.