Requirements for Applied Math Grad. Programs

[anonymity]

Hello everyone,

I am an undergrad double majoring in mechanical engineering and mathematics. I want to say, up front, that I cannot really see myself ever pursuing a degree in pure math. I expect (at least, for now this is the case -- who knows what the future actually holds), that I will stay in some field of engineering or applied math.

The reason I am posting this question is that my school has very lenient requirements for their mathematics degree. I am essentially allowed to pick whichever courses I want to take, and am only required to take 30 credits (caclulus, ODEs, linear algebra, etc.. All lower-level things that engineers and science majors would be taking, with the exception of an intro to proofs course, on set theory). As for all of the other courses (mostly upper-level) the student has a high level of decision power (assuming they fulfill the math credit requirements, and the upper level math requirements -- both credit number requirements, not specific courses).

Currently, I am planning on taking all "applied" courses (ie, no pure math -- no real/complex analysis or proof based LA or abstract algebra). Everything is basically differential equations, mathematical modeling, or numerical analysis.

So I guess my question has two parts:

a) What is the absolute-minimum, got to have it list of courses for someone looking to get into an applied math Masters/PhD program? (I assume the answer is different for the two cases?)

b) I have always heard that Grad programs prefer depth over breadth. Does this apply to my situation? I ask because I would much rather go deeper into applied math (by taking graduate level courses in numerical analysis or differential equations) in my undergrad as opposed to stepping back from what I would like to study in grad school, just to glance at real analysis or abstract algebra, and have it forgotten in a year..

EDIT:

My post does not seem to be very well received (atleast in the immediate sense), so I will try and define "the absolute minimum list" a little better. I think it is clear that I am leaning away from pure maths, but I am looking to find out if not having the really basic/fundamental pure math courses that most schools will require for one acquire a math degree (eg, Real Analysis or proof based LA) will hurt me in the admission process for an applied math program.

 

[gungywamp]

I too am looking to apply to Applied Math grad programs, so I can't offer too much advice, but I'll try. From what I've seen, most programs will require that you take the Math GRE, which covers topics such as real/complex analysis, statistics, combinatorics, abstract algebra, topology, etc., on top of linear algebra, calculus, ODEs. So at the very least you should be familiar enough with these topics to not fail horrifically on the subject test. Applied programs may not care as much as Pure programs about how high you score, but I can imagine that doing poorly will not help your application.

I suppose that it would make sense for you to take some 'pure math' courses to give breadth to your undergrad education and to prepare you for the GRE. I would suggest taking analysis courses at the very least. Also, don't shy away from proof based courses because they aren't applied enough. You will have to do plenty of proofs throughout a mathematical career, and it would be a good idea to try to take one proof class each semester just to get yourself ready. I've only taken three heavily proof based courses so far, but they have changed the way I look at math in a very large way. One of the courses was actually an introductory applied math course, and I had to prove special cases for the heat, wave, and Laplace equations. It was easily the most difficult class I have ever taken, and I've taken a grad class in number theory!