Theorem proofs in applied math grad programs

[creepypasta13]

I find myself switching my mind a lot when deciding whether to apply to aerospace engineering or applied math programs. One thing that will be a factor is how much proving of theorems is required in the applied math grad courses. Does anyone know how much proving of theorems is required in Applied Math graduate courses? I'm ok with doing light proofs, such as in my undergrad ODEs, PDEs, and numerical analysis classes. But I struggled with them in abstract algebra and Fourier analysis as they required a lot more proofs. I see from some Applied Math programs that graduate-level ODEs and PDEs classes are required, but classes in real analysis and abstract algebra aren't.

I had some other questions also: Does anyone know of any Applied Math programs where I can get exposed lots of research dealing with using math for physical problems, such as CFD? Has anyone heard of grad students transferring to other departments? I haven't seen too many programs that combine AE and applied math other than for Scientific Computing programs. I must not be the only one struggling so much between deciding between two different departments..

 

[creepypasta13]

so does anyone know how much proofs are required for the graduate-level PDEs, ODEs, etc graduate math courses that applied math students take? I guess what I really love about applied math is using it for derivations in physics and engineering. Using math methods to solve PDEs, etc.

 

[Shackleford]

I'm considering an Applied Math M.S., too. They have one sequence titled "Applicable Analysis." I just wonder how different this is than the pure math analysis graduate courses.

 

[Simfish]

Well, I go to a school with a top-5 department in Applied Math, and I've taken a few grad lvl courses in it.

In general, no, you don't really need hardcore proofs. Yes, you do need to prove a few things, but certainly nothing on the level of delta-epsilon or abstract algebra proofs.

 

[Shackleford]

Well, I go to a school with a top-5 department in Applied Math, and I've taken a few grad lvl courses in it.

In general, no, you don't really need hardcore proofs. Yes, you do need to prove a few things, but certainly nothing on the level of delta-epsilon or abstract algebra proofs.

Interesting. Here are the required courses for the Applied Math program at my school. They have several different specializations. This is for the general case. I've narrowed it down to picking two out of the following sequences. I'd take Applicable Analysis. I'm not sure on the other two.

6360:6361: Applicable Analysis
Cr. 3 per semester. (3-0). Prerequisite: graduate standing or consent of instructor. Solvability of finite dimensional, integral, differential, and operator equations, contraction mapping principle, theory of integration, Hilbert and Banach spaces, and calculus of variations.

6382:6383: Probability Models and Mathematical Statistics
Cr. 3 per semester. (3-0). Prerequisites: MATH 3334, MATH 3338 and MATH 4378, or consent of instructor. A survey of probability theory, probability models, and statistical inference. Includes basic probability theory, stochastic processes, parametric and nonparametric methods of statistics.

6366:6367: Optimization and Variational Methods
Cr. 3 per semester. (3-0). Prerequisites: MATH 4331 and MATH 4377, or consent of instructor. Constrained and unconstrained finite dimensional nonlinear programming, optimization and Euler-Lagrange equations, duality, and numerical methods. Optimization in Hilbert spaces and variational problems. Euler-Lagrange equations and theory of the second variation. Application to integral and differential equations.

 

[Simfish]

Wow interesting - that looks more hardcore than the courses at my school. Maybe it's under a pure math dept?

It seems that Applied Math courses under Math depts are more hardcore than Applied Math courses under Applied math departments.

Here's the dept of my school:

http://www.washington.edu/students/crscat/appmath.html#amath507

 

[Shackleford]

Wow interesting - that looks more hardcore than the courses at my school. Maybe it's under a pure math dept?

It seems that Applied Math courses under Math depts are more hardcore than Applied Math courses under Applied math departments.

Here's the dept of my school:

http://www.washington.edu/students/crscat/appmath.html#amath507

Oh, yes, sorry. It's from the Department of Mathematics. We don't have an Applied Math Department.

http://www.mathematics.uh.edu/graduate/master-programs/msam/index.php

Your AM courses look interesting. It really is an applied math program.

 

[creepypasta13]

Well, I go to a school with a top-5 department in Applied Math, and I've taken a few grad lvl courses in it.
.

which courses?

Anyways, I was just skimming through some graduate level PDE course webpages and textbooks. From the webpages, the HW assignments and exams had almost no proofs, but the textbooks seemed very theoretical and required advanced knowledge of real analysis. Anyways, for Applied Math PhD programs, my top choices are Maryland and Cornell

 

[Simfish]

Anyways, I was just skimming through some graduate level PDE course webpages and textbooks. From the webpages, the HW assignments and exams had almost no proofs, but the textbooks seemed very theoretical and required advanced knowledge of real analysis. Anyways, for Applied Math PhD programs, my top choices are Maryland and Cornell

Oh interesting. Well, it really depends on textbook. Lots of Applied Math courses use Numerical Methods textbooks, which don't really require any knowledge of real analysis.

Now that I think of it though - there are actually very few applied math textbooks at the graduate level. So it's just easier to use the math textbooks I suppose.

Well, I'm familiar with the numerical methods courses and the 567-568 sequence, and none of those are heavy on proofs. The courses at Washington are very computational in general. The AMath department here is heavy on Matlab, and you don't really see courses that are both heavy on real analysis and Matlab at the same time. ;) But yes - one example is that Bender and Orszag textbook, which has REALLY difficult problems - hell - it even included Putnam problems (there is a course here that sort of uses the textbook, but that makes its own (easier) problems).