I find myself switching my mind alot 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 alot 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..