Hi, I'm going to be entering my senior year of undergrad and I'm pursuing a math and physics degree. I've got a good, high GPA, and really enjoy all of the math classes I've been in. Physics, however (especially particle physics and classical mechanics) were not so enjoyable. With respect to math, I really enjoy the topics of functional analysis and operator theory, although I have a very limited knowledge of the subjects. If I were to go to grad school for math, it would only be in one of those subjects, or a closely related analysis topic. However, I have recently become more interested in applied topics. I have had no applied math classes and no engineering, but I've been reading a book on signals and systems, and I really enjoy the topic. I also like the idea of doing work that will be helpful or actually tangible. I'm also quite interested in working in the defense industry. So, what I'm curious about is, can a math/physics double major with a high GPA, some research experience in math, go to an engineering grad school for EE? I know I'd be behind everyone else because I don't have any of the undergrad classes, so I assume I would not be eligible for admissions. Should I instead apply to applied math programs? I'm looking more for insight and suggestsions I think. The thing that's pushing me away from going into pure math grad school is I'm worried the research is too hard and beyond me. I love the topics and haven't had any trouble at all with undergrad work, but I don't know if I'm cut out to go for research. I do however love teaching , and that's one of the major reasons I wanted to get a math Ph.D. was so I could teach at something like liberal arts school and do a bit of research. Sorry for this huge wall of text, I'm rather unsure of which direction to go and I'd love suggests ions from people that have gone in the engineering direction and the math direction. Thanks!