Hey everyone. I'm hoping to get some advice from you guys. I am a senior studying Electrical Engineering. I am currently applying for graduate schools and for graduate fellowships (everything is mostly due mid-December). I plan to pursue a PhD. The only problem is, I'm not entirely sure which subdiscipline of Electrical Engineering I would like to pursue. I have met with several of my teachers for advice, but I'm still not sure. I really like math. On the other hand, I really like physics. This has led me to narrow my decision down to two categories: 1) Control theory/control systems engineering, or 2) Optoelectronics or Electromagnetics. 1) Control theory: Control theory seems to be very mathematical, and if I go down a theoretical path in graduate school, it seems like my desire to learn advanced math will be satisfied, while providing me with an advanced degree with decent industry/government prospects. I am taking a control theory course now, and I really enjoy it, particularly the applications of linear algebra. I have also heard of control theory being applied to other non-engineering fields, like biology or economics. The prospect of having the opportunity to work in all sorts of areas is appealing. The only con is that I may not be learning any physics. 2) Optoelectronics/Electromagnetics (vague, I know): I took two quarters of engineering electromagnetics, and have also read Griffiths which I enjoyed. I also enjoyed learning about semiconductor devices in another course. I am taking senior/first year grad level quantum mechanics in the physics department which I like, but its lack of mathematical rigor is dissatisfying. Researching in an engineering field that would require me to learn more about these areas of physics is attractive. However, I worry that the level of mathematics will not satisfy me. It sounds as though the relevant math would basically just be things along the lines of solving boundary-value problems and PDEs. This is great and all, but from what I understand, control theory at the advanced level would expose me to differential geometry, calculus of variations, and lie theory to name a few topics. Can anyone give me some advice? Note: If I had to choose between learning more math vs. more physics, I would choose math. But obviously if I find out that choice (2) would involve the same level of math as choice (1), that may be the better choice. I want an advanced engineering degree because my end-goal is to work as an industry or government researcher, possibly starting my own business one day. I feel that an advanced engineering degree would satisfy my intellectual curiosity, while making me more marketable than I would be with, say, a math or physics PhD. Oh, and what might be examples of industry/government jobs one might have with either of these specializations? Thoughts?