I am currently a freshman majoring in electrical engineering and minoring in mathematics about to go into my sophomore year. While I enjoy the engineering aspect, I've found that what I've enjoyed most is the basic analysis in my proofs class and the basic topology my professor mentioned while discussing vector fields in Calc 3. Since I've already registered for classes next semester, it would be too late to switch. However, I plan on pursuing an emphasis in electrical engineering. I do like the problem-solving aspect, but would also like to be able to study mathematics at a more advanced level. My plan is to take sequences in abstract algebra and real analysis, as well as classes in topics on the applied side such as computation and numerical solutions to ODEs. I would already be taking classes in Physics 1, Physics 2, EE 201, Signals and Circuits, and Electrical Networks. How qualified would I be to work as an engineer with this program of study? If not, since I would have an extra semester, what sort of classes should I be taking in addition?