I was reading some of the nodes on graduate school and I couldn't help but think about how ill-prepared I was for it. So, I would advise if you are seriously considering graduate school to get a Master's Degree (or PhD) in an area of engineering as I once did, you should definitely visit the school, and while you're there, talk to the professors in your particular areas about the background in mathematics you will need. See, I did none of these things, and as a result I was almost kicked out of the graduate school at The University of Illinois at Urbana-Champaign while studying for my graduate degree in electromagnetics.

The first mistake I made is that my mathematics background was not sufficient, at the time, to study in the electromagnetics program. Had I taken the time to ask, before applying, what the recommended prerequisties in math were, I would have learned that on top of maths such a calculus and linear algebra, I would also require courses in vector calculus, complex analysis, partial differential equations and integral equations. These courses were not part of the undergraduate EE curriculum at Auburn University. I should have taken these at a local college first, but I didn't, and I ended up paying for it.

The first mistake led to the second mistake, in that I had to drop too many courses I was unprepared for, and take fewer courses (such as complex analysis) to make up for it. After two semesters of this, the Dean called me in and said that taking so few courses was unacceptable, and if I did it again I would lose my research assistantship. The RA position, where I was basically paid slave labor for my professor, is what allowed me to go to school there. It took three semesters for me to get the basic maths I would need. By then, regular grad students are supposed to have written their thesis and graduated, but I was just getting to where I could understand the math in the required coursework.

After the fourth semester, I had finally completed most of the required Master's level courses in electromagnetics. Then the Dean called me in again. He said that I had been there too long and that this was also unacceptable. He said that either I take the remaining courses the following summer semester, and write and submit my thesis, or I was to basically get the fuck out and don't come back. I finished that summer and left.

I might be somewhat justified by the fact that electromagnetics is not easy, and none of the faculty at Illinois asked if had taken certain math courses. If I was teaching graduate electromagnetics, I would definitely give each prospective student a list of math courses that they absolutely must take before coming to study under me. Having said this, I should have known that and at least asked a professor at Auburn what maths I should study before getting in over my head. Now, to show for it, I have a master's degree and I am totally qualified in the areas of electromagnetic theory and scattering. However, I have an entire department of academics at Illinois that won't return my emails.