<p>I'm planning on pursuing a PHD in aerospace engineering with the goal of a research based career, followed by teaching. I know the typical mathematics sequence for aerospace engineering pretty much just goes through all the basic courses (calculus, differential equations, linear algebra, etc.)</p>
<p>I'm wondering if it would be beneficial to go through some higher mathematics courses such as real/complex analysis, topology, differential geometry, etc.</p>
<p>Again, since I'm planning on a more research/science based career, I think it may be beneficial, but I don't know. If anyone has any suggestions that would be great.</p>
<p>Cannot really answer that without knowing in what area of Aerospace you would want to specialize. I think obtaining a high degree of competency in the “regular” coursework is very important, but only a few specializations will require much more advanced math, and not consistently the same - most engineering simply does not require that much higher math. I think gt is right that complex analysis is probably the most broadly useful, but I still think only about 1 out of 10 Aerospace PhD’s really use it, if that many.</p>
<p>This is something you can address your senior year, when you have had a chance to really explore the field and have some idea what you want to spend the rest of your life working on. Until then, just concentrate on learning the basics.</p>
<p>Depending upon your school, there may be a upper-division applied math sequence for engineers and others that addresses subjects such as analytical and numerical techniques for solving partial differential equations, etc. If not, graduate school will often give you another opportunity for applied math classes typically more applicable to problems you’ll encounter in engineering research than the average math major classes.</p>
<p>Once you’re a researcher/faculty member, you can always include a colleague from the math department as a consultant (or co-principal investigator, for that matter) on your funding proposals if you need additional mathematical firepower.</p>
<p>Buy a copy of Kreyszig’s “Advanced Engineering Mathematics” and make sure you are familiar with those topics first. Then move on to bigger and badder topics.</p>