I’m pretty excited about the course I’m enrolled in for this semester, though not for the most obvious reasons. Although I love mathematics, I tend to find applied math a bit tedious – manipulating functions, etc. So a math methods course for physicists would seem to be the epitome of such tedium. On the other hand, I’ve come to realize that just because the math is applied, doesn’t mean there isn’t any depth to it, or that it won’t provide a great deal of value in attempting to solve problems down the road (duh, why else would it be a required course for physicists?). So, in my new found effort to dive into even the most mundane topics when those topics are what I need to learn to move forward, I’m ready to get started and see if my attention span can keep up with my idealistic desire to be a physicist. At the end of the day, you need to do work in the trenches to get anywhere. Speculation about things from 10,000 feet doesn’t always get you anywhere. And problems at the heart of physics are likely to be solved by people who can navigate their way through complicated path integrals and tedious function expansions moreso than by people who have a command of algebraic geometry. Though knowledge of the latter doesn’t preclude you from knowledge of the former.
In short, even if I want to be a mathematical physicist, with the emphasis on the more abstract constructs (fiber bundles, differential geometry, etc.) I need to be firmly grounded in “physics on the ground”, or I’m not likely to have anything useful to say to the physicists.
Plus, from my brief interactions with the professor of the course, I am pretty sure this is the sort of course that will appeal to me. He has been described as very rigorous and apparently in the HW problems you have to give justifications for each step of the solution. That is exactly what Ive realized I need to do with just about every problem I work through myself. Not just rearranging symbols, which you can trick yourself into thinking you understand, but giving clarifying statements and explanations for each step. What does this theorem really mean? Why is it a reasonable thing to expand this function in terms of a Taylor Series to solve the problem?
