Math or Physics

  • Thread starter Cider
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  • #1
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I suppose I'll begin with an explanation detailing who and where I am academically. I'm currently a second semester sophomore working towards a B.S. in Math and a B.S. in Physics. Overall, though, the courses that I have taken and am taking are more representative of a Junior, moreso in math. That is, for math I have taken courses in Linear Algebra, Abstract Algebra (group theory and Galois theory), and a boundary-value oriented applied math course (covering things such as Fourier series and transforms, Sturm-Liouville theory, Bessel functions, and a little PDE) as a requirement for my physics major. In addition to that, I am taking courses on Graph Theory, Topology, and Complex Analysis (of which I have already self-studied with a teacher in high school 2 years prior in the same book nearly to the same extent). The lack of Calculus is due to my having completed multivariable calculus in my junior year of high school. On the physics side, I have taken the honors introductory courses in E&M and Modern Physics, an Elementary Astrophysics course, Classical Mechanics (Lagrangian and Hamiltonian), a Computational Physics course, and I am currently taking Quantum Mechanics. Happily, I have manipulated my schedule so that I have a lot of options for taking grad courses and other courses of interest in my senior year, as all of the requirements for my majors will have been satisfied at the end of my junior year.

On to the issue. I fully plan on continuing my academic career into graduate school in pursuit of a Ph.D., but the choice between the two subjects is daunting to me, to say the least. Over the course of this year, my inclination towards one or the other has varied, with neither gaining a favor of more than 60%. Obviously I am aware that I am only a sophomore at the moment and that I have a year and a half before I truly have to choose, being the indecisive person I am, the more methods to help me arrive at a decision, the better. Hopefully, my first true course in Quantum (barring the Modern Physics course) will help in this department. In addition to that, I have been trying to attend the colloquia of the physics department when I can and attending the lunches that my University's SPS schedules with professors. Unfortunately, the math department here isn't as large as the physics department, so it's more difficult as far as the colloquia are concerned, but I try to attend every talk organized by my University's SUMS sets up. I am also trying to take to the habit of reading physics papers that interest me as well, though I am ignorant of an easy way for someone such as myself to find an analog to that in mathematics (with the ease of access given through SPS). There's arXiv of course, but you never know exactly what you'll end up with there. I am also applying to several REUs in each to hopefully give me a better, hands-on feel for what the future in one will entail, though I can't help but find it ironic if I should have to choose between a physics or a math REU.

I'm not sure if I've illustrated an understandable clear-cut question here, which is something I tend to often do when asking questions of self-importance online, but it describes a good deal of my current situation. I also find that I have both a sort of arrogance and self-consciousness, where the former is most likely due to the subjects coming fairly easy to me and the latter due to not pushing myself enough beyond that. Sadly, these both seem to combine and halt me mentally, and this is also partly a way to facilitate that as well. So I guess the question(s) after explaining these aspects of myself boil down to the following: what are methods that would be useful in facilitating the process of making a decision and strengthening myself in both knowledge and work ethic? Additionally, any thoughts from people who have been faced with such a decision and their process of deciding would be helpful as well.

As an aside, two questions that don't fully fit with the topic. The first concerns the number of REUs I apply to. I currently have a list of 11 math programs and 9 physics programs, though obviously that is a bit much. Since I am applying to two fields, I feel that I should apply to a larger-than-"normal" total amount, but finding that number is difficult. The second is completely random, but I've never fully understood the situations/rules under which one would capitalize topics (e.g. math vs. Math and Abstract Algebra vs. abstract algebra).

Thanks for any help or advice given.
 

Answers and Replies

  • #2
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Are you a prodigy? You were studying graph theory and topology, senior/graduate courses in high school...
 
  • #3
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No, those are the courses that I have studied/am studying in University. I took calculus up to multivariable, complex analysis (albeit independent study with a former math professor in complex analysis who taught at my high school), and a linear algebra course that I took at the local University during my senior year of high school (which I didn't mention since I also took it in college). Sorry if something in my post made that unclear.
 
  • #4
901
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I see, I read "of which I have already self-studied with a teacher in high school 2 years prior in the same book nearly to the same extent" as "all of which I have already self-studied with a teacher in high school 2 years prior in the same book nearly to the same extent".
 
  • #5
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I've thought of a more easily-answered question that should be quite helpful, I think.

This is largely focused at those who do research in theoretical physics and pure mathematics, what is the process of such a life-style/job like? Obviously a simple query as to what a regular day is like won't work, since the process wouldn't really be done in a day. In both cases, what are effectively the processes of gaining inspiration for an idea? Does it usually come as a larger revelation or after trying and trying different methods for solving a specific problem of interest? Further, where does such a problem come from as far as why do you think to work on it? There are many different things that I think can happen after these, and probably a varied amount of answers for the questions I posited as well. In general, what is the process like for the actual research aspect of your career? I'm interested in hearing takes on teaching during this process as well.

Hopefully this generates more of a response since it's a more focused question.
 

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