To math or not to math?

Many among you, if you’re physics students, dream of doing theoretical physics (high energy theory, string theory, particle cosmology, among others), and there’s nothing wrong with one being motivated to study physics in order to, eventually, do research in a theoretical topic. And, in that case, surely you have realized that mathematics are everywhere in your field. If you’re an undergraduate at a typical US college with a physics department, regardless of whether the department grants graduate degrees or not, one may have realized that you can dual-major in mathematics and in physics while still fitting both majors within the complementary 120 semester credits. Case in point: Tulane (assume the recommended pre-graduate training is in effect)

  • At least 32 physics credits, including PHYS1310, 1320, 2350, 2360, 3630, 3740, 4230, 4470, 4650
  • Calculus I-II-III (MATH1210, 1220, 2210)
  • MATH3050, 3090 (real analysis I, linear algebra)
  • MATH3310, 4060, 4210, 4300 (scientific computing, real analysis II, differential geometry, complex analysis)
  • Honors thesis (and, as is usually the case with honors theses, some precious research experience is gained with it)

Now, compare the mathematics major requirements (this has to be one of the most content-free mathematics majors I’ve seen in my lifetime; however rigorous the mathematical content might be, there is just enough content in what follows to fill a math minor at my undergrad)

  • Calculus I-II-III
  • Real analysis I, linear algebra
  • At least four electives with some restrictions (3000-level and above, at least one at the 4000-level and above, at most one of MATH2170 or 2240 can be used to substitute for a 3000-level course, must be regularly scheduled math courses)

The physics pre-graduate training will fulfill all the mathematics major requirements, if only in a bare-bones manner. For so many, even with a physics major and the distribution requirements (unless one attends Amherst or Brown, in which case there aren’t any), there’s still some room to fulfill distribution requirements and often with electives to spare. End result: many Green Wave physics majors (even would-be experimentalists) and, if Tulane is actually representative of what happens at a typical American undergrad with a physics department, physics majors in general, end up double-majoring in physics and mathematics.

On a sidenote: many who study physics outside the US will not have access to such a luxury without extending their stay in school; the best-case scenario would, yes, amount to double-majoring with no change in how long one stays in school, but with some tradeoff in how much physics one covers and how much math one covers. Again, this highlights the propensity of US colleges to sacrifice depth for breadth at the undergraduate level. However, one must keep in mind that there are some jobs where one needs a broad education to do the job well, and other jobs where one needs to master a field in sufficient depth to do the work properly.

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