The following is a slightly edited email I sent to a friend who was considering a math major, since he enjoyed his calculus class. This was also before I switched from doing a math PhD to doing an atmospheric science PhD.
Whether you decide on majoring in mathematics depends on a few things.
One of the most difficult things in the world is deciding on a career. Some people find it easy, I guess, but for people that are interested in a lot of fields, its really hard. Part of the reason I chose math was to delay that decision – it is often said that a degree in mathematics can take you anywhere.
That claim requires a few caveats, however. Math as a degree can be useful in many fields but requires you to carefully plan your other classes, just as in studying biology before going to mad school.
If you want to do pure mathematics as a career, you can focus just on your math classes and do any minor. You will then need to get a PhD and are mostly limited to going into academia (becoming a professor). Not a bad option, but the field is becoming more and more crowded.
If you want to do applied mathematics as a career, you have more options. You can get a PhD and go into academia, as in the pure math track, or go work at a national lab or in industry. You can also get a masters degree for a more specific track: biomathematics, computational math, and financial mathematics being the main options.
At the national labs, you do interdisciplinary work. The last project I worked on had elements of biology, forensics, statistics, and computer science. Some of the coolest science happens at the intersections of fields, and that is where I think the future is. You can do especially interesting things if you have expertise in computer science and in another field. So doing math with a minor in CS is an excellent option.
What aspect of calculus is exciting to you? New methods of computation? Blanket statements about properties of functions? Applications to the “real world”?
If you enjoyed calculus and want more, here are some options for what to do next:
- Applied mathematics: numerical analysis, ordinary differential equations, linear algebra, partial differential equations, scientific computing, complex variables
- Pure mathematics: real analysis, number theory, abstract algebra
- Statistics: mathematical statistics, regression, Bayesian statistics
- Some things I didn’t look into very closely but use a lot of calculus: Mechanical engineering, physics, electrical engineering.
Look at the work being done at places like Oak Ridge, Pacific Northwest, Lawrence Berkeley/Livermore, Los Alamos national labs, and see what catches your interest.
If you were to take just a couple classes to get a flavor of a math degree, take a combined linear algebra and differential equations class, and take intro to mathematical analysis (a proofs class). Of course, talk to friends and professors at your school to see what class would be best for your specific interests.
I think mathematics was a good choice for me, although maybe I should have spent another year as an undergraduate rather than taking 17-18 credit semesters, taken more CS, statistics and physics, and taken at least one biology course. Most of my peers at Drexel are more interested in pure math, and my interests are mainly applied. I plan to take a lot of classes outside of mathematics, mainly in CS (data mining, AI, algorithms, distributed systems, perhaps parallel processing), and do supplemental reading in natural language processing, linguistics and biology. So I think that I’ll still be able to find my niche, although perhaps I should have done a better job researching graduate programs.
Since writing this, I did another internship at Los Alamos and met a bunch of the people who do climate modeling, and learned that atmospheric and oceanic science graduate programs prefer people with math or physics backgrounds over people with meteorology or oceanographic backgrounds. I left the Drexel math PhD program with a master’s degree and started a PhD in atmospheric science at Oregon State.