I’m a high school senior who's gone through quite the self-introspection the past few months while applying for college, and I have a bit of a dilemma. All my life, I've loved & excelled at mathematics, and want to study & explore it very much in depth in college. I get very excited when I read up on fields such as number theory, analysis, topology, and algebraic geometry. On top of that, I've also realized that although I have no experience programming, there are wonderful merits to applying math to computer science and would love to apply my math skills to a fast-growing industry.

I feel, however, that studying comp sci will "limit" the scope and depth of the math I study, because joint programs of math and comp sci will only make you take math classes relevant to the study of computer science. Out of the Common App colleges I'm applying to, Emory, NYU, and BU have joint majors in mathematics and computer science, while UMiami only has a BS in mathematics, and Georgia Tech has BSs in discrete and applied mathematics. For Emory, for instance, I'll be "missing out" on multivariable calculus, complex variables, real analysis, and abstract algebra if I did their joint program as opposed to majoring in Pure Mathematics.

If there is a way to combine these two interests without limiting the mathematics I learn, that'd be amazing, but if not, so be it. If you feel I have certain misconceptions, please feel free to point them out. Lastly, I know this is not the best place to ask this question, as it is directed towards professional mathematicians, but I would love your input and appreciate it ahead of time!

Thank you!

closed as off-topic by Jeremy Rouse, Will Jagy, Ryan Budney, Asaf Karagila, Jan-Christoph Schlage-Puchta Dec 31 '16 at 8:14

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    Usually joint programs provide a list of courses you "have to take", but usually you still have enough room to take other random courses which interest you but are not necessary for the joint program. – Will Chen Dec 30 '16 at 22:58

I studied mathematics at the undergraduate level, but I was always interested in computers and I spent my days as an apprentice at a super-computing center. Then I studied a mix of computer science and mathematics for my PhD at a computer science school. Nowadays I am a sort of amphibian: I work in a math department, my colleagues think I am a computer scientist, and my interests span from programming languages to homotopy type theory.

I can recommend doing math as a major at the undergraduate level first, and then switching to computer science later. It's not that hard to do, and having good general background in mathematics is a huge advantage in theoretical computer science. You never know when someone is going to come up with elliptic curves in cryptography, or homotopy theory in type theory, or advanced linear algebra in data mining, or Fourier transforms in video encoding, etc. I never heard any computer scientist say that they knew too much math. The math you learn as an undergraduate will stay with you. It will be much more difficult to learn new math later in your life.

While in college, you can still do lots of interesting things in computer science. Here are some from my area, hopefully someone else will suggest ideas from other areas. You can read computer-sciency mathematics on the side; you can participate in open-source projects, possibly ones that involve a lot of mathematics, such as formalization of mathematics with proof assistants; you can learn mathematically inspired programming languages; or the mathematical theory behind them. This way you might find out what interests you.

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    But why not do a double major, or a major in math and a minor in computer science? – H A Helfgott Dec 30 '16 at 23:34
  • Of course, you can do that. I am just saying that it wasn't hard for me to switch to computer science after having done a major in math. – Andrej Bauer Dec 31 '16 at 0:16
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    Your post reminds me of what Rota once wrote (the end of math.tamu.edu/~cyan/Rota/mitless.html): "When an undergraduate asks me whether he or she should major in mathematics rather than in another field that I will simply call X, my answer is the following: If you major in mathematics, you can switch to X anytime you want to, but not the other way around." – KConrad Dec 31 '16 at 3:57
  • (Computer scientist is not exactly the same as programmer. Programming is a science and an art, so practicing is as important as knowing the theory) – reuns Dec 31 '16 at 21:41

Certainly follow your interests, and avail yourself of counseling and other services.

One of the mistakes I made in graduate school was to severely limit my exposure to other subjects. A lot of public lectures, social events, and opportunities I passed up for lack of time, but some I passed up (this was the mistake) because they were outside my narrow field of interest of CS and math. You may find something even better, as long as you never stop looking.

Gerhard "Remember You Can Study Whenever" Paseman, 2016.12.30.

As HA Helfgott suggests, at many schools, it is quite feasible to simply double-major in math and in computer science.

NYU, as you mention, offers a joint major in math and computer science, including courses in Partial Differential Equations, Functions of a Complex Variable, and Abstract Algebra.

There are also programs in "Mathematical and Computational Science," e.g., @Stanford. Georgia Tech, another school which you mention, offers a "thread" in Theory, including courses in Number Theory and Cryptography, Abstract Algebra, Linear Programming, Monte Carlo Methods, Quantum Information and Quantum Computation.

I think you will have more options than you can imagine by just looking at the major requirements. There are many opportunities for "electives" to pursue your interests (as oxeiman suggests).

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