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What mathematics course should an advanced high school student take to prepare for a career in computer science?

  • I am currently a home-schooled junior in high school, and this year I completed multivariable calculus and linear algebra through MIT OCW Scholar. I've taken a number of discrete math courses as well in my preparation for the USAMO, including logic, set theory, and number theory. I'm not sure what math course to take next year, so I wonder if you could suggest a class that would help prepare me for majoring in computer science. Here are a few I am currently considering: graph theory, group theory, differential equations, knot theory. Any advice would be appreciated, as would resources for studying the suggested topics.

  • Answer:

    You are in great shape!  The answer to this will depend on what area of computer science you want to get into.  For instance, if your interests are in machine learning, probability and optimization are important.  If your interests are in theory, then things like theory of computation, graph theory, and algorithms might make more sense.  For some other areas, other than an algorithms class, you might not need any more math.

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I agree with that you’re in good shape. From the four courses you listed, I would recommend graph theory group theory differential equations knot theory in order of priority. I can provide a rationale if you want, but it should be clear.You might also consider a course in probability. It pairs sort of well with graph theory (random graphs), and is essential if you want to pursue ML, randomized/approximation algorithms, or game theory later on.

Vineet Apte

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