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I have completed my Master's in Mathematics.

I loved two subjects: Algebra (modules and non-commutative rings) and Cryptography (visual and algebraic). I wanted to work on them in my PhD. I scored good grades in both subjects.

Now when I am going to apply for a PhD program at different institutes. I am getting two options PhD in mathematics and PhD in Computer Science where Algebra comes under Mathematics and Cryptography under CS.

Question: Which PhD field offers better job opportunities in future: Math or Computer Science?

  • I think it depends on the exact meaning of the "better job". The moderation is very strict on the Stack Exchange, and "opinion based" or "too broad" are very common reasons of the question closures. So I suggest to commit every reasonable to make exact, what do you understand on "better job". – peterh - Reinstate Monica Jan 31 '18 at 19:16
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Assuming that you're interested in the private sector and holding all else equal, I'd guess that a Computer Science degree would tend to outperform a Math degree. It's just such an incredibly useful field to have expertise in.

That said, if you're going for competitive research positions in overlapping fields, e.g. cryptography, then it may not matter that much so long as you have the appropriate background for that sub-field. Then, you'll probably be evaluated against other applicants more heavily based on objective qualifications rather than the name that your degree has on it.

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If you're going to be a researcher, pick the one you care most about. You'll need the extra motivation and drive to stay passionate for the next 40+ years.

If you're going to be a professor, it really doesn't matter much which you pick, as they are both quite viable, and both have interesting sub-fields to focus on.

If you want just about anything else, pick the crypto. The demand is higher for practical comp sci, leading to better job stability in recession years. With the ever-increasing need for better encryption and foiling enemy systems, both the private and government sectors will continue to see a rise in demand (and pay) for any smart cryptographer.

Note that depending on individual university programs, computer science degrees may include a lot of emphasis on topics outside of cryptography, or may assume a working knowledge of certain comp sci topics. For example, if you don't have a background in programming, it would behoove you to chat up the professors and make sure they don't expect you to already be conversant in C++, Java, object oriented concepts, etc. With your masters I fully expect you could learn whatever you lack, but that's a choice you want to make and not have thrust on you after getting into a program.

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