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I am planning for a Master degree study, my major in college is computer science, but I also like math. I want to know which branch of computer science uses most math, not only discrete math, but also others like Calculus, Linear Algebra etc. I know theoretical computer science uses a lot of discrete math. I want to study more math in Master study (and better to cover different areas of math, not limited to a particular one), but I also want to use computer science knowledge I have learnt in future Master study.

user248023
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  • Cryptography is on the border of the two. A lot of the theoretical computer science people I have met studied it to some degree, some even learned the algebraic geometric cryptography. – Cameron Williams Jun 14 '15 at 03:17
  • Automated theorem proving will involve a lot of logic and foundations of math, but I don't know if it's what you're after... – Alex Nelson Jun 14 '15 at 03:28
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    Many of the branches of Computer Science, even if they are not overall strongly mathematical, have some subspecialties that are highly mathematical. – André Nicolas Jun 14 '15 at 03:28
  • I'm surprised no answer mentions formal verification. – Mark Nov 14 '17 at 20:25

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Areas of overlap between CS and mathematics include theoretical computer science (including theory of computation, computational complexity, programming language theory, type theory), algorithmics (sometimes but not always counted as part of TCS), numerical methods, cryptography, optimization ...

Many applied areas of CS are math-heavy too, such as image processing, computer graphics, media compression, etc. And of course most subfields of CS will apply math quite freely to analyze their problem domains and solutions.

hmakholm left over Monica
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-Computer Vision and Image Processing are highly math demanding. Calculus, Algebra, Probability Theory are used a lot. I've seen some papers on PDE applications too.

-Computer simulation has discrete event simulation (lots of Operational research, queueing theory, etc) and also continuous simulation which includes physics, and that means modelling with Diff Eq and numerical methods.

Also the application of CS to other areas, like cheminformatics or bioinformatics are quite math-heavy, but don't know if they fit in "CS branch"

bowman_d
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Recursion theory, also called computability theory, is quite mathematical. Computational complexity theory is closely related.

As Cameron Williams mentions in a comment, cryptography is on the boundary. Some of the mathematics involved is quite sophisticated.

Michael Hardy
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