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What are the areas of modern math?

What areas in computer science research require expertise in both math and programming?

  • In other words, what subfields in computer science require a lot of mathematics and programming (not with just pseudocode) in research?

  • Answer:

    Here are some areas off the top of my head: In most of these areas you can choose to work on theoretical work or real-world applications. For example, in machine learning if you didn't want to code, you could develop new statistical models or improve existing ones. But if coding is important to you, then you could work on applying existing machine learning models on real datasets.

Melissa Dalis at Quora Visit the source

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In addition to 's answer, Computer Graphics requires heavy use of linear algebra (at least rendering and computational photography do), as well as stochastic math (to simulate lighting and rendering skin/hair). Cryptography is also a good candidate; one would ideally implement the algorithms to demonstrate their practicality.

Sherry Wu

Every part of Computer Science can be treated with mathematical rigidity. It really depends a lot on how deeply you are willing to go with it. Computer Science classes are often marketed as "no math needed" because of the way we have raised a whole generation of math deprived students, but don't let that mislead you. When the mathematics is not used in directly solving the problems, it is used in proving the correctness of,  or in the characterization of the solutions to problems. From a research perspective, it is almost always required that you treat every topic with deep mathematical analysis. If you're in the hunt for a research area, think about what you want to change in the world first -- the math and the programming will be the tools that will allow you to affect the change.

Anurag Mendhekar

Rather than specifying topics in computer science, I would say any particular CS research that involves statistics, optimization, numerical analysis, signal processing require expertise in both math and programming.

Jianbo Ye

I have to second Sherry Wu's answer and say that Computer Graphics requires an incredibly deep understanding of both linear algebra as well as continuous mathematics, which is quite rare in other fields of Computer Science. In both graphics and vision we are often faced with approximating or measuring light, which accumulates according to the http://en.wikipedia.org/wiki/Rendering_equation. Although it isn't often written this way, the rendering equation is fundamentally an infinite integral over all rays of light passing through an area. I have always found the connection between mathematics and computer graphics incredibly rewarding. One of my favorite papers I wrote in grad school involved no code at all, just http://meekohi.com/Holroyd11/ :D

Michael Holroyd

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