What Math Course Comes After Partial Differential Equations?

[Math10]

For someone who learned the following courses:
Calculus 3 (Multivariable Calculus)
Linear Algebra
Differential Equations
Partial Differential Equations
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What math course should this person study/learn after Partial Differential Equations? This person has a strong interest in Computer Science and math.

 

[homeomorphic]

It's up to them. Math branches out in lots of different directions at that point, and there are many of those directions that have some relation to computer science, which also has lots of different branches. So, they would need to narrow it down a bit more, I think. Logic or combinatorics might be possibilties. Naive set theory and real analysis might be a possibility to get good at proofs. Prob/stat would go well with machine learning stuff, among other things. Some number theory would go with cryptography. Signal processing stuff and Fourier analysis could help with image processing and computer vision.

 

[homeomorphic]

Oh, and numerical analysis is another important one that overlaps a lot with programming.

 

[Math10]

How about Complex Variables? Is CV applied or pure math? Is Numerical Analysis applied or pure math?

 

[homeomorphic]

Numerical analysis is more applied.

Complex variables isn't really pure or applied. It's used in both pure and applied. I'm not sure that there's a huge relevance to computer science there, but it could come up at some point.

 

[Math10]

Also, is Complex Analysis and Complex Variables the same thing? Is Complex Analysis pure or applied math? What's the prerequisite of Complex Variables?

 

[homeomorphic]

Complex analysis and complex variables are the same thing. It's calculus with complex numbers. Prereqs are sometimes just calculus, but sometimes real analysis, if it's a more rigorous version of the course.

 

[Math10]

Is Real Analysis pure or applied math?

 

[homeomorphic]

Real analysis, like complex analysis isn't really pure or applied. It's a bit on the pure side, but you would need to know it for a lot of applied work, too. It would help if you were using heavy probability or doing numerical work, for example. It's not terribly relevant to computer science, but it is a class where you learn how to be good at proofs, so in that sense, it could still be relevant, if you want to be on the math side of computer science.

 

[Math10]

Thank you so much for the info.