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Is Theory of Algorithms Math or CS? Or Both?

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There are several schools of thought on this subject. Scott Aaronson is a computer scientist and blogger who has written a fair amount about it.

For me, though, the answer is obvious: the topics you list are unambiguously branches of mathematics.

As an undergraduate math major, I think theory of algorithms is a fine elective; also look for classes with "computation theory" or "theory of computation" in the name.
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>Would topics such as: Strings, formal languages, finite state machines, Turing machines, primitive recursive and recursive functions, and recursive unsolvability, be considered as mathematics or just exclusively Computer Science?

There is a substantial intersection between the set of things we label *mathematics* and the set of things we call *computer science*. All the topics you mention fall very firmly within that intersection.

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>Is it worth studying the theory of algorithms as an undergrad math major?

Are you interested in the theory of algorithms? If you are, then it's definitely worth it.

At a math department I worked at 10 years ago, I used to teach a class which covered some of the topics you mentioned above. I can tell you it was a fun class to teach and the students were generally interested in the subject.

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