Which areas of mathematics can be formally studied in a cognitive science major? Or: which areas of mathematics can support the study of brain. Some areas that seem relevant would be: mathematical logic, graph theory, linear algebra. Is any element of topology relevant? Please direct to links/sources if possible. Is network science being used in these fields? I am asking this question, as I want to study further in mathematics, and would love it if I could do so while pursuing cognitive science.
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Here's my list of math subjects that support the study of brain (from a computational neuroscientist's perspective):
Brain is quite noisy, you need tools to deal with noise. More applied math than pure math is needed.
I have only seen topology being used a handful of times, and they were not very useful nor impressive. I love set theory and mathematical logic, but sadly never used it nor seen it being used.
In addition, real/complex/functional analyses are also useful, just in general.
I will deviate from the other answers and give more pessimistic response based on my experience as a mathematician and theoretical computer scientist that spends some of his time in a psychology department.
If you want to do mathematics and prove theorems then your are better off in one of the following fields allied to cognitive science:
I would say that the maths that are most useful in cognitive science are the ones that have to do with decision theory. So I would include linear algebra (with its matrixes, and "transition" or changes of state analysis), as well as probability and statistics, with their "expected values" and resulting decision trees. Computational and information analysis, with their "data structures" might also be helpful. The last thing I would include is optimization.