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Here's my list of math subjects that support the study of brain (from a computational neuroscientist's perspective):

Linear algebra to understand high dimensions, to compute things quickly, foundation for other math

Calculus basics for everything continuous valued

Statistics to analyze any data, you need stats! basis for modeling, regression, clustering, classification, and all

Differential equations (basis for dynamical system)

(basis for dynamical system) Dynamical system intuition for neural dynamics (deterministic approximation) modeling single neuron, synapse, small network

Statistical physics modeling large scale noisy neural dynamics

Information theory quantify how much "information" is coded in neural signal

Numerical computation your data and algorithm needs to be implemented in a computer

Convex optimization your statistics/model requires optimization

Probability theory (basis for stochastic process and statistics)

(basis for stochastic process and statistics) Stochastic process model of neural signals, decision process (diffusion), basis for advanced statistics point process theory is useful for dealing with neural spike trains

Time series analysis (your data is a time series!)

(your data is a time series!) Signal detection theory psychophysics is often designed to be a detection task



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.