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Modern Analysis(including Measure theory and Functional Analysis)

Harmonic Analysis(Fourier Analysis would suffice)

Abstract Algebra(including Galois Theory, reviewing Linear Algebra in algebraic perspective is one of the most important thing in Deep Learning)

General Topology

Probability theory in Graduate course

Statistical Inference

Bayesian Statistics

Numerical Optimization Techniques

Algorithms

Optional(Some kinda things prevalent in research society)

Stochastic process(GP and Bayesian approach in Deep Learning)

Differential Geometry and Manifolds