What areas of math are relevant to Physics?

Statistics, linear algebra, differential equations for sure

>>8417292
algebraic topology so that you can understand phase transitions in exotic states of matter
you're not a real physicist without it

>>8417292
Linear algebra/functional analysis are kind of "in disguise" in intro QM/Q-chem
Those also use some basic results from group theory to simplify calculations
Relativity requires an acquaintance with manifolds and tensor analysis

>>8417292
Nearly all of them.

>>8417549
This. You will need most of math. Science is just theories based on math.

Linear Algebra, Statistics, linear and non-linear differential equations, partial differential equations, distribution theory, differential geometry, general algebra (for groups & symmetries mostly), symplectic geometry, functional analysis, graph theory, complex analysis, summation theory, combinatorial maps, the maths of signal processing, dynamical systems...

>>8417292

Changing the topic of the thread to this:

What areas of math are not relevant to Physics?

>>8417852
Also probability theory, algorithmics, tensorial algebra, tensorial analysis, Ito Calculus, Large deviation theory, Information theory, calculus of variations...

>>8417857
number theory, Lambda-calculus, Galois Theory, mathematical logic, metamathematics...

>>8417877
why mathematical logic?

>>8417812
Complex variables? Number theory?

>>8417994
....? do you really think complex numbers are not used in physics?

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Category theory

What about stochastic processes? Data mining? Bayesian statistics? Are those useful in any area of Physics?

Pretty much all of it.

>>8418625
Bayesian statistics is quite important to particle physics. Data mining is more compsci than "pure" maths, but analysing and extracting meaningful data sets is still hugely important to any scientist.
Stochastic processes are hugely important to physics, there's whole textbooks written about their applications in the field.

>>8417852
so basically everything?

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>>8417318
Is this book a good start? I'm still new to this level of mathematics

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>>8417292
everything in this book. 10/10 would recommend

Complex analysis, especially Fourier series and the Residue Theorem.