Branches in math do you really need for all types of physics

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What branches in math do you really need for all types of physics (classical, quantum, and relativistic)?
 
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Differential Geometry and its associated topics (including the calculus/differential/integral equations) are usually present in all of those areas.
 


I don't think there is a solid answer to that question, which is why a physics student needs to be able to pick up what they need, when they need it. When in Rome...
 


Basic analysis. Group theory. Linear algebra. ODE. PDE. Differential Geometry. Complex analysis. Functional analysis... the list goes on and on.