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

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Key branches of mathematics essential for various physics disciplines include differential geometry, which is crucial for classical, quantum, and relativistic physics. Fundamental topics like calculus, differential equations, and integral equations are also vital. While there isn't a definitive list of required mathematical knowledge, physics students should be adaptable and ready to learn specific areas as needed. Important mathematical concepts highlighted include basic analysis, group theory, linear algebra, ordinary differential equations (ODE), partial differential equations (PDE), complex analysis, and functional analysis, all of which contribute to a comprehensive understanding 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.
 


Analysis
 


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.
 

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