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- #2

eumyang

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With regards to undergraduate math courses (and beyond) there is no set, linear order. Instead, there are "branches" where different courses fall. The three main branches are:List as many math subjects as possible. But they need to be in order.

1) Analysis: Real analysis, complex analysis, ordinary diff. eq., partial diff. eq., harmonic analysis, functional analysis, ...

2) Algebra: abstract algebra, number theory, linear algebra, commutative rings/algebras, associative rings/algebras, ...

3) Geometry/topology: geometry, topology, differential geometry, algebraic topology, manifolds, ...

One could argue that logic & set theory is a fourth branch. Applied mathematics (numerical analysis, probability/statistics, operations research, game theory, ...) could be a fifth branch.

- #3

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From the courses you listed, it sounds as though you might be headed in the applied direction (are you an engineer?). You should consider looking into calculus of variations as it may come in handy.

- #4

Integral

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That isn't he order I did those courses.

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For physicists, usually group theory and differential geometry come next.

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