Mathematical Physics vs Applied Mathematics?

There's a lot of crossover between the two, and it's not always clear where one ends and the other begins.f
  • #1
(Sorry if these are the wrong forums)
All right, so, I know the difference between pure and applied mathematics as well as mathematical vs theoretical physics. But, I don't quite get the difference between mathematical physics and applied mathematics. Aren't they both working on mathematical methods? Is the former just a field of the latter? How does this work?
  • #2
Applied mathematics is typically defined as a branch of mathematics that deals with mathematical methods that are typically used in science, engineering, business, computer science, or industry. Historically, applied mathematics consisted principally of applied analysis (particularly differential equations and dynamical systems), approximation theory, and applied probability. More recently, areas of study like optimization, graph theory, information theory, computational complexity, and analysis of algorithms were often included within applied mathematics.

Typically, mathematical physics is often considered as a branch or subfield within applied mathematics, and depending on which department you're dealing with, statistics has at times been included under it as well.
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  • #3
You could call mathematical physics a subset of applied math, but there are big parts of mathematical physics that have strong ties to what people would normally call "pure math", like topology. That sort of thing is what I studied as a topology student, although I my adviser was more on the topology side and more superficially into mathematical physics, so I was dragged into being more of a topology student, even though I wanted to be more of a mathematical physicist.

Mathematical physics is a very vague term, so it's best not to take it too seriously. I remember when was thinking about applying to UCLA for grad school, they said on their website that they consider mathematical physics as a branch of pure math inspired by problems in physics.

For that matter, the words "pure" and "applied" are idealizations.

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