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Set theory is close to useless in physics. So only take it if you're particularly interested in it (it

Abstract algebra comes up occasionally in physics. In particular, groups and representations are important. The problem is however that abstract algebra is more about finite groups and a first course doesn't deal very much with the groups which are actually used in physics. In that sense, abstract algebra will only be useful to you to understand the basic concepts and definitions of groups. So while more useful than set theory, I don't consider it very useful on its own.

Again, this answer supposes you want to choose a math class based on how useful it is to physics. If you're interested also in the intrinsic mathematical beauty, then that changes a lot.

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I think something like "Advanced differential equations" or "numerical analysis" might be more suitable. Numerical analysis will be useful because it will (likely) ask you to program stuff in matlab (or similar) and this is always a very useful tool in research.

Differential equations show up everywhere in physics, so it's clear why this is important. Even if the course is about existence and uniqueness theorems, I think it's more applicable that set theory or abstract algebra.

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Maybe you should ask the teach what "com an-bound val" is, because I don't have a clue.

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Awesome, will do. Thanks a ton; really helped me out a lot!

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Anyway, "advanced differential equations" and "numerical analysis" sound most directly applicable, but as always it is a matter of the syllabi.

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Ah! Complex Analysis, of course!

Anyway, "advanced differential equations" and "numerical analysis" sound most directly applicable, but as always it is a matter of the syllabi.

Complex analysis is also quite useful in physics. Being able to calculate integrals using contours and residues comes up a lot. However, this is actually more often taught in "math methods" courses, which I think are better for physicists.

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Hello, I am a physics student studying set theory in his spare time, set theory is completely useless in the physics sense? What about the cartesian product of two sets and their respective ordered pairs that are mapped into Real/2-dimensional Euclidian space? Particularly if the two elements of the ordered pairs are scalars or a 2-dimensional vectors? Surely this applies to Classical mechanics when working with basic trajectories? Generally this can be done for 3-vectors or 4 vectors, if you do the cartestian product of three or four sets.

Set theory is close to useless in physics. So only take it if you're particularly interested in it (itisa rather beautiful theory!)

Abstract algebra comes up occasionally in physics. In particular, groups and representations are important. The problem is however that abstract algebra is more about finite groups and a first course doesn't deal very much with the groups which are actually used in physics. In that sense, abstract algebra will only be useful to you to understand the basic concepts and definitions of groups. So while more useful than set theory, I don't consider it very useful on its own.

Again, this answer supposes you want to choose a math class based on how useful it is to physics. If you're interested also in the intrinsic mathematical beauty, then that changes a lot.

Real analysis can then be done on this 3D Real/Euclidian space, which is where calculus comes from. Abstract algebra can be used to describe geometry, which when combined with calculus allows differential geometry, which is essential to Relativity. It also describes Hilbert space for QM.

The reason I am studying fundamental maths is so that I can understand physics beyond the normal level, and I feel this would be impossible without understand these areas of maths.

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You have it backwards. Real analysis comes from calculus, historically, and a lot of physicists and engineers get by pretty well without it.Real analysis can then be done on this 3D Real/Euclidian space, which is where calculus comes from.

There are abstract algebraic ways to describe geometry, but it doesn't "allow" differential geometry. There's a good portion of differential geometry that's just an extension of multi-variable calculus. You need abstract algebra if you want to understand connections on principal bundles or Cartan geometry, but those aren't really necessary to study GR. Hilbert spaces are functional analysis, not abstract algebra. You could view the vector space axioms as abstract algebra, but it's just one definition from abstract algebra, and at any rate, the defining completeness property of Hilbert spaces is a very analytic thing.Abstract algebra can be used to describe geometry, which when combined with calculus allows differential geometry, which is essential to Relativity. It also describes Hilbert space for QM.

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