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I asked this question on the Physics site, but it got closed, so I'll try here.

Basically, I was wondering what are the main differences between the maths you learn in a mathematics degree and the maths you learn in a physics degree? Of course, the maths in a physics degree is more applied, but to what extent?

For example, I understand that some very advanced mathematics is used in high-level physics, but in general do you still learn to do things like proof and number theory or is it just the applications of maths for physics?

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    $\begingroup$ You probably don't do much number theory in physics. Also physicists learn to do math a bit fast and loose, because the ultimate proof for them is in experimental validation. While in pure math there is more emphasis on rigor. $\endgroup$ Commented May 18, 2015 at 15:31
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    $\begingroup$ I concur with Gregory. I do like to be loose and fast with mathematics, as I don't work with anything hairy as a pure mathematician, but instead work with distilled gems of mathematics. $\endgroup$
    – Chinny84
    Commented May 18, 2015 at 15:34
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    $\begingroup$ Apart from what has been said in other comments, regarding curricula this may depend strongly on the country you are in and the place you visit. Later on it may also depend on your specialization, so if you do theoretical quantum physics you may need different kinds of math than if you go for experimental physics. $\endgroup$
    – Thomas
    Commented May 18, 2015 at 15:37
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    $\begingroup$ I remember in the final year of my degree my lecturer for QFT stopped at one point and addressed the physics students and the maths students seperately. I believe it was on the topic of renormalisation and just before he started he said to the physics students "you wont be bothered about why this works, nor should you be, because it works", at which point he turned to the 3 maths students in the class and said, "you probably wont like what we're about to do and I will explain after the lecture should you wish". I will admit as I grew more and more applied I did lose a little desire for rigour. $\endgroup$
    – Rammus
    Commented May 18, 2015 at 15:48
  • $\begingroup$ It may resemble the relation between the physics courses in an physics department and the physics courses in an engineering department, say. $\endgroup$
    – Yes
    Commented May 18, 2015 at 15:48

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It is true there is a lot of high level math in physics, some of which is done by physicists and some by mathematicians. For example the professor I am working with works with (and writes papers with) physicists very often, but the work he does is really math because it comes from a field called algebraic geometry which depends highly on pure math fields like commutative algebra and topology.

What you major in ultimately depends what you are most interested in. I am writing this from a pure math perspective, and I switched into math (from physics) because I liked the abstraction and the rigor with which everything is done. In a pure math degree almost everything you do is proofs. This is where you will take courses like number theory (or topology, group theory, analysis etc).

That being said my friends who remained in physics say that higher level physics has a lot more proofs than in the first couple of years, but they are not as abstract as the sort of proofs you would find in a mathematics course. The math courses you take with a physics degree are mostly calculus, linear algebra, differential equations. From what my friends say often the more advanced math in a physics degree is learned in physics courses (so its by nature an application) with just the introduction to the subjects in the math courses. In my university there is also an option to take a mathematical physics degree which would also allow you to take some analysis, which is more like the courses one would take in a math degree.

I unfortunately cannot say much for the kind of math you would learn in an applied math degree. The math courses you would take are similar to those you would take in a physics degree; however you would take higher level courses in these areas. From what I gather, you would learn much more of the theory behind these subject areas, which you don't necessarily get to do in a physics degree. I leave it to an applied mathematician to say more.

Despite my long answer, all in all I think the biggest differences between the math learned in math and physics, is that the math in math is very abstract, proofy, and often taught without any non-math applications. The math in physics is done always with a sense of application, but the mathematical rigor is not always taught. I would recommend taking some courses in both areas to see what interests you more.

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  • $\begingroup$ Thank you, this is very helpful $\endgroup$ Commented May 18, 2015 at 16:42

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