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It seems that a persons ability to understand physics at a high level is limited primarily by their understanding of math.

It also seems to be more efficient to learn the underlying math for a physics topic before trying to understand how the math is used to model the physical system.

So does it follow that one might do better by focusing primarily on learning math during an undergraduate degree?

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short answer: yes. Now the real question is "how much math?" –  Djaian Apr 9 '13 at 8:50
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I suggest that you start studying math, and when you know enough math to feel confident of your knowledge you can switch to physics (the joke is, that the more you know the less you are confident... so you will never learn physics! evil laugh here) –  Asaf Karagila Apr 9 '13 at 9:07
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There are couple of mathematical physicists here who might be more helpful. My personnel opinion is that to do string theories and so forth, you definitely need strong math. But you don't have to major in math to learn math needed to understand advanced physics. even if you pick 1 or two extra math courses every semester, that will suffice. You can also do other way around. Major in math and do 1/2 physics courses every semester. There are also 1/2 core physics courses every semester except some extra courses. –  user45099 Apr 9 '13 at 9:12
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In my experience, learning something "because I might need it later" just leads to not really understanding and frustration due to missing motivation. Ideal is to learn both hand in hand, so you see where, how and why the math is used in your principal interest. Hard to do with the typical courses... –  vonbrand Apr 9 '13 at 10:06
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I'd say it's better to study mathematics. Period. And it's also nice to know some physics, ok. –  DonAntonio Apr 9 '13 at 10:56

2 Answers 2

If your goal is to learn physics at a high level, postponing serious study until after a math degree can cause problems because the ways of thinking are different and in both subjects can take years to metabolize. There is room in each field for people first trained in the other, but I think the way may be more open for doing mathematics after physics than the other way around. If you want to do theoretical or highly mathematical physics as many mathematicians do, the physics graduate school treadmill moves much faster in those areas than in math in terms of requirements to produce papers and complete very specific classwork and exams, where you are ranked and evaluated compared to other students doing the same course of study. Advantages you will have from more math will probably be outweighed by not having sufficient background and intuition in physics or time to fully absorb it under pressure.

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TLDR..?​​​​​​​​​​​ –  Pacerier Dec 1 '13 at 2:50
    
WDYM..? $\quad$ –  zyx Dec 6 '13 at 21:14
    
a summary for your WOT? –  Pacerier Dec 10 '13 at 10:57
    
"No, and here are the reasons : ..." is the summary. But that can only be a conclusion for the reader to make after absorbing the information in the WOT. There is no universal advice possible here. –  zyx Dec 10 '13 at 18:01

I don't think there is a definite answer to that question. It depends on a lot of factors, most important of which is the way you learn best.

I'm currently doing my physics PhD and I have classmates who learn the underlying math best by learning it through the physics. That's fine.

Before starting my physics PhD, I had only one math class at the university level: a Calculus course. I decided to read Mary Boas' book Mathematical Methods in the Physical Sciences from the front to back. I found the perfect mix of mathematical proofs and applied examples. I don't read too many pure math texts since they can sometimes go through very long, tedious proofs that don't matter to my research.

It also depends on what field you'll be studying. There's a field called "Mathematical Physics" in which I suppose that a deep and wide knowledge of math would be helpful. Perhaps in that case, it would be helpful to study both at the same time, such as double-majoring in college.

In terms of being more efficient to study math first then phsyics, I would disagree with that. Studying them at the same time allows you to better judge what's important for you to know and focus on.

But of course, there are certain foundational mathematical fields which are important and are certainly efficient to learn: undergraduate courses in Linear Algebra, Differential Equations, Calculus, etc. I personally found that I benefited from reading through Rudin's Real Analysis book, but I did only after starting my research.

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