I do condensed matter physics modeling in my phd and I was struck up learning quite an amount of physics. But while having done lot of physics courses, I see that if I learn pure math I would understand lot of things better and also probably my modeling skills also might get better. A math prof asked me to do all courses from basic analysis to differential geometry. But that would take time as I see I am taking time studying Walter Rudin's Principles of mathematical analysis. So I am little confused whether am going the right way. Any suggestions?
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asked Mar 21, 2013 at 18:50
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1$\begingroup$ Possible duplicates: physics.stackexchange.com/q/234/2451 and links therein. Crossposted from math.stackexchange.com/q/337164/11127 $\endgroup$– Qmechanic ♦Commented Mar 21, 2013 at 19:14
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3$\begingroup$ @excited Just to be sure I'm understanding: It was suggested that during your PhD you do the bulk of an undergraduate degree in a different topic?? Yes you would no doubt gain skills, but at the expense of your career! Surely I'm misunderstanding the situation... $\endgroup$– user10851Commented Mar 21, 2013 at 20:53
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1$\begingroup$ Fully agree with Chris White. You're working towards a degree and a career in (it appears) condensed matter. That means that you should learn precisely the topics which will make you write better papers and become a better condensed matter researcher. If you feel that you are out of your depth in a specific problem, go and study that subject, but your current plan seems unproductive. (The same holds for particle physicists, string theorists, ...) $\endgroup$– VibertCommented Mar 21, 2013 at 21:01
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$\begingroup$ In your work start with the problem at hand and learn what you need to solve it. In your spare time learn what you like. Anything that doesn't fall into either of those categories can wait till sabbatical. :) $\endgroup$– MichaelCommented Mar 22, 2013 at 9:48
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1$\begingroup$ I don't think a physicist should ever stop learning mathematics. As your Professor said Analysis, Complex numbers, Differential geometry, group theory and so on will be very useful. Saying that it is not necessary that everything must be done immediately, and devoting 1-2 years just to learn mathematics In my opinion is not a good idea. As you progress as a researcher you will find time and discover the need to learn these topics. $\endgroup$– PrathyushCommented Mar 31, 2013 at 15:37
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2 Answers
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Without knowing more about your research interests it is difficult to offer an informed opinion. That said, here is my take on your question:
Before I did my Ph.D. work (in condensed matter physics) one of my undergraduate majors was pure mathematics. I took a year of analysis and in particular studied some of the same texts you are. I don't regret this. It was worthwhile.
That said, I suspect studying e.g. analysis will offer you little insight into your work in physics. It is certainly not something a condensed matter physicist is expected to know. It also seems unlikely to improve your "modeling skills", although it's not entirely clear what you mean by that.
Doing all the courses from "basic analysis to differential geometry" is a huge undertaking. In my experience, studying outside your field is valuable because drawing from a different set of influences (as compared to your peers) tends to foster original work. But that was not your stated motivation, and if it is, there is no reason to limit yourself to mathematics.
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I totally agree with previous comments . But if the new study makes your research more improved you should learn it and understand it completely. The book you are telling will take at-least two month in my opinion to go through and understand its concept completely because i took 3-4 month to go through it.
