Math Physics: What Is It & Is It Better?

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SUMMARY

Mathematical physics is a specialized field that combines rigorous mathematical methods with physical problems, focusing on analytical solutions to complex issues, such as partial differential equations (PDEs) and integral transforms. It differs from theoretical physics, which emphasizes empirical testing and collaboration with experimental physicists. Notable figures in this field, such as John Baez, exemplify the role of mathematical physicists as mathematicians tackling physics-related challenges. Career paths in mathematical physics extend beyond academia, potentially including roles in research and development within industries that require advanced problem-solving skills.

PREREQUISITES
  • Understanding of partial differential equations (PDEs)
  • Familiarity with integral transforms
  • Basic knowledge of quantum mechanics
  • Experience with mathematical proofs and problem-solving techniques
NEXT STEPS
  • Research advanced topics in mathematical physics, such as string theory
  • Explore career opportunities in research and development for mathematical physicists
  • Learn about the differences between theoretical physics and mathematical physics
  • Study applications of mathematical methods in solving physical problems
USEFUL FOR

Students and professionals in mathematics and physics, particularly those considering a career in mathematical physics or seeking to understand the interplay between these disciplines.

temaire
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What precisely is mathematical physics? Also, is it a better field to go into than just math or just physics?

Sorry if I'am being innaccurate with the "just math or just physics" but I think you guys know what I mean.
 
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I took 2 quarters of mathematical physics. In it, we learned various mathematical methods of solving physics problems. So for example, instead of just saying "Let the computer solve it", we actually did it by hand. It wasn't anything ugly, since it was meant to be methods that actually make it easier. So we spent a lot of time on solving harmonic oscillators in various ways.

I can't say for sure what a career in Math. Phys. would be like, though. Possibly researching ways to analytically solve problems that are "too complicated" to solve at the moment analytically.
 
Poop-Loops said:
I can't say for sure what a career in Math. Phys. would be like, though. Possibly researching ways to analytically solve problems that are "too complicated" to solve at the moment analytically.

Would this be what a prof. of Math. Phys. would be doing? Also, is becoming a prof. the only notible career path you can take with a degree in Math. Phys.?
 
i don't know how to differentiate it from "Theoretical Physics". both seem pretty hard-core. John Baez calls himself a Mathematical Physicist.
 
Traditonally, it is about solving mathematical problems that arise in physics (and are too difficult to be left to the physicist :-) ) - like finding a solution to some PDE, making integral transforms, minimizing some functional,...

But it can also mean mathematically rigorous study of physical models, which seems pretty interesting to me, but I'm afraid that not much can be gained out of that - or am I wrong?
 
temaire said:
What precisely is mathematical physics? Also, is it a better field to go into than just math or just physics?

Sorry if I'am being innaccurate with the "just math or just physics" but I think you guys know what I mean.

The way my quantum professor explained it to me: theoretical physicists are physicists, mathematical physicists are mathematicians. My understanding is that mathematical physics is a discipline within math departments. Mathematical physicists would probably be interested in proofs, and in solving problems in mathematics. Theoretical physicists, however, appear to be more interested in getting results that can be empirically tested, and they work fairly closely with experimental physicists. My advisor, for example, is an experimental physicist, but we have a theoretical professor in our group as well, and he's familiar with many of the details of our experiment.

Well, hope this helps.
 
With a degree in Math. Phys. is the only notible career path becoming a prof., or are there other worth while career paths with this degree, in terms of pay.
 
I guess if you have some familiarity with the stuff advanced physicists do, a good analogy is that mathematical physicists are more like string theorists. Theoretical physicists are like model builders.
 

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