Rigorousness of mathematics in physics classes

  • #26
mathwonk
Science Advisor
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har har! thats great. where in this case isomorphic means "has same meaning".
 
  • #27
Sojouner, I would suggest grabbing a few books on Modern Algebra, Linear Algebra, Real/Complex Analysis, Group Theory, Lie Algebras and some other math texts (perhaps a text on mathematical logic and proofs if you are more interested in rigor), if you are curious about quantum theory.

There is a lot of mathematics and physics involved in the construction of quantum models and theories, so one should be prepared to spend a lot of time studying mathematics if you plan on getting a doctorate in high energy or quantum theory (or something similar). If you are having problems teaching the mathematics to yourself, then perhaps you need to start with something easier.

You can start with modern algebra, which is self-contained and very elegant. It will introduce you to a lot of the concepts that mathwonk was discussing (such as isomorphism's, mappings, fields, rings, groups, surjectivity, injectivity, vector spaces, etc. and expose you to famous theorems that are often used in physics theories) which is a good springboard into more advanced modern abstract algebra, and other very beautiful fields of abstract mathematics. I would suggest trying to over-load yourself with extra math classes (maybe 18 credits if you can handle it), if you really want exposure to mathematical rigor.

Remember, they don't hand PhD's out, you have to spend a lot of work and effort into earning one. It's tough my friend but it takes some passion and dedication.

If you structure a schedule to study each day, you can still have a social life. I live with my girlfriend and we spend plenty of time together. I work part-time 25 hours a week and spend about 5-6 hours per day studying. I do a lot of partying and have absolutely no problems. I have to work hard to understand the math and physics, so I have to plan a lot of time for myself.

I am sure you are probably more intelligent than I, and probably wouldn't need to allocate as much time to studying. Anyways, homie, good luck.
 
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  • #28
Pyrrhus
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Well, some of us love rigor in math, doesn't matter where it is used. I don't know why, but i prefer it along an intuitive explanation. Although i am a engineer, and more importantly a Civil Engineer, i am more focused on procedures rather than much theory. This doesn't mean that i relegate theory, the problem is most of my work is pretty much documented on Building Codes, so i just need to satisfy those codes (on a simpler outlook, actually is much more), so it tends to become more monotone. Of course, once in a while i get my hands on projects that challenge my grasp of the theory. Anyway, i just like to do things right (everything clear, no doubts), and that's what i equate rigor too.
 

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