Good Physics Books For a Math PhD Student?

An anonymous reader writes "As a third-year PhD math student, I am currently taking Partial Differential Equations. I'm working hard to understand all the math being thrown at us in that class, and that is okay. The problem is, I have never taken any physics anywhere. Most of the problems in PDEs model some sort of physical situation. It would be nice to be able to have in the back of my mind where this is all coming from. We constantly hear about the heat equation, wave equation, gravitational potential, etc. I'm told I should not worry about what the equations describe and just learn how to work with them, but I would rather not follow that advice. Can anyone recommend physics books for someone in my position? I don't want to just pick up a book for undergrads. Perhaps there are things out there geared towards mathematicians?"

Comments

PDEs now?

[Anonymous Coward]

You are in your third year of a PhD program and are only now studying PDEs? Aren't they more of an undergrad topic, or have schools gotten weaker? :)

p.s. First post!

Re:PDEs now?

[NewbieProgrammerMan]

There can be a world of difference between graduate and undergraduate PDE courses; it's not like everything that's known about PDEs can be taught in a couple of undergraduate semesters. I expect most undergrad PDE courses are geared towards showing you the methods that work for a few classes of linear PDEs; a graduate course might be concerned with the analytical underpinning of those methods, or maybe about numerical and analytic techniques that are useful in solving classes of nonlinear PDEs, etc.

That being said, though, from the way the original question is worded, it sounds like it's the first time this person has seriously encountered PDEs. Not having this happen until the third year of a PnD program does seem a little odd.

p.s. No, you're not.

Re:PDEs now?

[Anonymous Coward]

PDEs are not normally part of a math degree. They do form the central basis to applied math degrees. People in the engineering and physical sciences have a great understanding of applied math, but they have little to no understanding of pure math. If you get a BS in a physical science or a BE from any decent university, you will basically have a minor in applied math (adv. calc, ODEs, PDEs, probability, statistics, nonlinear dynamics, complex analysis, and calculus of variations). But you have not even scratched the surface of pure math. Mathematicians worry primarily about pure math. To teach PDEs would be insulting to them due to its lack of generality. As many physicists and engineers have learned over time, if you have a difficulty in understanding mathematics that applies to your field, the worst person you can go to for help would be a mathematician that hasn't studied applied math. The best person you could go to would be a mathematician who specialized in applied math.

Making the math tangible does help

[EmbeddedJanitor]

If you're a practical sort of person then it really helps to understand what the math means in some sort of physical context. The academic purists be damned!

Some recommendations from another Math Ph.D

[tehgnome]

Most of the previous comments have been far too elementary. I too am a math Ph.D. student and I understand what you are looking for as for while I was working in mathematical physics on loop quantum gravity. Here are some big ones; -classical mechanics has one resounding answer http://www.amazon.com/Mathematical-Classical-Mechanics-Graduate-Mathematics/dp/0387968903/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1226901309&sr=8-1 -for quantum theory and such use http://www.amazon.com/Quantum-Physics-Stephen-Gasiorowicz/dp/0471057002/ref=sr_1_1?ie=UTF8&s=books&qid=1226901473&sr=1-1 -for GR and such http://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440/ref=sr_1_1?ie=UTF8&s=books&qid=1226901528&sr=1-1 I dont know a good thermal book, but I am sure you can come up with one. By the way, there was a very similar ask slashdot during the summer from an astronomer asking for the same thing. good luck and I dont know what you research field is, but in general a great read if you are in algebra is the book on quantum groups by Majid. This has a nice physical perspective on the objects. http://www.amazon.com/Foundations-Quantum-Group-Theory-Shahn/dp/0521648688/ref=sr_1_4?ie=UTF8&s=books&qid=1226901678&sr=1-4

Re:Books

[ReedYoung]

I agree. I picked up the set a few years ago based on Surely You're Joking and I'd recommend them to anybody beginning in physics, especially to Professors of freshman physics, which is usually not so much taught as shoveled. The lectures are taken from his lessons in first year physics, so not too difficult for a math grad student with no previous physics.

incorrect

[Trepidity]

Most areas of science strongly rely on philosophy, and most scientists understand it poorly, usually to the detriment of the technical quality of their work. You can see this all the time, from physicists publishing embarrassingly poor papers on how quantum mechanics "disproves free will" (apparently without even an undergraduate understanding of free will), to AI researchers with little background in philosophy of mind, to statisticians rediscovering the problem of induction every few years. Not to mention the very naive understanding of the "scientific method" that an intro course in philosophy of science might be useful in addressing.

In any case, pure (as opposed to applied) math has not very much to do with the hard sciences. And there is furthermore just not enough time to fit in everything people need. A good understanding of computer science is, for example, required for most technical fields these days as well, and also fairly under-taught; probably I'd put it ahead of physics in importance to most non-majors.

He said "Mathematician"

[refactored]

The trouble with 99% of the physics text out there, is you give them a mathematician and he reads the first two pages.

The mathematician goes off for three weeks filling in all the gaps and "leaps of faith".

He comes back to the book, and reads page three.

Mathematician flings book against the wall, and goes off and finds something more rigorous to read.

As I remember them, the Feynman lecture series were finely crafted instruments of torture for those who delight in rigor. Personally I think he entitled the wrong book "You must be Joking!"