Which Mathematical Physics Text Should I Choose?

[mathsciguy]

I found myself having a hard time choosing what mathematical physics text should I stick with. I'd like to think of myself as mathematically inclined, and I would really prefer a mathematical physics book that emphasizes 'the maths' and the proofs and not just the methods while maintaining its significance to physics. I'm thinking of sticking with this one:

https://www.amazon.com/dp/0521664020/?tag=pfamazon01-20

I have heard that this is a fairly good book about mathematical physics that seems to discuss the maths in a good depth. I am worried though, that I may be learning outdated stuff since the book is also fairly old.

This, or should I stick with the standard(?) Arfken and Weber book?

 

[rhombusjr]

If you're looking for a book which emphasizes the 'maths', don't go with Weber & Arfken. I don't recall there being any proofs in Weber & Arfken. Their book is general is pretty poor. Don't worry about using an old book, math at this level doesn't get outdated. Most of these techniques are from the 18th and 19th centuries. It's also not that much older than standard physics graduate texts. Looking through the table of contents, I see things that are still used as standard methods in physics. AFAIK, everyone still solves Laplace's Equation in spherical coordinates with Legendre Polynomials.

I think Byron & Fuller is more rigorous. Boas is supposed to be good. Generally speaking, you're either going to find a book that contains applications, or you'll find a book that has proofs. Most people who are concerned with one generally are not concerned with the other.

 

[jasonRF]

I must admit that while I have certainly heard of the book you refer to and have seen it referenced many times, I have never really attempted to read it.

Another, more modern book on mathematical physics that is more mathematical than something like Arfken is the book by Hassani,

https://www.amazon.com/dp/0387985794/?tag=pfamazon01-20

If it is in your library you may want to take a look at it.

jason

 

[mathsciguy]

The book I referenced was by Jeffreys & Jeffreys' Methods of Mathematical Physics. The book seems good, but I think it's more of a supplemental text than a main one that I could use for a course. I found myself progressing really slow; though the book was very interesting.

@rhombusjr: I've skimmed Arken's and I didn't really like it, maybe it's that bad, or just don't like its style.

I'm willing to take a book that's more geared towards proofs than applications.

I forgot to say that I'm still an undergrad, Byron and Fuller's textbook seems to be a graduate level textbook.

@jasonRF: Thanks, I'd take a look at it.

 

[Alesak]

I have Geroch on my bookshelf. I haven't read it yet, but if you are algebraicaly inclined you will find it interesting.

 

[MathematicalPhysicist]

The classical textbooks are:

Hilbert and Courant

Morse and Feshbach

Not an easy ride, that's for sure.

 

[espen180]

If you are not afraid of taking a detour, I suggest reading a book on manifolds (say, Madsen & Tornehave, or Loring W Tu),then reading "Introduction to mechanics and Symmetry" by Mardsen & Ratiu.

I think you can also read "Classical Mechanics" by Vladimir Arnold without any previous exposure to manifolds.

I think this will give you an introduction to modern mathematical physics.

 

[mathsciguy]

That one by Hassani seems good, I again, found myself progressing quite slowly, but it was nevertheless satisfying so far. I wish it could be a good stepping stone for me to get used to more rigorous mathematics. I might stick with this one.

@MathematicalPhysicist: Classical texts seems interesting, but since I'm a bit pressed for time, I think I'd prefer reading the more recent ones which give *I think* a more condensed yet general introduction to the subject. I am usually under the presumption that classical texts are quite specialized to be an introductory textbook.

@espen180: Thanks, I'll look at it.

 

[jasonRF]

I again, found myself progressing quite slowly, but it was nevertheless satisfying so far

Any book of proof-driven mathematics will be slow going. Read this preface for Axler's "Linear algebra done right,"

http://linear.axler.net/LADRPrefaceStudent.html

One page an hour is the right order of magnitude.

Enjoy,

jason

 

[dextercioby]

[...]I'm thinking of sticking with this one:

https://www.amazon.com/dp/0521664020/?tag=pfamazon01-20 [...]

Good choice. There are altogether 4 old books (gems) on this subject which I particularly cherrish:

Whittaker & Watson,
Courant & Hilbert
Jeffrey & Jeffrey
Morse & Feshbach.

The new books (Arfken & Webber, Boas, Hassani, etc.) are merely pale copies of them.

 

[radium]

For the math methods course I am taking this semester (a graduate course) we have three reference texts: Mathematics for Physics (Stone and Goldbart), Mathematical Methods for Physicists (Arfken and Weber), and Mathematical Methods of Physics (Mathews). I also like Mathematical Methods for Physics and Engineering (Riley), Mathematics for Physicists (Dennery), and A First Course in Partial Differential Equations (Weinberger).

 

[Meir Achuz]

https://www.amazon.com/dp/0486691934/?tag=pfamazon01-20

 

[mathsciguy]

I might be forced to use the Arfken and Weber text, what might be the best supplement book with it? I've read a lot of bad reviews for it.

I'm thinking of using Boas' but vector analysis starts at the latter part of the book and makes references from the earlier chapters, I might not be able to 'back-read' all of that.

 

[WannabeNewton]

If you want a mathematically rigorous book then don't use Boas.

 

[Meir Achuz]

Don't use Boas. You would do better with an earlier edition of Arfken, the earliest you can get. His first edition was a gem.

 

[mathsciguy]

@WannabeNewton: There's this math methods for physicists course that I'm required to take, I might put off the more 'mathematically rigorous' texts for now.

@Meir Achuz: I'd try to look for it; I'm finding it weird that the first edition was better than the latest, were the topics discussed with more depth? I think the 5th edition's a bit lacking.

 

[PKDfan]

I've never read it, but Michael Spivak recently wrote a book called "Physics for Mathematicians". I'm not sure if it's what your looking for, but it might be worth checking out.