I have some money for some reference books

In summary, the conversation revolves around the speaker's interests in different areas of physics, including optics, general relativity, and group theory. They are looking for book recommendations that are both comprehensive and affordable, and are considering titles such as Born and Wolf Optics, Principles of Quantum Mechanics by Shankar, and Whittaker and Watson's First Course in Analysis. They also discuss the Feynman Lectures and various other books for math and physics. The conversation ends with a discussion about the differences between Spivak and Pugh's books on real analysis.
  • #1
so I am finishing my UG course in physics in about a month or so. however, i had a grant that allowed me to buy books for my course. I have about 130 pounds left.

im probably going to go into the field of optics hence born and wolf is an often quoted choice (perahps the optical coherence text that wolf wrote afterwards also), however I've looked at it, and i dislike the typesetting quite a lot (petty i know but intend to read them) and it is somewhat dated. any other recomendations with the comprehensiveness of born and wolf would be good. but I am also thinking i would like to develop my interests in other areas. like a nice GR text (ideally MTW but that's expensive and impractical, i mean have you seen the size of her!) and definitely a good rigorous maths text with applicability to physics, that doesn't necessarily assume i have the full mathematical foundations of a maths UG. I have done some group theory and would be interested in pursuing that further, but i always felt at the time my lack of familiarity with vector spaces was a weakness (with obvious application to QM).

so here's a shortlist:

1) born and wolf optics (or similiar, perhaps optical coherence by wolf and the other guy)
2)principles of QM by shankar
3)whittaker and watson a first course in analysis (this was recomended by a frined who does maths. he worships it frankly)

other maybes are MTW, courant, or the morse and freschbach.

or maybe scrap the lot and invest in feynmann lectures complete...

any input is welcome. bang for buck is a consideration. if i can get two smaller concise books that are really good rather than one big book with a reputation I am always interested.

to put it in another context, during my UG course me and physics had a falling out, but i starting loving it again about halfway through last year. however passing with a decent grade by that point doesn't necessarily mean you actually learn stuff, and I've played the game quite alot. I want to go back and fill in the many gaps in my knowledge where i glossed over stuff just to pass an exam.
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  • #2
That's a lot of areas you're interested in - group theory, GR, optics, analysis, ...

If you want 'bang for buck', you should buy Dover books. E.g. Elementary Real and Complex Analysis, and Linear Algebra by Shilov are about 11 dollar each.

Whittaker and watson is, just like Born & Wolf, very old, with corresponding typesetting.

For QM, Shankar is a decent choice, as are Griffiths (low level), Sakurai, Ballentine and Cohen+Tannoudji.

I wouldn't invest all in Feynman Lectures. They are nice, but only for 'background reading'. You won't learn the real deal from them.

I'd suggest you specify your question :)
  • #3
yeah i know its pretty broad. my marks somewhat reflect that. try going from a group theory exam to a lasers and holography exam in the space of two days. It reminded me of the time i had my spanish and french oral exams back to back. "bonjour, me llamo bman! et j'ai diez y seis anos"

Im getting born and wolf cos that's almost certainly the field I am most likely to stay in touch with, as i will almost certainly be working with lasers and optics in any of the fields I am interested in. GR and optics might be somewhat exclusive, but then again look atg LIGO!.

Im fairly certain i would get over the typesetting issue, I am also interested in hearing whether people think something like whittaker and watson is appropriate to my wants and needs.

cheers for the feedback. Its appreciated. I want to develop a good breadth of knowledge as i think that can only help. I mean the inventor of FROG rick trebino claims he would never invented it if he hadnt known a fair amount of complex analysis (more than they teach physicists anyways).

Ill go and check out those dover books :)
  • #4
I'd get the Feynman Lectures hardbound, if you do get it. The paperbacks don't hold up to heavy usage (well, I suppose you could replace the paperbacks after your degrees make you rich).

There are so many good GR books now at different levels, but Carrol is probably the best modern reference, while Hartle is the best introduction.

I can't say I used Gradshteyn & Ryzhik's book of mathematical tables heavily enough to justify the price, but when you need it, you really need it. I can't speak to the quality of recent editions.

A good cheapie book of math tables is the Schaum's.
  • #5
So, I am looking for riogorous maths text that gives me the rigour and perspective of a mathematician, but is still appropriate for someone with physics background. possibly becuase it will be applicable. Though i am interested in maths for its own sake.

I looked at the real analysis book by pugh. looked really good. I also see Spivak mentioned a whole load on this forum, and qualitatively the two seemed to overlap a fair bit.

Im leaning towards spivak a bit more. as I am not sure i could jump directly to something like pugh, and also, i can see spivak being useful for physics applications every now and then and would prepare me for more advanced texts.

however I am also thinking that's spivak might be a bit redundant and would simply be going over stuff i already know (in terms of methods that is) and making it more rigorous. whilst i do want to consolidate, i do like methods. I think they are pretty neato.

Spivak vs. Pugh.


  • #6
Pugh comes after a book like Spivak. Spivak is analysis on the real line, i.e. rigorous calculus of the reals. Usually universities cover Spivak in the first year. Pugh covers real anlysis from the basics up to R^n and a bit of Lebesgue theory and is done by the senior undergrad. Pugh requires a bit of mathematical maturity, more than Spivak requires. Pugh's book is used to teach his honours real analysis class. The titles say it: Spivak is calculus, Pugh is real analysis. Logically one need not read Spivak before Pugh, but it would help. Ofcourse it's unnecessary if you're mature enough to handle Pugh straight away. Maybe working through the first few chapters of Spivak would be best (get the book from the library), then go on to Pugh. If you find Spivak too easy then skip it.

Btw, Pugh is one of my fav. books, way better than other real analysis books at a similar level *coff*Rudin*coff*.

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