Textbook recommendations, for a variety of topics.

[TheShrike]

Hello,

There are quite a few subjects in pure mathematics and physics that I'm quite interested in, and I would appreciate any help with the search for textbooks on them. So far I have Goldstein's 'Classical Mechanics' and Humphrey's 'A Course in Group Theory'.

Some of these I list below:

I took Tensor Field Theory this semester just passed, and while we covered some things on tensors, then some special relativity and electromagnetism, we ran out of time for general relativity. I would like to find a textbook that covers general relativity, but perhaps also some of these other applications of tensors. I'm tempted to ask for a book that covers purely mathematical aspects of tensors, but I strongly suspect such a book would be very dry.

In my second year I took a course on Fluid Mechanics - I would like to know more about this, it was quite an interesting subject.

I also would like to know more about Electromagnetism - I've seen the name Griffiths thrown about a lot, but I've also come across quite negative comments about his books, so I'm not sure here.

In the realms of pure mathematics, I eventually want to be able to look at things like metric spaces and measure theory, and probably some topology or functional analysis as well. While these topics probably appear in some form or other in physics, I've found that I understand them much better when I've had some exposure to a pure maths treatment. This occurred to me in my first year, when I took Linear Algebra & Analysis. I really couldn't grasp what vectors were or how calculus was allowed to divide by zero before seeing how dimensions occur in vector spaces and how the concept of a limit works.

Some other topics I hope to read about some day are Set Theory & Logic, Category Theory, Complex Analysis and an axiomatic treatment of Statistics (although this probably comes under measure theory (I recently discovered Kolmolgorov's axioms on Wikipedia - fascinating!)).

I know that's a long list of things, but I do expect to spend many years on this. I always find there are more things to be interested in than I have time for (always wanted to find out more about psychology, for example). Anyway, I thank and congratulate anyone who manages to get though all this in advance. :)

(Some might note I've left out quantum mechanics - my MSci year (next year) will have quite a lot of quantum mechanics in it, so I'm not too worried that I'll miss out on it.)

 

[Jorriss]

I've heard very little negative about Griffiths E&M book. There is more of a divide about his quantum text, which I personally am not a huge fan of, but his E&M book is great.

For Fluid Mechanics, there is Landau & Lifgarbagez. I don't know a lot of current fluid mechanics so I don't know if this book is out of date or what but it's really good at explaining what it goes over.

In terms of Measure theory/metric spaces, etc, etc try Pugh, Real Mathematical Analysis.

Can't comment on the rest.

 

[intwo]

An excellent fluid dynamics textbook is Elementary Fluid Dynamics by Acheson. Some schools use An Introduction to Fluid Dynamics by Batchelor, but I have only skimmed through it at the library. It's the next book on my "to-purchase" list.

Griffith's textbooks are very conversational and I did not find them very enlightening from a pure mathematics perspective. You might want to try Electromagnetic Fields by Wangsness or just jump into the graduate-level Classical Electrodynamics by Jackson.

I know that you already listed a classical mechanics textbook, but I really enjoyed Classical Mechanics by Gregory. It takes on Newtonian Mechanics from a definition-theorem-proof perspective.

For set theory, try Introduction to Set Theory by Hrbacek and Jech and for Logic, try A Mathematical Introduction to Logic by Enderton.

 

[kloptok]

There's also the book by Kolmogorov on Functional Analysis and metric spaces, here is an amazon link: Amazon link. There are two volumes where the second is more devoted to metric spaces, Hilbert spaces and such. I have only glimpsed through it and read the first few chapters with very basic stuff, but many seem to like it and I found it enjoyable.

Personally I am very fond of Griffiths style, but that is a question of personal taste, he has a quite conversational style. Regarding GR books, there are a lot of them out there and it seems like a good idea to concentrate on a more modern treatment as many of the older books are outdated. This is a great link for lots of tips regarding GR, both the related mathematics and more physics: GR books

 

[Daverz]

For GR, you may be ready for Sean Carroll's book. Ohanian's approach may also tie in nicely with your tensor field course.

My usual recommendation for E&M is Schwartz, Principles of Electrodynamics.

 

[TheShrike]

Thanks for the info people.

I think you're right Jorriss, it was likely Griffith's QM book that I'd heard reports about. I'm tempted by the Jackson text, and have been before, but the phrase 'graduate level' scares me a little. Although I think Goldstein is supposed to be a graduate level text, so perhaps I shouldn't be so intimidated.

 

[Jorriss]

I think you're right Jorriss, it was likely Griffith's QM book that I'd heard reports about. I'm tempted by the Jackson text, and have been before, but the phrase 'graduate level' scares me a little. Although I think Goldstein is supposed to be a graduate level text, so perhaps I shouldn't be so intimidated.

Graduate level conveys a large range. I have Goldstein and Jackson and Jackson is a lot more difficult. Personally, I use Goldstein freely as necessary as a reference but my E&M is not ready for Jackson yet (I never took an upper division series on E&M).

 

[Mépris]

Thanks for the info people.

I think you're right Jorriss, it was likely Griffith's QM book that I'd heard reports about. I'm tempted by the Jackson text, and have been before, but the phrase 'graduate level' scares me a little. Although I think Goldstein is supposed to be a graduate level text, so perhaps I shouldn't be so intimidated.

Since you're about to start an MSci, I take it you're in England? That 4th year consists of (probably) graduate level courses. I have a friend in Germany who used Jackson in the second year of his B.Sc.

Take a copy from the library and see if you can handle it. I'm nowhere near that level (yet) but I tried working through Courant and couldn't, so I toned things down a little (using notes by Ian Craw for a while) and will go to Courant's book soon enough again. :-)

 

[atyy]

For GR, in addition to Carroll's notes, Blau has a great set of notes
http://www.blau.itp.unibe.ch/lecturesGR.pdf

Blau's notes are in index notation. Winitzki's has a really nice set of notes with more geometric notation.
https://sites.google.com/site/winitzki/index/topics-in-general-relativity

 

[TheShrike]

Since you're about to start an MSci, I take it you're in England? That 4th year consists of (probably) graduate level courses. I have a friend in Germany who used Jackson in the second year of his B.Sc.

Take a copy from the library and see if you can handle it. I'm nowhere near that level (yet) but I tried working through Courant and couldn't, so I toned things down a little (using notes by Ian Craw for a while) and will go to Courant's book soon enough again. :-)

I'm in Northern Ireland actually, but it's close enough. ;)

That's interesting to know. I ended up with the Goldstein during my second year when I took Classical Mechanics. It turned out to be too much for me at the time, especially since it started mostly with Lagrangian mechanics as the simplest things, whereas I had only just found out about it. But I'm having more fun with it now.

 

[Meir Achuz]

Franklin, "Classical Electromagnetism", has more detail than Griffiths, which is an undergraduate text. Franklin is easier to follow on your own than Jackson, but is on the same level.