Readable books on advanced topics

Question

I realise that there are already a few questions looking for general book recommendations, but the motivation and type of book I'm looking for here is a little different, so I hope you can indulge me.

I enjoy reading quite a lot, and tend to prefer books that teach me something new, rather than straight up fiction. When I was younger I used to read a lot of popular science books, and at the time I thought these were teaching me something, but then I got older and went to university and studied theoretical physics, and that killed the genre for me.

Now, I know that I can learn about a topic simply by seeking out review papers on it, or finding an appropriate textbook. That's what I do when I need to do something for work. However, most of the time this material does not make for light reading, and requires a significant amount of effort to work through, and is not necessarily the kind of thing I'd want to use as a way to relax.

However, occasionally one comes across a very readable book on some aspect of physics. Nielsen and Chuang's Quantum Computation and Quantum Information strikes me as an example of this. There are probably better examples of this, but what are they?

This brings me to my question:

Beyond the standard undergraduate topics, which areas of physics or mathematics have books which both provide fairly comprehensive introductions and which are actually enjoyable to read?

To be clear, by "enjoyable" I mean something more than that they simply be accessible or well written. I mean that it should be something that I could read for relaxation rather than work. To some people this will probably sound like an insane thing to want to do. However modern physics is huge, and it bothers me that I don't know very much about, say, string theory beyond bosonic string theory, and if it is something I can learn more about in my spare time, then that would be great.

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UPDATE: There appears to be some confusion in the answers over the type of book I am looking for. I am not looking for popularisations. Rather I am looking for something at the level of a graduate text, but only those which are particularly readable.

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Comments

Does Gödel, Escher, Bach count?

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@PratikDeoghare: No.

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Answer 1

I really like The Princeton Guide to Mathematics (Amazon, Google)

Even though I believe it was meant more as a sort of Encyclopedia rather than an actual Textbook, I really like to read it as a "normal" book.

Basically, whenever I understand some new mathematical concept I look it up in the Guide and see how it branches out and often find new interesting topics I'd like to read about.

Furthermore it gives an excellent overview of all the mathematical topics there are and is very well written and easy to understand.

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Comments

Ah yes. Actually, I already have that one!

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I have this one also, is great for browsing!

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Answer 2

A perfect example for what I think you are looking for is J.S. Bell's Speakable and unspeakable in quantum mechanics (Amazon, Google). Although it is a collection of papers, this is a very readable account of some aspects of quantum foundations.

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Answer 3

I find the book Geometry of quantum states: An Introduction to Quantum Entanglement by Ingemar Bengtsson and Karol Życzkowski both readable and useful. I already referred to it in three different occasions on this site. It focuses on the geometrical description of the spaces of quantum states and maps of finite level quantum systems. This subject is rapidly developing and even the book was only recently published (2006), it may have become a little outdated. Nevertheless, I think that it is very useful as a research level introductory reference.

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Answer 4

I found Connes's Noncommutative Geometry a very good book.

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Comments

It is an interesting book but there's a point beyond which it becomes more difficult than it should be. But then, maybe it's only me

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Answer 5

Perhaps, the best mathematics book in this category is "What is Mathematics?" by Richard Courant. Courant wrote this book in the 40's to help his son. It is still good.

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Comments

As I commented on ver's post, I am not looking for popularizations, but rather advanced texts that manage to be readable at the same time.

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I think "What is Mathematics" is an "advanced text". But then "advanced" is a relative term.

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Ah, I've just looked at a few reviews, and this probably fits my query better than I first thought. Sorry.

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Answer 6

A brief list of miscellaneous "technical" (not popular science) books I read on the bus, and I enjoyed every page:

Everything from R.P. Feynman, from his "Lectures on physics" to "Statistical mechanics", the "Lectures on computation" or "Gravitation". "QED: the strange theory of light and matter" may be considered as (extremely good) popular science, but it contains more insight than most technical reviews.

General Relativity: Misner, Thorne and Wheeler, "Gravitation", but also Foster and Nightingale, "A short course on general relativity". Also Taylor and Wheeler, "Spacetime physics" on special relativity. J. Weeks, "The shape of space" on topology is a true jewel.

About fractals and surface growth, A.L. Barabasi, "Scaling concepts in surface growth" is extremely readable. M. Schroeder's "Fractals, chaos and power laws" is both easy to read, lovely and accurate.

In abstract algebra, I. Stewart, "Galois theory" is very nice, but also the book from H.E. Edwards. They are both like novels.

Marsden and Weinstein, "Calculus unlimited". From M. Spivak, "Calculus" and "Calculus on manifolds". His books in differential geometry are also very nice.

Jaynes, "Lectures on probability theory".

Ufff, this was just out of the box. The books I cite are a bit old, I know, but they are still highly recommendable.

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Answer 7

Let me list the books on various topics in physics which I find the best in their fields:

1) Arnold "Mathematical Methods of Classical Mechanics" (contains a beautiful intro into various mathematical topics -- symplectic geometry, contact geometry, differential forms, Lie groups, etc. -- and their applications in Hamiltonian and Lagrangian formalisms of mechanics);

2) Schwinger "Classical Electrodynamics" (standard course in EM in vacuum and media, but given from more modern viewpoint and describes relatively advanced techniques, such as Green's functions);

3) Rubakov "Classical Theory of Fields" (an excellent course for undergraduates, introducing many advanced topics -- solitons, instantons, monopoles, non-commutative fields theories, index theorems -- but requires only knowledge of classical mechanics and electrodynamics);

4) Shankar "Principles of Quantum Mechanics" (as for me, the best book on QM, introducing it from quite a formal point of view. Contains all the standard material + Feynman Integral for bosons and fermions, density matrix, etc. The only shortcoming is easy problems). May be supplemented by some good book of problems, such as "Exploring Quantum Mechanics: a Collection of 700+ Problems for Students, Lecturers and Researchers" by Galitski and Karnakov;

5) Carroll "Spacetime and Geometry: an Introduction to General Relativity" (good book presenting GR from a modern geometrical point of view. Moreover, contains some modern topics -- Hawking Radiation, Unruh Effect, etc). "General Relativity" by Wald and "Gravitation" by Misner, Thorne and Wheeler are also good, but I don't think one should begin studying the subject with them. There is also a very good problem book on GR -- "Problem Book in Relativity and Gravitation" by Lightman, Press, Price and Teukolsky.

6) Nakahara "Geometry, Topology and Physics" (contains basically all the math needed to study GR, QFT and String Theory);

7) Srednicki "Quantum Field Theory" (my favorite textbook on QFT, containing introduction to all the essential topics in QFT. Can be supplemented by some more advanced textbooks, such as Weinberg's "The Quantum Theory of Fields");

8) Green, Schwarz, Witten "Superstring Theory" (a classical reference on String Theory. Doesn't discuss any modern topic, but the material it contains covered wonderfully. May be read in parallel with Polchinski's "String Theory"). The best place to study more modern topics in the field is "D-branes" by Johnson, as for me.

Answer 8

Personally, I found In Search of Schrödinger's Cat by John Gribbin very entertaining. It is quite old now and I'm not sure whether you'll find anything new in there after studying theoretical physics, though.

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Comments

Perhaps I should have made it clearer, but I am not looking for popularizations.

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Answer 9

The New Physics by Paul Davies.

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Comments

Why the downvote?

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While I did not vote, but judging from the Amazon page, this book does look like a popularisation.

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