Over at Cosmic Variance, Clifford has asked for opinions on your favourite text book. Me, joining in only as commentator number 85, would like to repost my $.02 worth here:
Number one are by far the Feynman Lectures (Vol. I and II). From these I learned how physicists think.
When it comes to a GR text, it’s clearly MTW. And yes, a tensor is a machine with slots (egg crates etc) and not something with indices that transforms in a particular way (as Weinberg wants to make you believe). [I have to admit, I haven’t really looked at Sean’s book,yet].
Both these are 100% pure fun to read but admittedly, none of them can probably be used to accompany a lecture course. This is why many people who were busy with their courses never properly used them. Due to biographical oddities (three months of spare time between highschool and uni for Feynman, one year of compulsory [German] community/civil service after two years of uni) I actually read these books from beginning to end. I doubt that many other people can claim this. But it’s worth!
In addition, our library had a German/English bilingual edition of the Feynman lectures. So besides physics I could also learn physicists’ English (which is different from the literature English I learned in highschool).
Some other books: Jackson makes a great mouse pad and I have used it to this end for years. Plus it contains everything you ever wanted to know about boundary value problems. But clearly it’s not fun to read.
The writeup of Witten’s lectures in the IAS physics lectures for mathematicians contain lots of interesting insights.
And there is (admittedly not a physics text) “Concrete Mathematics” by Graham, Knuth (the Knuth of TeX) and Patashinik. This is a math book for computer scientists. It’s my standard reference for formulas containing binomials, for generating functions, sums, recurrence relations, and asymptotic expressions. And (probably thanks to Knuth) it’s full of jokes and fun observations. And there are hundreds of problems of a variety of difficulties, rated from “warmups” to “research problems". Therefore it’s also a source for Great Wakering.
Finally, there are the books by Landau and Lifshits. Since my first mechanics course. I have a strong disliking for them, probably based on my own poor judgement. When I first opened vol. 1 I was confused (admitedly I shouldn’t have been) by the fact that they use brackets for the vector product rather than \times like everybody else. Okok, it’s a Lie bracket but still, it makes formulas ugly. And then there is the infamous appendix on what a great guy Landau has been.
Marco Zagermann, who was in my year can still recite the highlights from this appendix: About the logarithmic scale for physicists and how Landau promoted himself on this scale later in his life, how he only read the abstracts of the papers in the Physical Review and then judged the papers either as pathological or how he rederived the results of the paper just from the abstract for himself. And there are more pearls like this.