Definitive math books for a physics major

[zheng89120]

So as a physics undergrad, I have been studying extensively into the popular (and useful) textbooks books by Stewart (Calc), Boas (Methods), and Riley (Methods). Any ways, I was just wondering, is there another book on mathematics for that a physics major should probably like to look, say after after spending a good amount of time with Riley's book? (Though if such a book would be on mathematical methods, it may be at a graduate school level.) thanks

[deluks917]

I think this book has a rather nice high level treatments of some applications of the calculus of variations to physics: http://www.amazon.com/Applied-Mathematical-Methods-Theoretical-Physics/dp/3527405348#reader_3527405348

Maybe you would like the Princeton companion to mathematics. The quality of the articles is very high on average. It has introduction to many areas of mathematics and often their applications to physics. It is a very good sampler of high level mathematics. http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809