I made a book recommendation thread recently which got deleted, so I'm hoping this one doesn't have the same fate as the question seems much more defined.

I was reading an interesting article by VI Arnold where he recommends that all math classes should be taught such that the connection of math to the physical world is brought to the surface. He recommends various books throughout the lecture, but they are mainly hints rather than a full bibliography. Therefore, I was hoping that we can have a small bibliography of math books that include many physical applications; and preferably not just in an appendix at the back (otherwise there wouldn't be a point: just read a pure math book followed by a physics/engineering book), but rather intertwined throughout with the math.

An extremely good example of this is Zorich's two analysis volumes. There is a review on the back cover of this book by Arnold himself, who calls this book the best modern course of analysis. This book is known for its many beautiful physical applications which are tightly knitted to the math, and so it is a perfect example of the type of teaching Arnold advocates in his lecture. I am also aware that Courant's classic analysis book follows the same pattern. However, I am struggling to find a general abstract algebra book that does the same thing; perhaps there are books on individual topics (groups, etc.)?

If the question isn't defined enough please let me know what I can do to improve it. Also, if you recommend a book please keep it at one book per post - thanks.

  • $\begingroup$ The only abstract algebra topics that most physicists use to my knowledge are representation theory and Lie groups (both are group theory topics). Physicists seem to mostly just use the different varieties of calculus (differential equations, complex analysis, differential geometry, etc). On an unrelated note, Arnold's own books deserve to be on this list. For instance his book Ordinary Differential Equations. $\endgroup$ – got it--thanks Sep 24 '15 at 1:02

The road to reality by Roger Penrose

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