Group Theory and Physics
– by Shlomo Sternberg
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Math for dummies? Well, actually, it is rigorous, just not as general as it could potentially be. Also, many people’s optimal learning style is quite concrete; I believe your first experience with a subject should be example-based, to fix ideas. After all, when you were a kid you played around with numbers long before you defined the integers. There’s something to the old Dewey idea of “learning by doing.” And I have only seen it tried once in advanced mathematics.
Fulton and Harris won’t do this. The representation theory section in Lang’s Algebra won’t do this — it starts about three levels of abstraction up and stays there. Weyl’s classic The Theory of Groups and Quantum Mechanics isn’t actually the best way to learn — the group theory and the physics are in separate sections and both are a little compressed and archaic in terminology. Sternberg is really a different thing entirely: it’s almost more like having a teacher than reading a textbook.
The treatment is really most relevant for physicists, but even if you’re not a physicist (and I’m not), if you have general interest in math, and background up to a college abstract algebra course, you should check this out just to see what unusually clear, intuitive mathematical writing looks like. It will make you happy.” – Posted by SarahC at http://lesswrong.com/lw/3gu/the_best_textbooks_on_every_subject/ – by Books2Learn – 2018-02-27