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I haven't picked it up yet, but I remember reading about "The Princeton Companion to Mathematics" on here a while ago. It looks like a pretty complete guide to all of modern mathematics and sounded like it was easy enough for a beginner to get through while still being able to teach math experts some new things.

Thanks for reminding me about it - I think I'm going to order my self a copy!

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My own math background is through Calculus II right now, so I'm a beginner, but I can't say the Companion (though it is excellent) is something I could 'get through' in the sense that people usually mean it. By necessity it is terse, despite its massive size. I personally find it useful as a survey on the field, but I wouldn't recommend it as a teaching guide in and of itself for people who happen to be as dumb as me.

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