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by Spivak 1593 days ago
My username comes to mind. Spivak's Calculus is hands down the best intro Calc book if you want to learn math for its own sake. His book on manifolds is also amazing but definitely not intro.

If you want stats I highly recommend Statistical Inference by Casella & Berger -- it's extremely dry but so many stats books out there try to "make it easy" but the simplification means that you can't actually grok what's really going on. HOWEVER if you want to actually apply anything in this book you'll need to grab something more practical as well. Going through an applied stats book after having done SI is like having superpowers.
2 comments
l33t2328 1593 days ago
Spivak’s Calculus is hands down an excellent book for a first course in real analysis, and I’ll die on that hill(it’s only real competition is Analysis 1 by Tao, in my opinion).

Anyone that says “it’s just a calculus book; it’s not good for introductory real analysis” is invited to go solve every problem in, for example, the chapter which defines integration, and compare the difficulty with problems in “traditional” analysis books.

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mjh2539 1593 days ago
If they know how to do (rigorous) proofs, then Spivak would be good. Otherwise it would be far too advanced. It's essentially an introduction to analysis.
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Spivak 1593 days ago
That's fair. I don't really know what counts as advanced anymore. There just aren't that many books on theoretical math that aren't "graduate level" (which is way scarier than it sounds) -- Spivak was my Real Analysis 101 book as a freshman math major.

Spivak at least has the nice property that it doesn't assume you know much.

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