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Which books have made the biggest impact on your understanding as a mathematician? And why?

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*Analysis I* by Terence Tao finally got me over the *pons asinorum* of mathematical analysis. If I'd read it as an undergraduate, I'd probably have decided to become a mathematician instead of a physicist.
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Not a book, but Terence Tao's blog had very frequently clarified my understanding and giving me insight that I did not have. As an example, I was thoroughly confused with analytic number theory, like the prime number theorem, but music note analogy and the self-defeating conspiracy argument from Tao's blog make it so intuitive.

The blog also cover a wide range of topic. Sure he's an analyst, but that does not mean he can't cover other topics, with his own perspective.
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In my formative years,

* Stewart's calculus
* Mathematical Proofs by Chartrand, Polimeni, and Zhang
* Galois Theory by Cox
* Number Fields by Marcus
* undergrad Hungerford was a really pleasant intro to algebra

And as someone doing a PhD in some automorphic forms stuff I can't say I have read a text that has made anything crystal clear lol. Seems to be a topic that is best understood by reading it in 7 different places at once. Or maybe I'm just dumb.
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Aluffi, aluffi, aluffi. Oh wait… have I said aluffi?
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Donald Knuth’s The Art of Computer Programming. Took me out of Software Engineering and am now a PhD student studying theoretical comp sci
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Stein and Shakarchi’s Real Analysis, mainly because it was the first book I carefully worked through. The more I look back, the more I realize how their presentation covered many of the most important techniques in measure theory despite only specializing to Rn.
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Analysis NOW by Pedersen for Functional Analysis. I had a qualifier based on that book. So much grinding, but by the end of a summer with that book, I really felt like I understood the subject.
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Erwin Kreyszig - "Introductory functional analysis with applications" is a perfect book.
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I doubt that very many of you know it but Boris Levins "Lectures on Entire functions". It is extremely interesting but very difficult to read so I have learned a lot trying to understand it.
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I really liked Munkre's Topology, my first encounter with the subject.

I *vibed* very well with his approach to the proofs/exposition, and after solving the exercises I felt well prepared on the subject

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