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Introduction to Analysis (Dover Books on Mathematics)
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Digression: Terry Tao wrote a book on analysis? That's awesome!
I wouldn't recommend Spivak for self-study and a first exposure to analysis. It's known to be notoriously difficult even for good students.
I learned from this Dover book; I think it's pretty good. From there you might move up to Baby Rudin, but it might have a lot of typos, or big gaps in the exposition that are taken to be obvious but require several steps to fill in, since that was certainly the case for Papa Rudin.
: https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat... : https://www.amazon.com/Principles-Mathematical-Analysis-Inte... : https://www.amazon.com/Real-Complex-Analysis-Higher-Mathemat...
I highly recommend this book for Real Analysis http://www.amazon.com/Introduction-Analysis-Maxwell-Rosenlic...
We used it at the University of Texas at Austin for the first semester in Real Analysis. I found it very clear and easy to follow.
⬐ caesiumI used this for my undergrad analysis class and then relied on it as a foundation for reading Rudin/Royden in grad school. Killed qualifying exams. Use it. Sure, it's all Riemann integration but you will not suffer until you get to measure-theoretic integration later.⬐ talbinaWhy are these books from Dover Publications so cheap?⬐ pingsweptBecause the copyright has expired, or the copyright owner has put the work in the public domain due to bankruptcy, or similar.