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> I've been starting into real analysis myself via Pugh's textbook[1] after not taking a serious math class since multivariable calculus

Do you have recommendations for other books? I stopped at multivariable calculus as well. For what it's worth those yellow Graduate Texts in Maths books feel like reading TaoCP or CLRS; I'm looking for more approachable textbooks. I feel like I'm not even up to the 1800s, math-wise, not even up to Gauss.

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There are hundreds of good math textbooks to recommend, it really depends on your interests.

For a broad overview at an undergraduate level, with a great job explaining the context of various mathematics topics, these Russian books from the 50s, Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov, and Lavrentiev, are pretty fun. Amazon link to the one-volume Dover reprint (but I’d recommend finding a used three-volume hardback copy): http://amzn.com/0486409163

Or check out John Stillwell’s Mathematics and its History: http://amzn.com/144196052X

Are you comfortable with proving math statements? If not, How to Think About Analysis by Lara Alcock is an amazing intro to Analysis. http://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/01...

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