4 ms·

Can anyone recommend analysis textbooks suitable for self study?

slack3r 9y ago
Try Terence Tao's Analysis I and II.
npr11 9y ago
Calculus, by Spivak (an analysis textbook despite the name). I found this book clear, with good exercises, and it starts at the very beginning. I think the most difficult exercises are in the early chapters, so stick with it!
monaghanboy 9y ago
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[1]; I think it's pretty good. From there you might move up to Baby Rudin[2], 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[3]. [1]: https://www.amazon.com/Introduction-Analysis-Dover-Books-Mathematics/dp/0486650383/ref=sr_1_1?ie=UTF8&qid=1515186291&sr=8-1&keywords=introduction+to+real+analysis+dover https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat... [2]: https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X/ref=sr_1_2?s=books&ie=UTF8&qid=1515186407&sr=1-2&keywords=rudin+analysis https://www.amazon.com/Principles-Mathematical-Analysis-Inte... [3]: https://www.amazon.com/Real-Complex-Analysis-Higher-Mathematics/dp/0070542341/ref=sr_1_4?s=books&ie=UTF8&qid=1515186407&sr=1-4&keywords=rudin+analysis https://www.amazon.com/Real-Complex-Analysis-Higher-Mathemat...
gtani 9y ago
Without knowing your background, Pugh's and Abbott's are usually good choices as are Schramm's Dover, and while not really analysis texts, don't forget the classic fundamentals/foundations books by Courant/Robbins What is Mathematics, Ian Stewart/D Tall Foundations of Math, Felix Klein etc Here's lots of reviews: https://www.maa.org/tags/real-analysis https://www.maa.org/tags/real-analysis https://math.stackexchange.com/questions/tagged/real-analysis+book-recommendation?sort=votes&pageSize=15 https://math.stackexchange.com/questions/tagged/real-analysi... https://www.reddit.com/r/math/wiki/faq#wiki_what_are_some_good_books_on_topic_x.3F https://www.reddit.com/r/math/wiki/faq#wiki_what_are_some_go...

Try Terence Tao's Analysis I and II.

Calculus, by Spivak (an analysis textbook despite the name). I found this book clear, with good exercises, and it starts at the very beginning. I think the most difficult exercises are in the early chapters, so stick with it!

monaghanboy 9y ago

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[1]; I think it's pretty good. From there you might move up to Baby Rudin[2], 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[3]. [1]: https://www.amazon.com/Introduction-Analysis-Dover-Books-Mathematics/dp/0486650383/ref=sr_1_1?ie=UTF8&qid=1515186291&sr=8-1&keywords=introduction+to+real+analysis+dover https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat... [2]: https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X/ref=sr_1_2?s=books&ie=UTF8&qid=1515186407&sr=1-2&keywords=rudin+analysis https://www.amazon.com/Principles-Mathematical-Analysis-Inte... [3]: https://www.amazon.com/Real-Complex-Analysis-Higher-Mathematics/dp/0070542341/ref=sr_1_4?s=books&ie=UTF8&qid=1515186407&sr=1-4&keywords=rudin+analysis https://www.amazon.com/Real-Complex-Analysis-Higher-Mathemat...

gtani 9y ago

Without knowing your background, Pugh's and Abbott's are usually good choices as are Schramm's Dover, and while not really analysis texts, don't forget the classic fundamentals/foundations books by Courant/Robbins What is Mathematics, Ian Stewart/D Tall Foundations of Math, Felix Klein etc Here's lots of reviews: https://www.maa.org/tags/real-analysis https://www.maa.org/tags/real-analysis https://math.stackexchange.com/questions/tagged/real-analysis+book-recommendation?sort=votes&pageSize=15 https://math.stackexchange.com/questions/tagged/real-analysi... https://www.reddit.com/r/math/wiki/faq#wiki_what_are_some_good_books_on_topic_x.3F https://www.reddit.com/r/math/wiki/faq#wiki_what_are_some_go...