Best introductory analysis book?

[DarkEternal]

I need a recommendation for the best introductory real analysis book to use for self-study. I haven't really had much experience with rigorous proofs and also need a good introduction to that. This coming year I will be using Rudin's Principles of Mathematical Analysis, so any book that would prepare me for that would be great. Thanks!

 

[graphic7]

From what I've heard Rudin's is supposed to be top-notch, very difficult, though. I had a friend that used Bartle's "Elements of Real Analysis 2nd Edition", and he was pleased with it. Some people say that Rudin's text shouldn't be used at an undergrad level, I can't say I know (being a physics major).

 

[hhegab]

One highly recommended introductory analysis book for self-study is "Understanding Analysis" by Stephen Abbott. This book covers the basics of real analysis in a clear and approachable manner, with a focus on building intuition and understanding rather than just memorizing theorems. It also includes a good introduction to rigorous proofs, making it an excellent preparation for Rudin's Principles of Mathematical Analysis. Another highly recommended book is "Real Analysis: A Long-Form Mathematics Textbook" by Jay Cummings. This book provides a thorough and comprehensive introduction to real analysis, with a heavy emphasis on developing problem-solving skills and intuition. It also includes many worked examples and exercises, making it a great resource for self-study. Both of these books would be excellent choices for preparing for Rudin's Principles of Mathematical Analysis and building a strong foundation in real analysis.