Comparing Textbooks for Real Analysis Self-Study

[ehrenfest]

I am trying to decide which textbook to use to self-study real analysis. I am debating between https://www.amazon.com/dp/0716721058/?tag=pfamazon01-20 and
https://www.amazon.com/dp/007054235X/?tag=pfamazon01-20

It seems like Rudin is pretty ubiquitous on the course websites I have looked at, but I am not really sure why, seeing as the book is physically tiny and rather old. I used Marsden for complex analysis and it seemed pretty well-explained and rigorous. Can someone fill me in on why everyone uses Rudin? Has anyone used the Marsden textbook? What are the advantages and disadvantages of each?

 

[PowerIso]

It hurts to read. I mean it. You will think very hard learn very much and progress very far if you work through Rubin. It's very difficult, mostly because there are a lot of theorems, and definitions. Your world in this book will be theorems and definitions. Unlike other analysis books, the author makes you come to his level instead of going down to your level. In doing this, you push yourself further than you thought you could and learn a lot more from it than you would from other easier books. I highly suggest Rubin, but I say you should get a supplement book if you need more concrete ideas on the topics he presents.

 

[redrzewski]

Haven't read Marsden, so I can't comment. But Rudin + Munkres' Topology is the path I took (followed by Royden and then daddy Rudin).

I really recommend the topology book as a supplement since it has a lot more examples than the corresponding section in Rudin.