I'm self-teaching math at home. After learning Calculus by MIT OCW and a bit of easy Linear Algebra and set theory, I have decided to study Analysis.
As many have recommended Baby Rudin, I've tried to study Analysis with it. But it was so tough and hard that I could only solve 1 or 2 problems on the exercises. I thought that this is not the book which I can deal with. So I look around at other books.
Since I'm studying only by myself, solution availability is somewhat important as I should check my answers and be given some feedback.
Here's a list:
- Tao's Lecture Notes (Solutions available and it seems to be approachable)
- Marsden (I didn't carefully read the contents, so I don't know what the level of this book is. But I've heard after some chapters, it has lots of errors.)
- Abbott (it looks like the easiest one I've seen among Analysis books)
- Apostol (It deals with a lot of stuff, which I'd like to know. But the exercises look difficult for me.)
Which book should I use? If I choose a book and after studying the book, should I study harder Analysis book like Rudin?
Best Answer
Choosing the right book is a very personalized experience. I think it is best for you to pick the book which you can follow comfortably and has sufficient motivation and examples. Once you are comfortable with the material, you could try solving problems from some other book which you think is harder.
Maybe it is just me, but I do not find Rudin very comfortable. It seems dry and provides no motivation for the material. I do not think a textbook should be presented as a bunch of theorems and proofs.
The most intriguing book I found was Understanding Anlaysis by Stephen Abott. I have also seen it being recommended elsewhere on StackExchange.
There is a rather soft book on Analysis called How to think about Analysis. It is not a textbook, per se, but if you feel overwhelmed, you could look into it. It discusses some basic things about Analysis.