Analysis Real Analysis (Baby Rudin vs Apostol)

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The discussion revolves around self-studying Real Analysis, specifically the experiences with Rudin's "Principles of Mathematical Analysis" and Apostol's "Mathematical Analysis." The user expresses initial progress with Rudin but struggles to grasp some proofs, feeling that Rudin's concise style may not be suitable as a sole resource. There is a consideration of using Apostol as a supplementary text, with inquiries about how to effectively combine the two books. Suggestions include using Apostol for theoretical understanding and Rudin for problem-solving. Other recommended resources include Carothers' book for its gentler approach and Abbott's "Understanding Analysis," although the user found Abbott's pace too slow. Overall, the conversation highlights the challenges of mastering Real Analysis and the importance of selecting complementary texts for a more comprehensive understanding.
Falgun
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I am currently trying to self study Real analysis . I have completed Hubbard's Multivariable book & Strang's Linear algebra book. I have Apostol's Mathematical Analysis & Baby Rudin . I started with rudin yesterday and was making excellent headway until I encountered a theorem about 15 pages in. After some difficulty I managed to prove it but when I saw rudin's proof I was completely baffled. He did in three lines what took me a page . I am still trying to understand the proof as of now. But I am beginning to feel rudin might not be as good as a sole textbook. I am considering using apostol's book as a supplement.
How does it compare to Rudin?

Does anyone have any suggestions about using apostol & rudin in conjunction?

Feel free to recommend other resources and tips to learn analysis.Thanks in advance.
 
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I know that people have issues with it, but if you feel that a verbose approach would work better for you, take a look at Strichartz.

Many people recommend Abbott Understanding Analysis.
 
caz said:
I know that people have issues with it, but if you feel that a verbose approach would work better for you, take a look at Strichartz.

Many people recommend Abbott Understanding Analysis.
I flipped through a pdf of abbott before I tried rudin but I didn't find it all that satisfying. Sure, the writing's excellent and very easy to read but I felt the pace was too slow. As for strichartz I don't think it will suit me for the same reason.

What are your thoughts on Apostol's Analysis book?

I was more hoping you would tell me how to use Rudin & Apostol together?
Like should I get the theory from apostol & problems from rudin or what?
 
I like Rudin a lot, but another option is Carothers' book. It's maybe a gentler read and has good exposition and problems from what I've looked at. I think it also covers more than Rudin (though it doesn't do any multivariable analysis from what I remember).
 
Infrared said:
I like Rudin a lot, but another option is Carothers' book. It's maybe a gentler read and has good exposition and problems from what I've looked at. I think it also covers more than Rudin (though it doesn't do any multivariable analysis from what I remember).
Sure I'll check it out.
 
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