Real Analysis Textbook Recommendation

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SUMMARY

The discussion centers on recommendations for self-studying real analysis after completing Apostol's Calculus, Vol. 2. Participants suggest considering Apostol's Mathematical Analysis as a continuation, while also evaluating other popular texts such as Rudin, Pugh, and Abbott. Abbott is highlighted for its clarity and suitability for self-study, while Rudin is recognized as a widely used but challenging option. The consensus indicates that if the individual has successfully solved most problems in Apostol, they are prepared to tackle Rudin.

PREREQUISITES
  • Understanding of calculus, specifically Apostol's Calculus, Vol. 2
  • Familiarity with mathematical proofs and logic
  • Basic knowledge of real analysis concepts
  • Experience with self-study techniques
NEXT STEPS
  • Read Apostol's Mathematical Analysis for a smooth transition from calculus
  • Study Abbott's "Understanding Analysis" for clear explanations and self-study guidance
  • Explore Rudin's "Principles of Mathematical Analysis" for a rigorous approach
  • Review Pugh's "Real Mathematical Analysis" for additional perspectives and exercises
USEFUL FOR

Students transitioning from calculus to real analysis, self-learners seeking structured study materials, and educators looking for effective textbooks for teaching real analysis concepts.

Tonzzi
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Does anyone have a recommendation for a book(s) to use for the self-study of real analysis? I have just finished Apostol Calculus, Vol. 2 and would like to move on to real analysis. I am not sure whether I should continue following Apostol and move on to Apostol mathematical analysis or something else. I have been looking at other real analysis books such as Rudin, Pugh, and Abbott. I know that Rudin is the most used textbook, but I'm not sure it's suited for self-study. My current plan is to do Abbott and then move on to Rudin. Would this be a good course of action?
 
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Abbot is good for self study. Really helpful explanations.

But since you did Apostol. Do you mean solved the majority of the problems without looking them up online? Etc. if you did do this. Then I think you are ready for Rudin.
 

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