Real Analysis Textbook Recommendation

In summary, the conversation revolves around finding a book for self-study of real analysis. The person has just finished Apostol Calculus and is considering moving on to either Apostol Mathematical Analysis or other options such as Rudin, Pugh, and Abbott. The group discusses the suitability of each book for self-study, with Abbott being recommended as a good option. The person also mentions their plan to do Abbott first and then move on to Rudin, seeking confirmation if this is a good course of action. The conversation also references a guide for self-studying analysis and asks about the person's progress with Apostol.
  • #1
Tonzzi
1
0
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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  • #3
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.
 

1. What is Real Analysis?

Real Analysis is a branch of mathematics that deals with the study of real numbers and their properties. It focuses on the rigorous development of concepts such as limits, continuity, differentiation, and integration.

2. Why is Real Analysis important?

Real Analysis is important because it provides a foundation for many other branches of mathematics, such as calculus, differential equations, and topology. It also has numerous applications in other fields, such as physics, engineering, and economics.

3. What should I look for in a Real Analysis textbook?

When choosing a Real Analysis textbook, it is important to look for a clear and concise presentation of concepts, plenty of examples and exercises, and a rigorous approach to proofs. It should also have a good balance between theory and applications.

4. Can you recommend a good Real Analysis textbook for beginners?

One highly recommended textbook for beginners is "Principles of Mathematical Analysis" by Walter Rudin. It provides a thorough introduction to the subject with clear and concise explanations, challenging exercises, and a rigorous approach to proofs.

5. Are there any online resources for Real Analysis?

Yes, there are many online resources for Real Analysis, such as lecture notes, video lectures, and practice problems. Some recommended websites include Khan Academy, MIT OpenCourseWare, and Paul's Online Math Notes. It is important to supplement textbook learning with additional resources for a better understanding of the subject.

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