Real Analysis Textbooks - What are the Best Options?

In summary, the conversation discusses suggestions for textbooks on real analysis. Baby Rudin is recommended by some, but others find it difficult to learn from. Other suggestions include Riesz Nagy and Wheeden and Zygmund. There is also mention of Dieudonne's Foundations of Modern Analysis, which covers metric spaces, Banach and Hilbert spaces, and real and complex calculus.
  • #1
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I'm planning to learn real analysis in the up and coming holidays, anybody have any good suggestions on which textbooks will be useful?

I've heard good comments about Baby Rudin, is this true?
 
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  • #2
michael c. reed's text was a decent real analysis book IMHO
 
  • #3
i found baby rudin to be very concise and hard to learn from. i like riesz nagy, but i am not an expert. friends of mine who are experts use wheeden and zygmund.
 
  • #4
i guess i do not know what you mean by real analysis on second thought. i am assuming you mean measure and integration, but some people just mean limits and metric spaces, which is what baby rudin suggests to me.

professional analysists mdo like baby rudin, so you mgiht try it to see if you are one opf them. i disliekd it myself. if your idea of fun is treating a real number as a dedekind cut, be my guest.

another excellent book is dieudonne's foundations of modern analysis for metric spaces, banach and hilbert spaces, and real and complex calculus in that setting. no measure theory though but it is a wonderful book.
 
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FAQ: Real Analysis Textbooks - What are the Best Options?

1. What is real analysis and why is it important?

Real analysis is a branch of mathematics that deals with the rigorous study of real numbers, functions, and sequences. It is important because it provides the foundation for many other mathematical concepts and is essential for understanding the behavior of systems in the physical world.

2. What makes a good real analysis textbook?

A good real analysis textbook should have clear and concise explanations, a variety of examples and exercises, and a logical progression of topics. It should also include proofs and applications to real-world problems.

3. What are some recommended real analysis textbooks for beginners?

Some recommended textbooks for beginners in real analysis include "Principles of Mathematical Analysis" by Walter Rudin, "Introduction to Real Analysis" by Robert G. Bartle and Donald R. Sherbert, and "Understanding Analysis" by Stephen Abbott.

4. Are there any online resources for learning real analysis?

Yes, there are many online resources for learning real analysis, including video lectures, interactive tutorials, and practice problems. Some popular websites for real analysis include Khan Academy, MIT OpenCourseWare, and Paul's Online Math Notes.

5. How can I choose the best real analysis textbook for my needs?

The best real analysis textbook for you will depend on your level of knowledge, learning style, and specific goals. It is recommended to read reviews and previews of different textbooks, and possibly consult with a professor or fellow mathematician for recommendations.

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