Need help finding graduate analysis book

In summary, the conversation discusses the topic of real analysis, particularly at a graduate level. The main text recommended is Rudin's "Principles of Mathematical Analysis", with additional suggestions for Royden's "Real Analysis" and Gamelin's "Complex Analysis" for more in-depth study. The subjects covered in a typical real analysis course include the real line, metric spaces, topological spaces, Lebesgue integration, Banach spaces, and measure theory. Complex analysis is also mentioned as a topic of interest for the individual looking to get a head start on the subject.
  • #1
jav
35
0
I have just taken real analysis I and II (single and multivariable respectively) as an undergrad. I am planning on taking the grad analysis course next year.

From what I gather Rudin seems to be the time-tested bible of analysis, but I don't know at what level the book is written. Can anyone recommend a graduate level real analysis book?

Also, I am looking to get a head start on complex analysis, so if anyone could share the name of a good complex analysis text, I would appreciate it.

Thanks
 
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  • #2
Please elaborate on the course. What are the subjects treated? Analysis is a big subject. Rudin already has three textbooks (principles, real and complex, functional) on analysis.
 
  • #3
Royden's Real Analysis is a classic and features chapters on the Real line, Metric spaces, Topological spaces, Lebesgue integration, Banach spaces, and Measure theory. It doesn't feature complex analysis, however. Complex analysis by Gamelin is a good book and covers a year long course in the subject (or more or less depending on what you know).
 

1. Can you recommend a specific book for graduate analysis?

It depends on your level of expertise and the specific area of analysis you are interested in. Some popular books for graduate analysis include "Real Analysis" by Royden and Fitzpatrick, "Measure and Integration Theory" by Axler, and "Functional Analysis" by Rudin. It is best to consult with your professor or academic advisor for personalized recommendations.

2. What are the key topics covered in a graduate analysis book?

A graduate analysis book typically covers topics such as real numbers and sequences, metric spaces, continuity, differentiation, integration, and series. Some books may also include topics like normed and Banach spaces, Hilbert spaces, and Lebesgue measure and integration.

3. Are there any online resources for graduate analysis books?

Yes, there are many online resources for graduate analysis books. Some popular websites include Amazon, Barnes and Noble, and Google Books. You can also check your university's library website for electronic versions of graduate analysis books.

4. How do I know if a graduate analysis book is suitable for my level?

You can look at the preface or introduction of the book to see the intended audience and level of difficulty. You can also ask for recommendations from your professors or colleagues who have already taken graduate analysis courses.

5. Do I need to have a strong background in mathematics to understand graduate analysis?

Yes, a strong foundation in undergraduate mathematics, particularly in calculus, linear algebra, and basic analysis, is necessary to understand graduate analysis. It is also recommended to have a good understanding of mathematical proofs and logic.

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