Comparing Textbooks for Real Analysis Self-Study

In summary, The conversation is about choosing a textbook for self-studying real analysis. The two options being debated are Rudin's "Principles of Mathematical Analysis" and Marsden's "Real Analysis". Rudin is the more popular choice among course websites, despite being small and old. The advantages of Rudin are its difficulty level, which pushes readers to learn more and its emphasis on theorems and definitions. It is suggested to use Rudin along with Munkres' "Topology" for more examples. Marsden is not discussed in depth, but the person recommending Rudin also recommends using Munkres' "Topology" as a supplement.
  • #1
ehrenfest
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I am trying to decide which textbook to use to self-study real analysis. I am debating between https://www.amazon.com/dp/0716721058/?tag=pfamazon01-20 and
https://www.amazon.com/dp/007054235X/?tag=pfamazon01-20

It seems like Rudin is pretty ubiquitous on the course websites I have looked at, but I am not really sure why, seeing as the book is physically tiny and rather old. I used Marsden for complex analysis and it seemed pretty well-explained and rigorous. Can someone fill me in on why everyone uses Rudin? Has anyone used the Marsden textbook? What are the advantages and disadvantages of each?
 
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  • #2
It hurts to read. I mean it. You will think very hard learn very much and progress very far if you work through Rubin. It's very difficult, mostly because there are a lot of theorems, and definitions. Your world in this book will be theorems and definitions. Unlike other analysis books, the author makes you come to his level instead of going down to your level. In doing this, you push yourself further than you thought you could and learn a lot more from it than you would from other easier books. I highly suggest Rubin, but I say you should get a supplement book if you need more concrete ideas on the topics he presents.
 
  • #3
Haven't read Marsden, so I can't comment. But Rudin + Munkres' Topology is the path I took (followed by Royden and then daddy Rudin).

I really recommend the topology book as a supplement since it has a lot more examples than the corresponding section in Rudin.
 

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 and their properties. It is important because it serves as a foundation for many other areas of mathematics and has applications in fields such as physics, engineering, economics, and computer science.

What are the key factors to consider when comparing textbooks for real analysis self-study?

Some key factors to consider are the level of difficulty, the organization and structure of the book, the clarity and rigor of the explanations, the variety and relevance of the exercises, and the availability of additional resources such as solutions manuals or online lectures.

Should I choose a textbook based on my learning style?

Yes, it is important to choose a textbook that suits your learning style. Some textbooks may be more proof-oriented while others may focus on applications and examples. It is also helpful to consider whether you prefer a more self-paced approach or if you prefer more guidance from the author.

Are there any specific textbooks that are highly recommended for real analysis self-study?

There are many textbooks available for real analysis self-study, and the best one for you will depend on your individual needs and preferences. Some popular options include "Principles of Mathematical Analysis" by Walter Rudin, "Real Mathematical Analysis" by Charles Pugh, and "Understanding Analysis" by Stephen Abbott.

How important is it to supplement my self-study with additional resources?

Supplementing your self-study with additional resources such as online lectures, solutions manuals, or study guides can be very helpful. However, it is not necessary as long as the textbook you choose is well-written and includes a variety of exercises for practice.

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