# Is Baby Rudin a good choice for first my Real Analysis textbook?

• Analysis

## Main Question or Discussion Point

Summary: Is Baby Rudin a good choice for first Real Analysis textbook for someone without strong pure math background?

I've completed 2 semesters of college calculus, but not "pure math" calculus which is taught to math students. I'm looking for introductory text on Real Analysis and I've heard that Baby Rudin is a classic. However I've heard that it is very dense and requires a good deal of pure math experience. Is this book a good choice for someone with my background, or should I look for other options, also, what other options could be recommended?

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Math_QED
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2019 Award
What did you see in these college calculus classes? If you did not see $\epsilon-\delta$ proofs and those courses were only computational, don't even think about beginning Rudin. Without the proper background, Rudin will frustrate you until you give up and lose interest.

I recommend to begin with the book "Calculus" by Michael Spivak. Spivak trains you to think like a mathematician, and use intuition to guide you to a correct proof. After that, you can try Rudin but I think Apostol's "Mathematical analysis" is more gentle.

mathwonk
Homework Helper
agree 100%

What did you see in these college calculus classes? If you did not see $\epsilon-\delta$ proofs and those courses were only computational, don't even think about beginning Rudin. Without the proper background, Rudin will frustrate you until you give up and lose interest.

I recommend to begin with the book "Calculus" by Michael Spivak. Spivak trains you to think like a mathematician, and use intuition to guide you to a correct proof. After that, you can try Rudin but I think Apostol's "Mathematical analysis" is more gentle.
You are right, those were courses without any proofs, just computational methods.

Math_QED
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2019 Award
You are right, those were courses without any proofs, just computational methods.
Then go with Spivak. He will gently transition you to proof based maths. This book will already be hard enough if it is your first encounter with proof-based mathematics.

If you want a middle ground between Spivak and Rudin, then Bartle and Sherbert's Introduction... is quite reader-friendly. It is not as much fun as Spivak, but it does the job in a systematic manner starting from foundations. It is also a proper first real analysis book.

I kinda disliked the formatting in Bartles book.
I learned Analysis from Abbott: Understanding Analysis. The book is really user friendly and explanations are concise. Bartle supplements Abbot well. I would get both!

Math_QED
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2019 Award
I kinda disliked the formatting in Bartles book.
I learned Analysis from Abbott: Understanding Analysis. The book is really user friendly and explanations are concise. Bartle supplements Abbot well. I would get both!
I did not read this book, but skimmed through it and it seems definitely a good book. I like that it uses sequences early on and if I remember correctly it also treats interesting stuff like the category theorem of Baire and some basic Fourier analysis.

I did not read this book, but skimmed through it and it seems definitely a good book. I like that it uses sequences early on and if I remember correctly it also treats interesting stuff like the category theorem of Baire and some basic Fourier analysis.
Yes. The only issue that I have with the book, like most Springer text, is a lack of problems. But the problems are interesting and some challenging. The section on open and closed sets is very user friendly too.

What is your objective? What is your major? One year of calculus is not preparation for analysis.