What is the best real analysis textbook for math majors?

[Benzoate]

I'm a math major. I'm looking for the best real analysis textbook that clearly breaks every proof down ,step by step, explaining the purpose of each step , and why you this step is important for the proof.I want a real analysis textbooks that's the subject to comprehend better for all math majors of different aptitudes.

 

[JasonRox]

I want a real analysis textbooks that's the subject to comprehend better for all math majors of different aptitudes.

That's impossible. You just described a book I wouldn't want.

I would just want an Analysis textbook with the right number of problems and with the right problems too. I wouldn't want a textbook explaining every tiny little detail in a proof. I like the fact that it's my job to fill that in.

 

[mattmns]

Yeah, as Jason said, something like that is not really what you want. And if it is, then you will likely have trouble finding it. The "purpose" of a real analysis class is to get you to learn that you have to do everything yourself. If you are just having trouble with proofs in general, then check out a book on math reasoning (I recommend reading the first 100 pages (or more if you want) of An Introduction to Mathematical Reasoning by Peter Eccles.) This book is not difficult to work through, and there are thorough solutions to the exercises. He also explains proofs in more detail than your average real analysis book, which is probably what you want.

 

[Chris Hillman]

Ditto the others, no textbook author would even try to meet such desiderata.

Er... shouldn't this thread be in the Science book reviews subforum at PF? Suggest a followup question asking for a good analysis textbook at (fill in your level/aptitude).

 

[Benzoate]

Yeah, as Jason said, something like that is not really what you want. And if it is, then you will likely have trouble finding it. The "purpose" of a real analysis class is to get you to learn that you have to do everything yourself. If you are just having trouble with proofs in general, then check out a book on math reasoning (I recommend reading the first 100 pages (or more if you want) of An Introduction to Mathematical Reasoning by Peter Eccles.) This book is not difficult to work through, and there are thorough solutions to the exercises. He also explains proofs in more detail than your average real analysis book, which is probably what you want.

any other good proof book you recommend. i need all the help i can get. i suck at writing proves but i have an intense desire to do better

 

[Benzoate]

That's impossible. You just described a book I wouldn't want.

I would just want an Analysis textbook with the right number of problems and with the right problems too. I wouldn't want a textbook explaining every tiny little detail in a proof. I like the fact that it's my job to fill that in.

is there such a thing as a 'good analysis' book

 

[Chris Hillman]

Recommend a nice friendly real analysis textbook

Sure there is. One of the more user friendly textbooks is Robert G. Bartle, Elements of Real Analysis, 2nd ed., Wiley, 1976. Enjoy!

 

[mattmns]

any other good proof book you recommend. i need all the help i can get. i suck at writing proves but i have an intense desire to do better

Just read the first 100 pages of that book (An Introduction to Mathematical Reasoning) and you should be much better. Then practice, practice, practice! There are also some online sources (let me find the link) that someone posted on proof writing.

Here is that thread with a bunch of proof writing sources: How to write Math proofs

 

[BST]

Real Analysis Textbooks (PDF files)

On the topic of real analysis texts, some readers may prefer a rather cheaper alternative.

We have made free PDF copies of our texts available at the link
http://classicalrealanalysis.com/download.aspx
Since September we have had over 8,000 downloads which I take as
evidence that students find the price attractive.

These are the undergraduate and graduate real analysis texts formerly
published by Prentice Hall:

"Elementary Real Analysis," Brian S. Thomson, Judith B. Bruckner,
Andrew M. Bruckner. Prentice-Hall, 2001, xv 735 pp. [ISBN
0-13-019075-61]

"Real Analysis," Andrew M. Bruckner, Judith B. Bruckner, Brian S.
Thomson. Prentice-Hall, 1997, xiv 713 pp. [ISBN 0-13-458886-X]


There will also be a "dripped version" of the undergraduate text posted shortly.
The drip (Dump the Riemann Integral Project) program might appeal to physics students.