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Customer Review

566 of 620 people found the following review helpful
5.0 out of 5 stars Book should be called "Tada! You're a mathematican!", October 26, 2005
This review is from: Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) (International Series in Pure & Applied Mathematics) (Hardcover)
OK... Deep breaths everybody...

It is not possible to overstate how good this book is. I tried to give it uncountably many stars but they only have five. Five is an insult. I'm sorry Dr. Rudin...

This book is a good reference but let me tell you what its really good for. You have taken all the lower division courses. You have taken that "transition to proof writing" class in number theory, or linear algebra, or logic, or discrete math, or whatever they do at your institution of higher learning. You can tell a contrapositive from a proof by contradiction. You can explain to your grandma why there are more real numbers than rationals. Now its time to get serious.

Get this book. Start at page one. Read until you come to the word Theorem. Do not read the proof. Prove it yourself. Or at least try. If you get stuck read a line or two until you see what to do.

Thrust, repeat.

If you make it through the first six or seven chaptors like this then there shall be no power in the verse that can stop you. Enjoy graduate school. You half way there.

Now some people complain about this book being too hard. Don't listen to them. They are just trying to pull you down and keep you from your true destiny. They are the same people who try to sell you TV's and lobodemies.

"The material is not motivated." Not motivated? Judas just stick a dagger in my heart. This material needs no motivation. Just do it. Faith will come. He's teaching you analysis. Not selling you a used car. By the time you are ready to read this book you should not need motivation from the author as to why you need to know analysis. You should just feel a burning in you chest that can only be quenched by arguments involving an arbitrary sequence {x_n} that converges to x in X.

Finally, some people complain about the level of abstraction, which let me just say is not that high. If you want to see abstraction grab a copy of Spanier's 'Algebraic Topology' and stare at it for about an hour. Then open 'Baby Rudin' up again. I promise you the feeling you get when you sit in a hottub for like twenty minutes and then jump back in the pool. Invigorating.

No but really. Anyone who passes you an analysis book that does not say the words metric space, and have the chaptor on topology before the chaptor on limits is doing you no favors. You need to know what compactness is when you get out of an analysis course. And it's lunacy to start talking about differentiation without it. It's possible, sure, but it's a waste of time and energy. To say a continuous function is one where the inverse image of open sets is open is way cooler than that epsilon delta stuff. Then you prove the epsilon delta thing as a theorem. Hows that for motivation?

Anyway, if this review comes off a combative that's because it is. It's unethical to use another text for an undergraduate real analysis class. It insults and short changes the students. Sure it was OK before Rudin wrote the thing, but now? Why spit on your luck? And if you'r a student and find the book too hard? Try harder. That's the point. If you did not crave intellectual work why are you sitting in an analysis course? Dig in. It will make you a better person. Trust me.

Or you could just change your major back to engineering. It's more money and the books always have lots of nice pictures.

In conclusion: Thank you Dr. Rudin for your wonderfull book on analysis. You made a man of me.

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Tracked by 2 customers

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Showing 1-10 of 33 posts in this discussion
Initial post: Jan 1, 2007 7:55:07 PM PST
Justin Curry says:
<wipes tear from eye>

Well done good sir!

Posted on Apr 19, 2007 3:42:52 PM PDT
B. Ramsey says:
Bravo! Bravo! Well spoken.

Posted on May 19, 2007 3:53:04 PM PDT
I agree with the comment about TV sets and lobotomies, but learning how to spell "lobotomy", "chapter", etc., could not hurt the reviewer's credibility.

Posted on Jun 6, 2007 10:44:22 AM PDT
G. Basilio says:
you should be a motivational speaker!

Posted on Jul 23, 2007 10:43:34 AM PDT
Last edited by the author on Jul 23, 2007 10:44:01 AM PDT
Interesting review. I agree wholeheartedly that you definitely need to be intrinsically motivated to attempt college level math, and the upper division stuff like this requires extreme dedication. Thanks for your excellent review; I am now confident that this book is right for me.

Response to Michael Hardy: Perhaps English isn't his native tongue... Good ol' internet...

Posted on Nov 13, 2007 7:24:06 AM PST
Marius K says:
I am delighted by your review. Your enthusiasm provides a welcome contrast to the rather dry subject matter of the book. I wish there were more reviews of scientific literature of this kind.

However, I was disappointed to find that--at least in my edition--Rudin defines continuity using "the epsilon delta stuff", and only afterwards he proves as a theorem that the inverse image of an open set is open under a continuous function.

Posted on Feb 1, 2008 8:01:23 PM PST
Love your review, my friend!!

In reply to an earlier post on Feb 3, 2008 8:05:45 AM PST
"...but learning how to spell "lobotomy", "chapter", etc., could not hurt .."

Fair enough, but I still want to party with this person!

Well done!

Posted on Feb 12, 2008 10:27:36 PM PST
Andy W-T. H. says:
Wow. I couldn't help but comment, but that's the most well-thought, creative and energetic review I've read on Amazon. Especially in the presence of mathematics, that's just plain amazing. I'll definitely take a real look at this book(and several of Rudin's other works) for sure!

Posted on Mar 23, 2008 12:37:33 PM PDT
F. Li says:
For the most part, I agree with the author about what he said.
I do, however, think the author "over-stated" the level of the book.
After all, this book is a text book for freshman in Princeton. The content in this book are the basics for a math major.
How could you say that "You are half way through the grad school after you finish this book"?
It should be just a fresh start.
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