Holy crap guys!!, I just checked out this book called Princiapals of Matheamtical Analysis by this geezer dude Roodin and, HOLY MOTHER OF GOAT it was FRICKIN INCREDIBLE!! This guy Roodin does tones of analyzing things in a kinda math-y like way, wich is awesome for me because I just joined Menza like last year (my IQ has been mearured to be at like way over 180/180 GMAT SCORE) so everthings in these book is like hella smart lol!!

There were some parts tat were a little bit confusing, like what was all that stuff about metered spaces?? Quitre frankly, he probably just made all of that stuff up when like crazy bored 1 day LOL!! And then he talks about some wackyu tings like Leg Intervals (wtf is a leg interval lol??!!?!) So, as they say in the math buisness, the exportation was perfunctional.

Anywho, I just wasnted to say this guy Roodin is cool in my book, and is probably a pretty smart porfessor (but still not as smrat as me lol!!) Id maybe like invite him for some Halo 3 and I could give him some ideas for his next book XDD

Holy crap guys!!, I just checked out this book called Princiapals of Matheamtical Anaslys by this geezer dude Roodin and, HOLY MOTHER OF GOAT it was FRICKIN INCREDIBLE LOL!!! This guy Roodin does tones of analyzing things in sorta like a math-y kinda way, wich is awesome for me because I just jioned Mensa like last year (my IQ has been mearured to be at like way over 180/180 GMAT SCORES) so everthings in these book is like hella smart lol!!

There were some parts tat were a little bit confusing, like what was all that stuff about metered spaces lol?? Quitre frankly, he probably just made all of that stuff up when like crazy bored 1 day LOL!! And then he talks about some wackyu tings like Leg Intervals (wtf is a leg interval LOL??!!?!) So, as they say in the math buisness, the exportation was perfunctional.

Anywho, I just wasnted to say this guy Roodin is cool in my book, and is porbably a pretty smart dude (but still not as smrat as me LOL!!) Id maybe like invite him for some Halo 3 and I could give him some ideas for his next book XDDDD

Imagine that some intelligent aliens have landed on earth and demand to know how far human beings have progressed in mathematics? You may want to start them off with Rudin. This book is a model of how to convey mathematics economically and precisely.

But for those learning the subject for the first time, the book falls short in providing the required motivation and linkages. Unless these are provided by a very good teacher, those studying from this book are likely to come away with a very formal and unintuitive understanding of the subject.

One antidote against this may be reading about the history of analysis to better appreciate how the foundational concepts of the subject evolved. Two books I can recommend for that purpose are The Calculus Gallery: Masterpieces from Newton to Lebesgue and Lebesgue's Theory of Integration: Its Origins and Development (AMS Chelsea Publishing Series) (Ams Chelsea Publishing Series).

Also, multivariate calculus is not best learnt from this book. Better treatments can be found in Murkres' Analysis on Manifolds and in Spivak's classic Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus.

I had to grow to like this book. After looking through it several times, I had realised that Rudin is not so bad. He has a lot of challenging exercises. I am still trying to find solutions to some today even after using this text in a course. I do not like chapters 10 and 11 too much though. I think Rudin should have done a better job.

If you didn't use this classic in your first pass at elementary
analysis, you owe it to yourself to find a copy and work
through as many exercises as possible ... especially if you
plan to go further to graduate level work in mathematics.
Other books that are increasingly used for this subject still
leave readers with a 'maturity/sophistication' gap relative to
more advanced texts in real analysis, etc.

A course at MIT based on this text is presented at the link
below, with suggested coverage, exercises, solutions, etc. -
[...]