Real and Complex Analysis

by Walter Rudin

This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Genres: Mathematics, Textbooks, Science, Nonfiction, Academic, Technical, Physics

483 pages, Hardcover

First published January 1, 1970

Reviews

[Jacob]

This book works great as a reference (after having learned Real & Complex Analysis), but is a pain in the ass to learn it from. If you are looking for a good first text on Measure theory, I would recommend Eli Stein's book on Measure Theory or Folland's Real Analysis Everything contained in the book is useful, though - there are no throwaway theorems or rehashed proofs of earlier material. Most of what Rudin leaves out of the text shows up in the exercises - whether or not that is a plus to you really depends on how much you enjoy doing homework.

[Jace Davies]

Surveys the theorems, structures and proofs underpinning much of mathematics. Keep in mind that while comprehensive, it is not exhaustive. It presumes a great deal of maturity and a willingness to pause and explore a concept, often with other texts. The section on Hilbert Spaces, for instance, could be and has been dealt with in books of several hundred pages.

The exercises range from tricky to exceedingly challenging for anybody but the truly gifted, and a single solution could fill an entire tutorial.

[Thomas Bell]

This was a difficult book the first time I went through it. But it really is an incredible book and reference. Now, for the everyday person, this book would suck. But if you love math more than any normal person should, then this book is pretty awesome.

P.S. The answers to the odd problems are NOT in the back, and there is no instructors edition. :-)

[Wissam Raji]

A reference to abstract measure theory and to complex analysis. The book is difficult to navigate through for graduate students but must definitely be used as a supplementary reference for a course in measure theory. It comes as a shock if one wants to learn the basics of measure theory but not sure if it gets better or one gets more used to the dry language of this book.

[Liora Sophie]

Y'all let's be honest: Measure Theory is hella boring.
This book is a fair course companion but it's no page-turner.

[DJ]

supplementary text for math 525a

[Wissam Raji]

I cannot think of a better book to learn real analysis and its basic topics. Although the approach is an elite one but still a highly intuitive textbook that allows one to deeply understand the fundamentals of the theory. It might be a bit hard for undergraduates who haven't seen real analysis before. The problems in the book are worth solving...

[David Gentile]

Nightmare text. 5/5, every mathematician should read it. The proof of continuity for convex functions was honestly kind of funny.

[Aidan Farmayan]

AAAAAAAAAAHHHHHHHHH

[Hassaan Naeem]

Classic. Beautiful book.

[esteban]

saved my life type shit

[HikBook]

Chapter 3. Theorem. L^p(u) is a complete metric space, for 1<=p<=infinity and for every positive measure u.

Chapter 4.
4.5 Example (b). If u is any positive measure, L^2(u) is a Hilbert space with inner product
8f,g)=int_X f g du

[Suzanne]

if the emperor in star wars hadn't been thrown down the trash chute by darth vader, and he'd had another chance to torture luke skywalker, he would have pulled out this book. and not even the force would protect Luke then.

[Julia]

my rating is more representative my own [lack of] mathematical capability, rather than the merits of the book. it is great. possibly the greatest book on the subject. it's a shame I cannot understand it.

[sqrt2]

the pdf should be online somewhere. my professor has the first edition from when she took analysis, so m.rudin must be doing something right. but i recommend looking in a lot of other books if one really intends to understand what this book is alll about.

[Toivo Haapasaari]

Stopped after Radon-Nikodym, didnt get to Complex analysis stuff.

However the exposition in this book is really elegant and I hope to return after a short excurcion to functinal analysis and moreover *transfinite* mathematics.

[Detu]

too hard to read, but I'm trying to understand. It is kind of pure math book.

[Han Zhicheng]

If everyone could write a text as accessible as Walter Rudin did, my life will be much easier...

[Miikka Lahti]

The text is accessible albeit not easy. Some of the exercises however are far too difficult.