This looks to be a 5-star book, and I'll be purchasing it, but only in its physical incarnation. The Kindle version is hopelessly mangled, if the free sample is representative.
In the sample chapter, take a look at exercises 3, 4, and 5, each of which involves a typeset object of interest (a thing being defined, or something to prove). Comparing the Kindle version with the "Look inside" page scan, the Kindle version substitutes a seemingly random other block of typesetting, in no way related to the original text.
Other problems include frequent setting of the "is a member of" symbol on a line all by itself, and the occasional "type" error in running text, eg, failing to distinguish between a script A, sans-serif A, and Roman A, or mis-setting super/subscripts. It is unclear how often this is a limitation of the Kindle's character set and how often it is a mis-transcription, but it leads to some real head-scratchers.
This is an excellent book.
It must be said that this is not an elementary real analysis book. If you have zero experience with real analysis you'll find this book hard to read. The author lists some prerequisites:
-Every monotonic sequence of real numbers in a closed and bounded interval converges in that interval.
-Every concave function defined on an open interval is continuos and quasiconcave.
-Every differentiable function on R is continuous, but not conversely.
-Every continuous real function defined on a closed and bounded interval attains its maximum.
-A set of vectors that spans Rn has at least n vectors.
-A linear function defined on Rn is continuous.
-The (Rieman) integral of every continuous function defined on a closed and bounded interval equals a finite number.
-The fundamental theorem od calculus
-The Mean value theorem.
According to the author, if you can sketch a quick informal argument regarding the validity of about half of them you are well prepared to read this book. All of these results are proved in the book.
The book covers topics that are well beyond classical introductory texts in real analysis, like Rudin.
If you are looking for a shortcut to understanding Mas-Colell's Microecon textbook, this is not the way to go. Of course, if you manage to read and understand this book, Microeconomics should be no problem. But this will take you a lot of time and effort.
If you already have some background in math, this is a great reference for concepts, theorems and proofs.
This is a must have for economists wishing to understand in depht graduate level econ textbooks
This book has a wealth of material on analysis. A quick perusal of the contents list should be enough to convince anyone, even working mathematicians, that this is a book worth having (see author's website for the content list.) Don't let "with economic applications" fool you, this is a highly rigorous, compendious, well-exposited tome on real analysis.
The economic focus means that some of the topics that are covered exhaustively in this book are rarely seen in books of this level (e.g., emphasis on fixed point theorems and correspondences). There is also a very good chapter on differential calculus on normed spaces -- a topic that is (inexplicably) left out of many other functional analysis books. Another excellent book which covers differential calculus is Zeidler's book on applied functional analysis, Zeidler's exposition is actually better than Ok's for those who are interested in this topic specifically.
Any economist who is already fairly comfortable with analysis will enjoy this book. Mathematicians will also find things they've probably not seen before in standard analysis courses or texts. As an added bonus, the economic applications provide some direct motivation for the material. Normally, it is rare to find a textbook on analysis which includes accessible and non-mathematical applications, but this book is filled with them. You rarely have to learn any economics to be able to appreciate the applications in this book.
However, that said, this book is not suitable as an introduction to analysis. Although it is self-contained, a level of mathematical maturity is necessary. Ideally, you should have a couple of undergraduate analysis courses behind you before you attempt this book. That is, you should be fairly comfortable with limits, continuity, convergence, metric spaces, etc.
The only serious complaint I have about the book is that occasionally, rigor gets in the way of clarity. Sometimes, proofs can get cumbersome. Certain parts of the book seemed to be unnecessarily complicated by excessive formalism.
This is an excellent real analysis book with a lot of material that fits perfectly any one's interests in economic theory. Other real analysis books out there do not cover things that are very important in economics, e.g, fix point theorems, correspondences, and convexity. This books covers all that and much more in a rigorous way so it also fits perfectly the needs of any math grad student, particularly if he/she has some interest in economics. I strongly recommend this book to any econ grad student who wants to learn the tools needed in economic theory.
A fantastic book which fills a gaping hole. I have yet to find a comparable book. Incredibly well-written with an embarrassingly large wealth of material. The ideal book for graduate students in mathematics, economics or mathematical economics. Any mathematician with a strong interest in Analysis and curiosity about economics (or any economist with a strong interest in mathematics) would do well to read and re-read this book!
This is a very interesting book that explains real analysis focusing on economics issues and, I must say, it does its job beautifully and with no lack of rigour. When it comes to the mathematical aspects of microeconomics, the book turns out to be even better. A great book that will help very much Mas-Colell's Microeconomic Theory readers.
Product Details :
Hardcover: 664 pages
Publisher: Princeton University Press (January 2, 2007)
Language: English
ISBN-10: 0691117683
ISBN-13: 978-0691117683
Product Dimensions: 6.5 x 1.6 x 9.4 inches
More Details about Real Analysis with Economic Applications 1st edition
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