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Real Analysis with Economic Applications [Hardcover]

Efe A. Ok

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Book Description

22 Jan 2007

There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students.

The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory.

The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty.

This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.


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Review

"The book is intended as a textbook on real analysis for graduate students in economics. It is largely graduate level mathematics, and the students should have a solid undergraduate real analysis background. . . . The author's writing style is . . . in general quite attractive. The book should be quite successful for its intended purpose."--Gerald A. Heuer, Zentralblatt MATH

"Important and commendable, this indispensable resource should be highly prized by all concerned with courses on mathematics for economists and by graduate students working on economic theory. Rarely do books meet such high aspirations and carry out their aims, yet this one certainly does. Well written in an engaging style and impressively researched in the requirements of graduate students of economics and finance, Real Analysis with Economic Applications is sure to become the definitive work for its intended audience. Real Analysis with Economic Applications with its large number of economics applications and variety of exercises represents the single most important mathematical source for students of economics applications and it will be the book, for a long time to come, to which they will turn with confidence, as well as pleasure, in all questions of economic applications."--Current Engineering Practice

From the Inside Flap

"Because of its comprehensive coverage of the basic topics of real analysis that are of primary interest to economists, this is a much-needed contribution to the current selection of mathematics textbooks for students of economics, and it will be a good addition to any economist's library. It includes a large number of economics applications that will motivate students to learn the math, and its number and variety of exercises--forty to fifty in each chapter--is a further asset."--Susan Elmes, Columbia University

"This book is poised to be a standard reference. Its author gets high marks for care of execution and obvious devotion to, and command of, the topics."--Wei Xiong, Princeton University

"This very well written book displays its author's engaging style, and offers interesting questions between topics that make them entertaining to read through."--Darrell Duffie, Stanford University, author of Dynamic Asset Pricing Theory

"The idea of doing such a math book directed toward graduate students of economics and finance is an excellent one. There are many students who are interested in this topic, and--until now--the existing math books have not directed their examples and exercises toward an economics approach."--Salih Neftci, City University of New York


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Front Cover | Copyright | Table of Contents | Excerpt | Index
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Amazon.com: 4.1 out of 5 stars  12 reviews
18 of 20 people found the following review helpful
5.0 out of 5 stars Great book for mathematical economics 12 May 2007
By Bruno LEO - Published on Amazon.com
Format:Hardcover|Verified Purchase
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.
14 of 15 people found the following review helpful
5.0 out of 5 stars One of a kind 25 April 2009
By Heraclitus Junior - Published on Amazon.com
Format:Hardcover
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.
8 of 10 people found the following review helpful
2.0 out of 5 stars kindle edition is hopeless 25 Feb 2012
By John Smallberries - Published on Amazon.com
Format:Kindle Edition
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.
4 of 5 people found the following review helpful
5.0 out of 5 stars A Masterpiece! 12 April 2011
By Bohrs - Published on Amazon.com
Format:Hardcover|Verified Purchase
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
4 of 5 people found the following review helpful
5.0 out of 5 stars Excellent Book 4 Feb 2009
By Ivan Duran - Published on Amazon.com
Format:Hardcover|Verified Purchase
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.
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