Real Analysis with Economic Applications

By Efe A. Ok

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.

• Format: Hardcover
• Language: English
• ISBN: 0691117683
• ISBN13: 9780691117683
• Release Date: January 2007
• Publisher: Princeton University Press
• Length: 832 Pages
• Weight: 2.80 lbs.
• Dimensions: 1.6" x 6.4" x 9.3"

Customer Reviews

Gift for an economist -- he loves it and is reading and re-reading it

Bought this as a gift -- the economist/recipient loves it and is reading and re-reading it.

One of a kind

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.

Excellent Book

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.

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!

Great book for mathematical economics

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.