Real Analysis with Economic Applications by Efe A. Ok (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Conte con mucha suerte y llegó un libro nuevo.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

⭐I am an MA student in mathematics and am planning on getting my PhD in economics so I bought this book for that reason. The most valuable parts of this book for me are the applications. I have taken 2 real analysis courses at the graduate level and I can tell this book is not written by a mathematician. There was one topic in this book that I couldn’t seem to put my finger on what he was trying to get across so I looked it up in one of my other real analysis books and it was clear and concise.That being said, I am trained to read math books. I prefer a certain style, clarity and mathematical writing. For a purely economics student I could see how this book would be easier to read. I give it 4 stars because while I pointed out one downfall it is not that big of a downfall. A lot of the topics in this book are very well covered. And the applications to economics are very good. I would buy it again and recommend it to someone pursuing their PhD in economics.

⭐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.

⭐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.

⭐Provides very detailed explanations and lots of problems with selected hints in the back. Helped me improve on my proofs a great deal! Would recommend to all economics grad students!

⭐The book is excellent. However, it came to me with many pages falling down, probabily because some product defect. More than that: some page are in the wrong place (page 64 came between pages 14 and 16).I really loved the text, though. The contents of the book are good. All topics are excellent.

⭐Great book! It presents a comprehensive and deep treatment of analysis. But some (undergrad) math background is required though. Worth every dollar.

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