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

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.