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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.
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.
Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory
A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.
Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.
Quantitative Methods and Applications in GIS integrates GIS, spatial analysis, and quantitative methods to address various issues in socioeconomic studies and public policy. Methods range from basic regression analysis to advanced topics such as linear programming and system of equations. Applications vary from typical themes in urban and regional analysis - trade area analysis, accessibility measures, analysis of regional growth patterns, land use simulation - to issues related to crime and health analyses. The book covers common tasks such as distance and travel time estimation, spatial smoothing and interpolation, and accessibility measures. It also covers the major issues that are encountered in spatial analysis including modifiable areal unit problems, rate estimate of rare events in small populations, and spatial autocorrelation. Each chapter has one subject theme, introduces the method (or a group of related methods) most relevant to the theme, and then uses case studies to implement the method in a GIS environment.
Penguins jumping off a cliff, economic forecasters and financial advisors speculating against a currency, and farmers using traditional methods in India are all practising social learning. Such learning from the behavior of others may and does lead to herds, crashes, and booms. These issues have become, over the last ten years, an exciting field of research in theoretical and applied economics, finance, and in other social sciences. This book provides both an informal introduction and in-depth insights into the subject. Each chapter is devoted to a separate issue: individuals learn from the observations of actions, the outcomes of these actions, and from what others say. They may delay or make an immediate decision; they may compete against others or gain from cooperation; they make decisions about investment, crop choices, and financial investments. The book highlights the similarities and the differences between the various cases.

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