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3 books match the query 'Economics, Mathematical'
Analytical Methods in Economics
Akira Takayama
University of Michigan Press, 1993
In Analytical Methods in Economics Akira Takayama presents an exposition of the essential mathematical tools of economics and illustrates their applications to selected economic problems. Drawing on his own teaching experiences and research to provide concrete macro- and microeconomic illustrations of the concepts featured, Takayama clarifies the unifying analytical structure of economic theory and elucidates the mathematical tools that underlie it.Following a thorough review of preliminary mathematical tools, Takayama discusses the nonlinear programming, uncertainty, differential equations, and optimal control theory. Emphasizing "why" rather than "how-to" questions, the author focuses on explanation, considerations of motivation, and economic application.Analytical Methods is designed to enable economists, graduate students, and advanced undergraduates in economics to achieve a high level of comfort in the use of analytical techniques.
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How Economics Became a Mathematical Science
E. Roy Weintraub
Duke University Press, 2002
In How Economics Became a Mathematical Science E. Roy Weintraub traces the history of economics through the prism of the history of mathematics in the twentieth century. As mathematics has evolved, so has the image of mathematics, explains Weintraub, such as ideas about the standards for accepting proof, the meaning of rigor, and the nature of the mathematical enterprise itself. He also shows how economics itself has been shaped by economists’ changing images of mathematics.
Whereas others have viewed economics as autonomous, Weintraub presents a different picture, one in which changes in mathematics—both within the body of knowledge that constitutes mathematics and in how it is thought of as a discipline and as a type of knowledge—have been intertwined with the evolution of economic thought. Weintraub begins his account with Cambridge University, the intellectual birthplace of modern economics, and examines specifically Alfred Marshall and the Mathematical Tripos examinations—tests in mathematics that were required of all who wished to study economics at Cambridge. He proceeds to interrogate the idea of a rigorous mathematical economics through the connections between particular mathematical economists and mathematicians in each of the decades of the first half of the twentieth century, and thus describes how the mathematical issues of formalism and axiomatization have shaped economics. Finally, How Economics Became a Mathematical Science reconstructs the career of the economist Sidney Weintraub, whose relationship to mathematics is viewed through his relationships with his mathematician brother, Hal, and his mathematician-economist son, the book’s author.
Whereas others have viewed economics as autonomous, Weintraub presents a different picture, one in which changes in mathematics—both within the body of knowledge that constitutes mathematics and in how it is thought of as a discipline and as a type of knowledge—have been intertwined with the evolution of economic thought. Weintraub begins his account with Cambridge University, the intellectual birthplace of modern economics, and examines specifically Alfred Marshall and the Mathematical Tripos examinations—tests in mathematics that were required of all who wished to study economics at Cambridge. He proceeds to interrogate the idea of a rigorous mathematical economics through the connections between particular mathematical economists and mathematicians in each of the decades of the first half of the twentieth century, and thus describes how the mathematical issues of formalism and axiomatization have shaped economics. Finally, How Economics Became a Mathematical Science reconstructs the career of the economist Sidney Weintraub, whose relationship to mathematics is viewed through his relationships with his mathematician brother, Hal, and his mathematician-economist son, the book’s author.
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Increasing Returns and Path Dependence in the Economy
W. Brian Arthur
University of Michigan Press, 1994
In Complexity, the widely applauded work by Mitchell Waldrop that introduced the exciting and important work of the Santa Fe Institute to a wide audience, Brian Arthur and his ideas played a pivotal role and were shown connecting creatively with the many aspects of the Institute's work. This book brings together Professor Arthur's pioneering articles and provides a comprehensive presentation of his exciting vision of an economics that incorporates increasing returns. After a decade of resis-tance from economists, these ideas are now being widely discussed and adopted, as Kenneth Arrow recounts in his foreword. In fundamental ways they are changing our views of the working economy. The essential ideas are first introduced at a popular level with an article originally published in the Scientific American. They are then shown in powerful and convincing application to a variety of questions, including competition between technologies and the development of industrial clusters such as Silicon Valley. The volume also contains the technical articles that underpin the creation of this important and original work in economics. Brian Arthur's work establishes a whole new domain for economics, a new perspective on many contemporary economic problems, and an explanation for many puzzling features of the high technology economy. This book provides the ideal introduction to and a comprehensive exposition of Arthur's work.
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