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Author: Michael Carter Publisher: MIT Press ISBN: 9780262531924 Category : Business & Economics Languages : en Pages : 678
Book Description
This book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics. Features include an extended presentation of separation theorems and their applications, an account of constraint qualification in constrained optimization, and an introduction to monotone comparative statics. These topics are developed by way of more than 800 exercises. The book is designed to be used as a graduate text, a resource for self-study, and a reference for the professional economist.
Author: Michael Carter Publisher: MIT Press ISBN: 9780262531924 Category : Business & Economics Languages : en Pages : 678
Book Description
This book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics. Features include an extended presentation of separation theorems and their applications, an account of constraint qualification in constrained optimization, and an introduction to monotone comparative statics. These topics are developed by way of more than 800 exercises. The book is designed to be used as a graduate text, a resource for self-study, and a reference for the professional economist.
Author: E. Roy Weintraub Publisher: Duke University Press ISBN: 0822383802 Category : Business & Economics Languages : en Pages : 329
Book Description
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.
Author: Vasily E. Tarasov Publisher: MDPI ISBN: 303936118X Category : Business & Economics Languages : en Pages : 278
Book Description
This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.
Author: Michael Hoy Publisher: MIT Press ISBN: 9780262582018 Category : Business & Economics Languages : en Pages : 164
Book Description
This text offers a presentation of the mathematics required to tackle problems in economic analysis. After a review of the fundamentals of sets, numbers, and functions, it covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics.
Author: Kelvin Lancaster Publisher: Courier Corporation ISBN: 0486145042 Category : Mathematics Languages : en Pages : 450
Book Description
Graduate-level text provides complete and rigorous expositions of economic models analyzed primarily from the point of view of their mathematical properties, followed by relevant mathematical reviews. Part I covers optimizing theory; Parts II and III survey static and dynamic economic models; and Part IV contains the mathematical reviews, which range fromn linear algebra to point-to-set mappings.
Author: Rakesh V. Vohra Publisher: Psychology Press ISBN: 9780415700085 Category : Business & Economics Languages : en Pages : 212
Book Description
This textbook presents students with all they need for advancing in mathematical economics. Higher level undergraduates as well as postgraduate students in mathematical economics will find this book extremely useful.
Author: Reghinos D. Theocharis Publisher: Springer ISBN: 1349129925 Category : Business & Economics Languages : en Pages : 362
Book Description
This sequel to the author's "Early Development in Mathematical Economics" covers developments in this field after the appearance of Cournot's "Recherches" in 1838 and until the publication of Jevons' "Theory" in 1871.
Author: Jean-Pierre Aubin Publisher: Courier Corporation ISBN: 048646265X Category : Mathematics Languages : en Pages : 658
Book Description
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.
Author: Michael Carter
Author: Michael Carter
Author: E. Roy Weintraub
Author: Vasily E. Tarasov
Author: Michael Hoy
Author: Kelvin Lancaster
Author: Rakesh V. Vohra
Author: Reghinos D. Theocharis
Author: Akira Takayama
Author: Reghinos D. Theocharis
Author: Jean-Pierre Aubin