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The use of Mathematica in performing computations takes the tediousness out of solving mathematical problems. The book is self-contained, and provides the material to learn the mathematics as well as programming skills to learn the Mathematica language.
A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.
This volume presents mathematical formulas and theorems commonly used in economics. It offers the first grouping of this material for a specifically economist audience, and it includes formulas like Roy’s identity and Leibniz's rule.
Mathematica is a computer program (software) for doing symbolic, numeric and graphical analysis of mathematical problems. In the hands of economists, financial analysts and other professionals in econometrics and the quantitative sector of economic and financial modeling, it can be an invaluable tool for modeling and simulation on a large number of issues and problems, besides easily grinding out numbers, doing statistical estimations and rendering graphical plots and visuals. Mathematica enables these individuals to do all of this in a unified environment. This book's main use is that of an applications handbook. Modeling in Economics and Finance with Mathematica is a compilation of contributed papers prepared by experienced, "hands on" users of the Mathematica program. They come from
This is a book on the basics of mathematics and computation and their uses in economics for modern day students and practitioners. The reader is introduced to the basics of numerical analysis as well as the use of computer programs such as Matlab and Excel in carrying out involved computations. Sections are devoted to the use of Maple in mathematical analysis. Examples drawn from recent contributions to economic theory and econometrics as well as a variety of end of chapter exercises help to illustrate and apply the presented concepts.
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.
The ability to conceptualize an economic problem verbally, to formulate it as a mathematical model, and then represent the mathematics in software so that the model can be solved on a computer is a crucial skill for economists. Computational Economics contains well-known models--and some brand-new ones--designed to help students move from verbal to mathematical to computational representations in economic modeling. The authors' focus, however, is not just on solving the models, but also on developing the ability to modify them to reflect one's interest and point of view. The result is a book that enables students to be creative in developing models that are relevant to the economic problems of their times. Unlike other computational economics textbooks, this book is organized around economic topics, among them macroeconomics, microeconomics, and finance. The authors employ various software systems--including MATLAB, Mathematica, GAMS, the nonlinear programming solver in Excel, and the database systems in Access--to enable students to use the most advantageous system. The book progresses from relatively simple models to more complex ones, and includes appendices on the ins and outs of running each program. The book is intended for use by advanced undergraduates and professional economists and even, as a first exposure to computational economics, by graduate students. Organized by economic topics Progresses from simple to more complex models Includes instructions on numerous software systems Encourages customization and creativity
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.
Mathematics for Economists, a new text for advanced undergraduate and beginning graduate students in economics, is a thoroughly modern treatment of the mathematics that underlies economic theory. An abundance of applications to current economic analysis, illustrative diagrams, thought-provoking exercises, careful proofs, and a flexible organisation-these are the advantages that Mathematics for Economists brings to today's classroom.
A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.