Conservation Laws and Symmetry: Applications to Economics and Finance

Business & Finance, Economics, Microeconomics, Theory of Economics
Cover of the book Conservation Laws and Symmetry: Applications to Economics and Finance by , Springer Netherlands
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Author: ISBN: 9789401711456
Publisher: Springer Netherlands Publication: June 29, 2013
Imprint: Springer Language: English
Author:
ISBN: 9789401711456
Publisher: Springer Netherlands
Publication: June 29, 2013
Imprint: Springer
Language: English

Modem geometric methods combine the intuitiveness of spatial visualization with the rigor of analytical derivation. Classical analysis is shown to provide a foundation for the study of geometry while geometrical ideas lead to analytical concepts of intrinsic beauty. Arching over many subdisciplines of mathematics and branching out in applications to every quantitative science, these methods are, notes the Russian mathematician A.T. Fomenko, in tune with the Renais­ sance traditions. Economists and finance theorists are already familiar with some aspects of this synthetic tradition. Bifurcation and catastrophe theo­ ries have been used to analyze the instability of economic models. Differential topology provided useful techniques for deriving results in general equilibrium analysis. But they are less aware of the central role that Felix Klein and Sophus Lie gave to group theory in the study of geometrical systems. Lie went on to show that the special methods used in solving differential equations can be classified through the study of the invariance of these equations under a continuous group of transformations. Mathematicians and physicists later recognized the relation between Lie's work on differential equations and symme­ try and, combining the visions of Hamilton, Lie, Klein and Noether, embarked on a research program whose vitality is attested by the innumerable books and articles written by them as well as by biolo­ gists, chemists and philosophers.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Modem geometric methods combine the intuitiveness of spatial visualization with the rigor of analytical derivation. Classical analysis is shown to provide a foundation for the study of geometry while geometrical ideas lead to analytical concepts of intrinsic beauty. Arching over many subdisciplines of mathematics and branching out in applications to every quantitative science, these methods are, notes the Russian mathematician A.T. Fomenko, in tune with the Renais­ sance traditions. Economists and finance theorists are already familiar with some aspects of this synthetic tradition. Bifurcation and catastrophe theo­ ries have been used to analyze the instability of economic models. Differential topology provided useful techniques for deriving results in general equilibrium analysis. But they are less aware of the central role that Felix Klein and Sophus Lie gave to group theory in the study of geometrical systems. Lie went on to show that the special methods used in solving differential equations can be classified through the study of the invariance of these equations under a continuous group of transformations. Mathematicians and physicists later recognized the relation between Lie's work on differential equations and symme­ try and, combining the visions of Hamilton, Lie, Klein and Noether, embarked on a research program whose vitality is attested by the innumerable books and articles written by them as well as by biolo­ gists, chemists and philosophers.

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