Overview

Mathematical aesthetics is not discussed as a separate discipline in other books than this, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as aesthetic and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, i.e. the results of integration depend on the integration path. The topic of nonintegrable systems has not been given much attention in other books. Hence we discuss techniques for dealing with such systems.Contents: Mathematical AestheticsNonintegrable SystemsCommutator MethodNonintegrability and the Arrow of TimeThe Gamma Equations as a Source of Fundamental Building BlocksA Study of Some Additional Solutions to the Gamma EquationsMathematical Aesthetics: Additional TopicsElements of the CalculusTheorem of the Calculus Requiring Path Independence for Integrable SystemsElements of TensorsElements of Determinant TheoryCurvilinear CoordinatesReadership: Graduate students, researchers in applied mathematics and mathematical analysis.

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9781299635784

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