Qualitative Computing: A Computational Journey into Nonlinearity - Couverture rigide

Chatelin, Francoise

 
9789814322928: Qualitative Computing: A Computational Journey into Nonlinearity
Couverture rigide
ISBN 10 : 981432292X ISBN 13 : 9789814322928
Editeur : World Scientific Publishing Co Pte Ltd, 2012

Synopsis

High technology industries are in desperate need for adequate tools to assess the validity of simulations produced by ever faster computers for perennial unstable problems. In order to meet these industrial expectations, applied mathematicians are facing a formidable challenge summarized by these words -- nonlinearity and coupling. This book is unique as it proposes truly original solutions: (1) Using hypercomputation in quadratic algebras, as opposed to the traditional use of linear vector spaces in the 20th century; (2) complementing the classical linear logic by the complex logic which expresses the creative potential of the complex plane.The book illustrates how qualitative computing has been the driving force behind the evolution of mathematics since Pythagoras presented the first incompleteness result about the irrationality of √2. The celebrated results of Gödel and Turing are but modern versions of the same idea: the classical logic of Aristotle is too limited to capture the dynamics of nonlinear computation. Mathematics provides us with the missing tool, the organic logic, which is aptly tailored to model the dynamics of nonlinearity. This logic will be the core of the "Mathematics for Life" to be developed during this century.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

High technology industries are in desperate need for adequate tools to assess the validity of simulations produced by ever faster computers for perennial unstable problems. In order to meet these industrial expectations, applied mathematicians are facing a formidable challenge summarized by these words - nonlinearity and coupling. This book is unique as it proposes truly original solutions: (1) Using hypercomputation in quadratic algebras, as opposed to the traditional use of linear vector spaces in the 20th century; (2) complementing the classical linear logic by the complex logic which expresses the creative potential of the complex plane. The book illustrates how qualitative computing has been the driving force behind the evolution of mathematics since Pythagoras presented the first incompleteness result about the irrationality of ?2. The celebrated results of Gödel and Turing are but modern versions of the same idea: the classical logic of Aristotle is too limited to capture the dynamics of nonlinear computation. Mathematics provides us with the missing tool, the organic logic, which is aptly tailored to model the dynamics of nonlinearity. This logic will be the core of the “Mathematics for Life” to be developed during this century.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
World Scientific Publishing Co Pte Ltd
Date d'édition
2012
Langue
anglais
ISBN 10 
981432292X
ISBN 13 
9789814322928
Reliure
Relié
Nombre de pages
600
Coordonnées du fabricant
non disponible
Personne responsable
non disponible