Qualitative computing : a computational journey into nonlinearity
 Responsibility
 Françoise Chatelin.
 Language
 English.
 Imprint
 Hackensack, N.J. : World Scientific, c2012.
 Physical description
 xv, 582 p. : ill ; 24 cm.
Access
Available online
 www.worldscientific.com World Scientific
 ebrary
Math & Statistics Library
Stacks
Call number  Status 

QA402.5 .C43 2012  Unknown 
More options
Creators/Contributors
 Author/Creator
 ChaitinChatelin, Françoise.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 567576) and index.
 Contents

 Introduction to Qualitative Computing Hypercomputation in Dickson Algebras Scales of Complexity and Linear Reachability Singular Values for the Multiplication Maps Computation Beyond Classical Logic Complexification of the Arithmetic Homotopic Deviation in Linear Algebra The Discrete and the Continuous Arithmetic in the Alternative Dickson Division Algebras The Real and the Complex.
 (source: Nielsen Book Data)
 Publisher's Summary
 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: Using hypercomputation in quadratic algebras, as opposed to the traditional use of linear vector spaces in the 20th century; and 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 Godel 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.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2012
 ISBN
 9789814322928 (hbk.)
 981432292X (hbk.)