Qualitative computing: a computational journey into nonlinearity
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
©2012
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 567-576) and index 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 [symbol]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 |
| Beschreibung: | 1 Online-Ressource (xv, 582 pages) |
| ISBN: | 9789814322928 9789814322935 981432292X 9814322938 |
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| spelling | Chaitin-Chatelin, Françoise Verfasser aut Qualitative computing a computational journey into nonlinearity Françoise Chatelin Singapore World Scientific ©2012 1 Online-Ressource (xv, 582 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 567-576) and index 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 [symbol]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 COMPUTERS / Computer Literacy bisacsh COMPUTERS / Computer Science bisacsh COMPUTERS / Data Processing bisacsh COMPUTERS / Hardware / General bisacsh COMPUTERS / Information Technology bisacsh COMPUTERS / Machine Theory bisacsh COMPUTERS / Reference bisacsh Algebra, Abstract fast Computer science / Mathematics fast Numbers, Complex fast Informatik Mathematik Computer science Mathematics Algebra, Abstract Numbers, Complex http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=478634 Aggregator Volltext |
| spellingShingle | Chaitin-Chatelin, Françoise Qualitative computing a computational journey into nonlinearity COMPUTERS / Computer Literacy bisacsh COMPUTERS / Computer Science bisacsh COMPUTERS / Data Processing bisacsh COMPUTERS / Hardware / General bisacsh COMPUTERS / Information Technology bisacsh COMPUTERS / Machine Theory bisacsh COMPUTERS / Reference bisacsh Algebra, Abstract fast Computer science / Mathematics fast Numbers, Complex fast Informatik Mathematik Computer science Mathematics Algebra, Abstract Numbers, Complex |
| title | Qualitative computing a computational journey into nonlinearity |
| title_auth | Qualitative computing a computational journey into nonlinearity |
| title_exact_search | Qualitative computing a computational journey into nonlinearity |
| title_full | Qualitative computing a computational journey into nonlinearity Françoise Chatelin |
| title_fullStr | Qualitative computing a computational journey into nonlinearity Françoise Chatelin |
| title_full_unstemmed | Qualitative computing a computational journey into nonlinearity Françoise Chatelin |
| title_short | Qualitative computing |
| title_sort | qualitative computing a computational journey into nonlinearity |
| title_sub | a computational journey into nonlinearity |
| topic | COMPUTERS / Computer Literacy bisacsh COMPUTERS / Computer Science bisacsh COMPUTERS / Data Processing bisacsh COMPUTERS / Hardware / General bisacsh COMPUTERS / Information Technology bisacsh COMPUTERS / Machine Theory bisacsh COMPUTERS / Reference bisacsh Algebra, Abstract fast Computer science / Mathematics fast Numbers, Complex fast Informatik Mathematik Computer science Mathematics Algebra, Abstract Numbers, Complex |
| topic_facet | COMPUTERS / Computer Literacy COMPUTERS / Computer Science COMPUTERS / Data Processing COMPUTERS / Hardware / General COMPUTERS / Information Technology COMPUTERS / Machine Theory COMPUTERS / Reference Algebra, Abstract Computer science / Mathematics Numbers, Complex Informatik Mathematik Computer science Mathematics |
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