Huygens and Barrow, Newton and Hooke

Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals

Author: Vladimir I. Arnold

Publisher: Birkhäuser

ISBN: 3034891296

Category: Mathematics

Page: 118

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Translated from the Russian by E.J.F. Primrose "Remarkable little book." -SIAM REVIEW V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.

The Unreasonable Effectiveness of Number Theory

Author: Stefan Andrus Burr,George E. Andrews

Publisher: American Mathematical Soc.

ISBN: 9780821855010

Category: Mathematics

Page: 125

View: 540

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This book is based on the AMS Short Course, The Unreasonable Effectiveness of Number Theory, held in Orono, Maine, in August 1991. This Short Course provided some views into the great breadth of applications of number theory outside cryptology and highlighted the power and applicability of number-theoretic ideas. Because number theory is one of the most accessible areas of mathematics, this book will appeal to a general mathematical audience as well as to researchers in other areas of science and engineering who wish to learn how number theory is being applied outside of mathematics. All of the chapters are written by leading specialists in number theory and provides excellent introduction to various applications.

Catastrophe Theory

Author: Vladimir I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 3642581242

Category: Mathematics

Page: 150

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The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.

Optimization

Insights and Applications

Author: Jan Brinkhuis,Vladimir Tikhomirov

Publisher: Princeton University Press

ISBN: 9781400829361

Category: Mathematics

Page: 680

View: 4453

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This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.

Chaos, Gaia, Eros

A Chaos Pioneer Uncovers the Three Great Streams of History

Author: Ralph Abraham

Publisher: Harper San Francisco

ISBN: N.A

Category: Philosophy

Page: 263

View: 3374

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A modern philosophy suggests that there are three main forces working to shape our lives

Choice

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

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Spirals

from Theodorus to chaos

Author: Philip J. Davis,Walter Gautschi,A. Iserles

Publisher: A K Peters Ltd

ISBN: N.A

Category: Mathematics

Page: 237

View: 1492

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Quantum Field Theory

Competitive Models

Author: Bertfried Fauser,Jürgen Tolksdorf,Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 376438736X

Category: Science

Page: 436

View: 393

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The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.

Quicksilver

The Baroque Cycle #1

Author: Neal Stephenson

Publisher: Harper Collins

ISBN: 0060833165

Category: Fiction

Page: 480

View: 1075

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In which Daniel Waterhouse, fearless thinker and courageous Puritan, pursues knowledge in the company of the greatest minds of Baroque-era Europe -- in a chaotic world where reason wars with the bloody ambitions of the mighty, and where catastrophe, natural or otherwise, can alter the political landscape overnight.