MATHEMATICS BY EXPERIMENT 2ND EDITION PLAUSIBLE REASONING IN THE 21ST CENTURY

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Author : Jonathan M. Borwein
ISBN : 1568812116
Genre : Computers
File Size : 75.17 MB
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This new approach to mathematics---the utilization of advanced computing technology in mathematical research---is often called experimental mathematics. The computer provides the mathematician with a "laboratory" in which she can perform experiments---analyzing examples, testing out new ideas, or searching for patterns. This book presents the rationale and historical context of experimental mathematics, and includes a series of examples that best portray the experimental methodology. For more examples and insights, the book, "Experimentation in Mathematics: Computational Paths to Discovery" is a highly recommended companion.

Author : Jonathan Borwein
ISBN : 9781439865361
Genre : Mathematics
File Size : 23.7 MB
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This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational Paths to Discovery is a highly recommended companion.

Author : Jonathan M. Borwein
ISBN : 1568811365
Genre : Mathematics
File Size : 74.85 MB
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New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and replicating experiments. The authors address the role of experimental research in the statement of new hypotheses and the discovery of new results that chart the road to future developments. Following the lead of Mathematics by Experiment: Plausible Reasoning in the 21st Century this book gives numerous additional case studies of experimental mathematics in action, ranging from sequences, series, products, integrals, Fourier series, zeta functions, partitions, primes and polynomials. Some advanced numerical techniques are also presented. To get a taste of the material presented in both books view the condensed version.

Author : David H. Bailey
ISBN : 156881271X
Genre : Computers
File Size : 43.77 MB
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With the continued advance of computing power and accessibility, the view that “real mathematicians don't compute” no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doing to highlight some of the key algorithms and to teach some of the key experimental approaches. This book is an excellent choice for researchers [in mathematics] interested in exploring new avenues.

Author : Peter Dear
ISBN : 0226139433
Genre : Science
File Size : 67.50 MB
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Although the Scientific Revolution has long been regarded as the beginning of modern science, there has been little consensus about its true character. While the application of mathematics to the study of the natural world has always been recognized as an important factor, the role of experiment has been less clearly understood. Peter Dear investigates the nature of the change that occurred during this period, focusing particular attention on evolving notions of experience and how these developed into the experimental work that is at the center of modern science. He examines seventeenth-century mathematical sciences—astronomy, optics, and mechanics—not as abstract ideas, but as vital enterprises that involved practices related to both experience and experiment. Dear illuminates how mathematicians and natural philosophers of the period—Mersenne, Descartes, Pascal, Barrow, Newton, Boyle, and the Jesuits—used experience in their argumentation, and how and why these approaches changed over the course of a century. Drawing on mathematical texts and works of natural philosophy from all over Europe, he describes a process of change that was gradual, halting, sometimes contradictory—far from the sharp break with intellectual tradition implied by the term "revolution."

Author : Stephen Jay Gould
ISBN : 9780393340402
Genre : Science
File Size : 65.58 MB
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The definitive refutation to the argument of The Bell Curve. When published in 1981, The Mismeasure of Man was immediately hailed as a masterwork, the ringing answer to those who would classify people, rank them according to their supposed genetic gifts and limits. And yet the idea of innate limits—of biology as destiny—dies hard, as witness the attention devoted to The Bell Curve, whose arguments are here so effectively anticipated and thoroughly undermined by Stephen Jay Gould. In this edition Dr. Gould has written a substantial new introduction telling how and why he wrote the book and tracing the subsequent history of the controversy on innateness right through The Bell Curve. Further, he has added five essays on questions of The Bell Curve in particular and on race, racism, and biological determinism in general. These additions strengthen the book's claim to be, as Leo J. Kamin of Princeton University has said, "a major contribution toward deflating pseudo-biological 'explanations' of our present social woes."