Author: Jörg Arndt
Publisher: Springer Science & Business Media
ISBN: 3642567355
Category : Computers
Languages : en
Pages : 275
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Book Description
In the 4,000-year history of research into Pi, results have never been as prolific as present. This book describes, in easy-to-understand language, the latest and most fascinating findings of mathematicians and computer scientists in the field of Pi. Attention is focused on new methods of high-speed computation.
Author: David H. Bailey
Publisher: Springer
ISBN: 3319323776
Category : Mathematics
Languages : en
Pages : 507
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Book Description
This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., “Is pi normal?”), articles presenting new and often amazing techniques for computing digits of pi (e.g., the “BBP” algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are “normal”). This volume is a companion to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe “quadratically convergent” algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Moore’s Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.
Author: J.L. Berggren
Publisher: Springer
ISBN: 1475742177
Category : Mathematics
Languages : en
Pages : 812
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Book Description
This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein fall into various classes. First and foremost there is a selection from the mathematical and computational literature of four millennia. There is also a variety of historical studies on the cultural significance of the number. Additionally, there is a selection of pieces that are anecdotal, fanciful, or simply amusing. For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, and new translations of works by Viete and Huygen.
Author: Robert A. Nowlan
Publisher: Springer
ISBN: 9463008934
Category : Education
Languages : en
Pages : 24
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Book Description
The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”
Author: Kevin R. Grazier
Publisher: Springer
ISBN: 331954215X
Category : Science
Languages : en
Pages : 420
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Book Description
Informative, entertaining and upbeat, this book continues Grazier and Cass's exploration of how technology, science, and scientists are portrayed in Hollywood productions. Both big and small-screen productions are featured and their science content illuminated—first by the authors and subsequently by a range of experts from science and the film world. Starring roles in this volume are played by, among other things, computers (human and mechanical), artificial intelligences, robots, and spacecraft. Interviews with writers, producers, and directors of acclaimed science-themed films stand side by side with the perspectives of scientists, science fiction authors, and science advisors. The result is a stimulating and informative reading experience for the layperson and professional scientist or engineer alike. The book begins with a foreword by Zack Stentz, who co-wrote X-Men: First Class and Thor, and is currently a writer/producer on CW’s The Flash.
Author: Nathan Sidoli
Publisher: Springer Science & Business Media
ISBN: 3642367364
Category : Mathematics
Languages : en
Pages : 583
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Book Description
This book honors the career of historian of mathematics J.L. Berggren, his scholarship, and service to the broader community. The first part, of value to scholars, graduate students, and interested readers, is a survey of scholarship in the mathematical sciences in ancient Greece and medieval Islam. It consists of six articles (three by Berggren himself) covering research from the middle of the 20th century to the present. The remainder of the book contains studies by eminent scholars of the ancient and medieval mathematical sciences. They serve both as examples of the breadth of current approaches and topics, and as tributes to Berggren's interests by his friends and colleagues.
Author: Jonathan Borwein
Publisher: CRC Press
ISBN: 1439865361
Category : Mathematics
Languages : en
Pages : 393
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Book Description
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 P
Author: Elliott Ostler
Publisher: Lulu.com
ISBN: 0996674101
Category : Education
Languages : en
Pages : 392
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Book Description
STEMathematics is an instructional resource designed primarily for secondary level mathematics teachers and students interested in discovering how mathematics describes (and is applied to) our natural world. This resource provides both the historical elements and the technical aspects of various topics in mathematics that provide instructional context in the sciences, technology, and engineering, (STEM) disciplines. The purpose of STEMathematics is to help teachers become more personally interested in the topics they teach and to gain a broader perspective of how mathematics can be integrated with other subject disciplines.
Author: Stenio Musich
Publisher: Stenio Musich
ISBN: 6500981073
Category : Mathematics
Languages : en
Pages : 1050
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Book Description
M.U.S. (Mathematical Uniform Space) is a new number of π (pi), representing the reality of the Universe in which we live. With this number, we created a new geometry, Hyperelliptical Geometry, which will provide the unification of physics, thus uniting the Theory of Relativity and Quantum Theory. A new geometry for a new Mathematics and a new Physics. (ISBN 978-65-00-98107-0).
Author: Jörg Arndt
Publisher: Springer Science & Business Media
ISBN: 364214764X
Category : Computers
Languages : en
Pages : 966
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Book Description
This book provides algorithms and ideas for computationalists. Subjects treated include low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Various optimization techniques are described and the actual performance of many given implementations is examined. The focus is on material that does not usually appear in textbooks on algorithms. The implementations are done in C++ and the GP language, written for POSIX-compliant platforms such as the Linux and BSD operating systems.
