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Pi And The Agm
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Book Synopsis Pi and the AGM by : Jonathan M. Borwein
Download or read book Pi and the AGM written by Jonathan M. Borwein and published by Wiley-Interscience. This book was released on 1998-07-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critical Acclaim for Pi and the AGM: "Fortunately we have the Borwein's beautiful book . . . explores in the first five chapters the glorious world so dear to Ramanujan . . . would be a marvelous text book for a graduate course."--Bulletin of the American Mathematical Society "What am I to say about this quilt of a book? One is reminded of Debussy who, on being asked by his harmony teacher to explain what rules he was following as he improvised at the piano, replied, "Mon plaisir." The authors are cultured mathematicians. They have selected what has amused and intrigued them in the hope that it will do the same for us. Frankly, I cannot think of a more provocative and generous recipe for writing a book . . . (it) is cleanly, even beautifully written, and attractively printed and composed. The book is unique. I cannot think of any other book in print which contains more than a smidgen of the material these authors have included.--SIAM Review "If this subject begins to sound more interesting than it did in the last newspaper article on 130 million digits of Pi, I have partly succeeded. To succeed completely I will have gotten you interested enough to read the delightful and important book by the Borweins."--American Mathematical Monthly "The authors are to be commended for their careful presentation of much of the content of Ramanujan's famous paper, 'Modular Equations and Approximations to Pi'. This material has not heretofore appeared in book form. However, more importantly, Ramanujan provided no proofs for many of the claims that he made, and so the authors provided many of the missing details . . . The Borweins, indeed have helped us find the right roads."--Mathematics of Computation
Book Synopsis Pi and the AGM by : Jonathan M. Borwein
Download or read book Pi and the AGM written by Jonathan M. Borwein and published by Wiley-Interscience. This book was released on 1987-01-19 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new research revealing the interplay between classical analysis and modern computation and complexity theory. Two intimately interwoven threads run through the text: the arithmetic-geometric mean (AGM) iteration of Gauss, Lagrange, and Legendre and the calculation of pi.
Download or read book Pi - Unleashed written by Jörg Arndt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis From Analysis to Visualization by : David H. Bailey
Download or read book From Analysis to Visualization written by David H. Bailey and published by Springer Nature. This book was released on 2020-03-16 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students and researchers from all fields of mathematics are invited to read and treasure this special Proceedings. A conference was held 25 –29 September 2017 at Noah’s On the Beach, Newcastle, Australia, to commemorate the life and work of Jonathan M. Borwein, a mathematician extraordinaire whose untimely passing in August 2016 was a sorry loss to mathematics and to so many members of its community, a loss that continues to be keenly felt. A polymath, Jonathan Borwein ranks among the most wide ranging and influential mathematicians of the last 50 years, making significant contributions to an exceptional diversity of areas and substantially expanding the use of the computer as a tool of the research mathematician. The contributions in this commemorative volume probe Dr. Borwein's ongoing legacy in areas where he did some of his most outstanding work: Applied Analysis, Optimization and Convex Functions; Mathematics Education; Financial Mathematics; plus Number Theory, Special Functions and Pi, all tinged by the double prisms of Experimental Mathematics and Visualization, methodologies he championed.
Book Synopsis Pi: A Source Book by : J.L. Berggren
Download or read book Pi: A Source Book written by J.L. Berggren and published by Springer. This book was released on 2014-01-13 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pi: A Source Book by : Jonathan M. Borwein
Download or read book Pi: A Source Book written by Jonathan M. Borwein and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our intention in this collection is to provide, largely through original writings, an ex tended account of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. A surprising amount of the most important mathematics and a signifi cant number of the most important mathematicians have contributed to its unfolding directly or otherwise. Pi is one of the few mathematical concepts whose mention evokes a response of recog nition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty-five hundred years. The computation of pi is virtually the only topic from the most ancient stratum of mathematics that is still of serious interest to modern mathematical research. To pursue this topic as it developed throughout the millennia is to follow a thread through the history of mathematics that winds through geometry, analysis and special functions, numerical analysis, algebra, and number theory. It offers a subject that provides mathe maticians with examples of many current mathematical techniques as weIl as a palpable sense of their historical development. Why a Source Book? Few books serve wider potential audiences than does a source book. To our knowledge, there is at present no easy access to the bulk of the material we have collected.
Book Synopsis Modern Computer Arithmetic by : Richard P. Brent
Download or read book Modern Computer Arithmetic written by Richard P. Brent and published by Cambridge University Press. This book was released on 2010-11-25 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favorite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors.
Book Synopsis Turning Adversity to Advantage by : Nancy McGown Minor
Download or read book Turning Adversity to Advantage written by Nancy McGown Minor and published by University Press of America. This book was released on 2009-10-05 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tells the story of the Lipan Apaches, once one of the largest and most aggressive tribes of the Rio Grande region. The story of the history of the Lipan Apaches is a tale of survival and preservation in the face of incredible challenges.
Download or read book The AGM in Europe written by Anne Lafarre and published by Emerald Group Publishing. This book was released on 2017-11-02 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anne Lafarre combines wide ranging empirical legal and economic research to analyse and understand the real role of the AGM in the European businesses and corporate governance frameworks today.
Book Synopsis Theory of Correspondences by : Erwin Klein
Download or read book Theory of Correspondences written by Erwin Klein and published by Wiley-Interscience. This book was released on 1984 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pi: The Next Generation by : David H. Bailey
Download or read book Pi: The Next Generation written by David H. Bailey and published by Springer. This book was released on 2016-07-19 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Light Gray People by : Nancy McGown Minor
Download or read book The Light Gray People written by Nancy McGown Minor and published by University Press of America. This book was released on 2009-10-05 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although Lipan Apache culture was studied by one of the most eminent anthropologists of the twentieth century, many important questions remain. What is the meaning of the tribal name Lipan? Did Morris Opler's 1935 study of historical Lipan culture conform to practices seen by eighteenth century Spaniards? Only four in situ observations of Lipan Apache culture survive - observations made by a Spanish priest, a Spanish military officer, a Swiss botanist and an Anglo captive. Each source reveals fascinating insights into a hitherto unseen world of Lipan beliefs and practices. The sources reported, for example, that the Lipans were able to predict both solar and lunar eclipses, a practice which went far beyond the vision quest posited by Opler. The Light Gray People seeks to complete a comparative analysis of traditional Lipan Apache culture, as seen through the eyes of four eighteenth and nineteenth century observers and Morris Opler's theories.
Download or read book The Maple Book written by Frank Garvan and published by CRC Press. This book was released on 2001-11-28 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maple is a very powerful computer algebra system used by students, educators, mathematicians, statisticians, scientists, and engineers for doing numerical and symbolic computations. Greatly expanded and updated from the author's MAPLE V Primer, The MAPLE Book offers extensive coverage of the latest version of this outstanding software package, MAPL
Book Synopsis Matters Computational by : Jörg Arndt
Download or read book Matters Computational written by Jörg Arndt and published by Springer Science & Business Media. This book was released on 2010-10-01 with total page 980 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Equation for Every Occasion by : John M. Henshaw
Download or read book An Equation for Every Occasion written by John M. Henshaw and published by Johns Hopkins University Press. This book was released on 2016-06-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smartly conceived and fast paced, his book offers something for anyone curious about math and its impacts.
Book Synopsis Excursions in Calculus by : Robert M. Young
Download or read book Excursions in Calculus written by Robert M. Young and published by Cambridge University Press. This book was released on 1992 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the interplay between the two main currents of mathematics, the continuous and the discrete.
Book Synopsis Rules and Reasoning by : Guido Governatori
Download or read book Rules and Reasoning written by Guido Governatori and published by Springer Nature. This book was released on 2022-12-13 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the International Joint Conference on Rules and Reasoning, RuleML+RR 2022, held in Berlin, Germany, during September 26–28, 2022. This is the 6th conference of a new series, joining the efforts of two existing conference series, namely “RuleML” (International Web Rule Symposium) and “RR” (Web Reasoning and Rule Systems). The 18 full research papers presented in this book were carefully reviewed and selected from 54 submissions. The papers cover the following topics: answer set programming; foundations of nonmonotonic reasoning; datalog; queries over ontologies; proofs, error-tolerance, and rules; as well as agents and argumentation.
