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Pi And The Agm


Pi And The Agm


File Size : 41,5 Mb
Total Download : 484

Author : Jonathan M. Borwein
language : en
Publisher: Wiley-Interscience
Release Date : 1998-07-13



Download Pi And The Agm written by Jonathan M. Borwein and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-13 with Mathematics categories.


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

Pi Unleashed


Pi Unleashed


File Size : 45,9 Mb
Total Download : 304

Author : Jörg Arndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2001



Download Pi Unleashed written by Jörg Arndt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.


CD-ROM contains: hfloat; 400,000,000 decimal places of pi; tutorial on the Fast Fourier Transformation; arithmetical algorithms for high precision; codes from the text; additional C-programs.

Pi The Next Generation


Pi The Next Generation


File Size : 45,5 Mb
Total Download : 621

Author : David H. Bailey
language : en
Publisher: Springer
Release Date : 2016-07-19



Download Pi The Next Generation written by David H. Bailey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-19 with Mathematics categories.


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.

The Computer As Crucible


The Computer As Crucible


File Size : 50,7 Mb
Total Download : 595

Author : Jonathan Borwein
language : en
Publisher: CRC Press
Release Date : 2008-10-28



Download The Computer As Crucible written by Jonathan Borwein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-28 with Mathematics categories.


Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time.

Gems In Experimental Mathematics


Gems In Experimental Mathematics


File Size : 42,8 Mb
Total Download : 647

Author : Tewodros Amdeberhan
language : en
Publisher: American Mathematical Soc.
Release Date : 2010



Download Gems In Experimental Mathematics written by Tewodros Amdeberhan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.


These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume. Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor. The development of a broad spectrum of mathematical software products, such as Mathematica® and Maple™ has allowed mathematicians of diverse backgrounds and interests to use the computer as an essential tool as part of their daily work environment. This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.

The Mathematical Function Computation Handbook


The Mathematical Function Computation Handbook


File Size : 52,6 Mb
Total Download : 375

Author : Nelson H.F. Beebe
language : en
Publisher: Springer
Release Date : 2017-08-20



Download The Mathematical Function Computation Handbook written by Nelson H.F. Beebe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-20 with Computers categories.


This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.

Experimental And Computational Mathematics


Experimental And Computational Mathematics


File Size : 43,5 Mb
Total Download : 773

Author : Jonathan M. Borwein
language : en
Publisher: PSIpress
Release Date : 2010



Download Experimental And Computational Mathematics written by Jonathan M. Borwein and has been published by PSIpress this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Experimental mathematics categories.


A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.