Neverending Fractions

Author : Jonathan Borwein
Publisher : Cambridge University Press
ISBN 13 : 0521186498
Total Pages : 223 pages
Book Rating : 4.90/5 ( download)

DOWNLOAD NOW!

Download or read book Neverending Fractions written by Jonathan Borwein and published by Cambridge University Press. This book was released on 2014-07-03 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.

Author : Jonathan Borwein
Publisher : Cambridge University Press
ISBN 13 : 1139991396
Total Pages : 223 pages
Book Rating : 4.91/5 ( download)

DOWNLOAD NOW!

Download or read book Neverending Fractions written by Jonathan Borwein and published by Cambridge University Press. This book was released on 2014-07-03 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature subject. Beginning with a standard introduction to continued fractions, the book covers a diverse range of topics, from elementary and metric properties, to quadratic irrationals, to more exotic topics such as folded continued fractions and Somos sequences. Along the way, the authors reveal some amazing applications of the theory to seemingly unrelated problems in number theory. Previously scattered throughout the literature, these applications are brought together in this volume for the first time. A wide variety of exercises guide readers through the material, which will be especially helpful to readers using the book for self-study, and the authors also provide many pointers to the literature.

Author : Tomas Sauer
Publisher : Springer Nature
ISBN 13 : 3030843602
Total Pages : 275 pages
Book Rating : 4.01/5 ( download)

DOWNLOAD NOW!

Download or read book Continued Fractions and Signal Processing written by Tomas Sauer and published by Springer Nature. This book was released on 2021-09-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Besides their well-known value in number theory, continued fractions are also a useful tool in modern numerical applications and computer science. The goal of the book is to revisit the almost forgotten classical theory and to contextualize it for contemporary numerical applications and signal processing, thus enabling students and scientist to apply classical mathematics on recent problems. The books tries to be mostly self-contained and to make the material accessible for all interested readers. This provides a new view from an applied perspective, combining the classical recursive techniques of continued fractions with orthogonal problems, moment problems, Prony’s problem of sparse recovery and the design of stable rational filters, which are all connected by continued fractions.

Author : David H. Bailey
Publisher : Springer
ISBN 13 : 3319323776
Total Pages : 507 pages
Book Rating : 4.70/5 ( download)

DOWNLOAD NOW!

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.

Author : Alin Bostan
Publisher : Springer Nature
ISBN 13 : 3030843041
Total Pages : 544 pages
Book Rating : 4.45/5 ( download)

DOWNLOAD NOW!

Download or read book Transcendence in Algebra, Combinatorics, Geometry and Number Theory written by Alin Bostan and published by Springer Nature. This book was released on 2021-11-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Author : Jürgen Sander
Publisher : Springer
ISBN 13 : 3319282034
Total Pages : 552 pages
Book Rating : 4.39/5 ( download)

DOWNLOAD NOW!

Download or read book From Arithmetic to Zeta-Functions written by Jürgen Sander and published by Springer. This book was released on 2016-12-29 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

Author : Thomas A. Garrity
Publisher : Cambridge University Press
ISBN 13 : 1009009192
Total Pages : 417 pages
Book Rating : 4.95/5 ( download)

DOWNLOAD NOW!

Download or read book All the Math You Missed written by Thomas A. Garrity and published by Cambridge University Press. This book was released on 2021-07 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fill in any gaps in your knowledge with this overview of key topics in undergraduate mathematics, now with four new chapters.

Author : François Brunault
Publisher : Cambridge University Press
ISBN 13 : 1108889190
Total Pages : 185 pages
Book Rating : 4.93/5 ( download)

DOWNLOAD NOW!

Download or read book Many Variations of Mahler Measures written by François Brunault and published by Cambridge University Press. This book was released on 2020-05-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise introduction to the Mahler measure is a valuable resource for both graduate courses and self-study. It provides the reader with the necessary background material, before presenting the recent achievements and the remaining challenges in the field. The first part introduces the univariate Mahler measure and addresses Lehmer's question, and then discusses techniques of reducing multivariate measures to hypergeometric functions. The second part touches on the novelties of the subject, especially the relation with elliptic curves, modular forms and special values of L-functions. Finally, the Appendix presents the modern definition of motivic cohomology and regulator maps, as well as Deligne–Beilinson cohomology. The text includes many exercises to test comprehension and challenge readers of all abilities.

Author : Pierre Dardot
Publisher : Verso Books
ISBN 13 : 1786634759
Total Pages : 194 pages
Book Rating : 4.57/5 ( download)

DOWNLOAD NOW!

Download or read book Never Ending Nightmare written by Pierre Dardot and published by Verso Books. This book was released on 2019-04-16 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do we explain the strange survival of the forcesresponsible for the 2008 economic crisis, one of the worst since 1929? How do we explain the fact that neoliberalism has emerged from the crisis strengthened? When it broke, a number of the most prominent economists hastened to announce the 'death' of neoliberalism. They regarded the pursuit of neoliberal policy as the fruit of dogmatism. For Pierre Dardot and Christian Laval, neoliberalism is no mere dogma. Supported by powerful oligarchies, it is a veritable politico-institutional system that obeys a logic of self-reinforcement. Far from representing a break, crisis has become a formidably effective mode of government. In showing how this system crystallized and solidified, the book explains that the neoliberal straitjacket has succeeded in preventing any course correction by progressively deactivating democracy. Increasing the disarray and demobilization, the so-called 'governmental' Left has actively helped strengthen this oligarchical logic. The latter could lead to a definitive exit from democracy in favour of expertocratic governance, free of any control. However, nothing has been decided yet. The revival of democratic activity, which we see emerging in the political movements and experiments of recent years, is a sign that the political confrontation with the neoliberal system and the oligarchical bloc has already begun.

Author : Jonathan M. Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 1461466423
Total Pages : 395 pages
Book Rating : 4.20/5 ( download)

DOWNLOAD NOW!

Download or read book Number Theory and Related Fields written by Jonathan M. Borwein and published by Springer Science & Business Media. This book was released on 2013-05-16 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.​