In Pursuit Of Zeta 3

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In Pursuit of Zeta-3

Paul J. Nahin
In Pursuit of Zeta 3 Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 342 pages
File Size : 53,5 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9780691206073

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In Pursuit of Zeta-3 by Paul J. Nahin Pdf

"For centuries, mathematicians have tried, and failed, to solve the zeta-3 problem. This problem is simple in its formulation, but remains unsolved to this day, despite the attempts of some of the world's greatest mathematicians to solve it. The problem can be stated as follows: is there a simple symbolic formula for the following sum: 1+(1/2)^3+(1/3)^3+(1/4)^3+...? Although it is possible to calculate the approximate numerical value of the sum (for those interested, it's 1.20205...), there is no known symbolic expression. A symbolic formula would not only provide an exact value for the sum, but would allow for greater insight into its characteristics and properties. The answers to these questions are not of purely academic interest; the zeta-3 problem has close connections to physics, engineering, and other areas of mathematics. Zeta-3 arises in quantum electrodynamics and in number theory, for instance, and it is closely connected to the Riemann hypothesis. In In Pursuit of zeta-3, Paul Nahin turns his sharp, witty eye on the zeta-3 problem. He describes the problem's history, and provides numerous "challenge questions" to engage readers, along with Matlab code. Unlike other, similarly challenging problems, anyone with a basic mathematical background can understand the problem-making it an ideal choice for a pop math book"--

In Pursuit of Zeta-3

Paul J. Nahin
In Pursuit of Zeta 3 Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 342 pages
File Size : 50,9 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9780691227597

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In Pursuit of Zeta-3 by Paul J. Nahin Pdf

An engrossing look at the history and importance of a centuries-old but still unanswered math problem For centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem. Math genius Leonhard Euler attempted it in the 1700s and came up short. The straightforward puzzle considers if there exists a simple symbolic formula for the following: 1+(1/2)^3+(1/3)^3+(1/4)^3+. . . . But why is this issue—the sum of the reciprocals of the positive integers cubed—so important? With In Pursuit of Zeta-3, popular math writer Paul Nahin investigates the history and significance of this mathematical conundrum. Drawing on detailed examples, historical anecdotes, and even occasionally poetry, Nahin sheds light on the richness of the nature of zeta-3. He shows its intimate connections to the Riemann hypothesis, another mathematical mystery that has stumped mathematicians for nearly two centuries. He looks at its links with Euler’s achievements and explores the modern research area of Euler sums, where zeta-3 occurs frequently. An exact solution to the zeta-3 question wouldn’t simply satisfy pure mathematical interest: it would have critical ramifications for applications in physics and engineering, such as quantum electrodynamics. Challenge problems with detailed solutions and MATLAB code are included at the end of each of the book’s sections. Detailing the trials and tribulations of mathematicians who have approached one of the field’s great unsolved riddles, In Pursuit of Zeta-3 will tantalize curious math enthusiasts everywhere.

Dr. Euler's Fabulous Formula

Paul J. Nahin
Dr Euler s Fabulous Formula Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 416 pages
File Size : 54,9 Mb
Release : 2017-04-04
Category : Mathematics
ISBN : 9780691175911

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Dr. Euler's Fabulous Formula by Paul J. Nahin Pdf

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

When Least Is Best

Paul J. Nahin
When Least Is Best Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 406 pages
File Size : 41,8 Mb
Release : 2021-05-18
Category : Mathematics
ISBN : 9780691218762

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When Least Is Best by Paul J. Nahin Pdf

A mathematical journey through the most fascinating problems of extremes and how to solve them What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes—with values becoming as small (or as large) as possible—and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.

Number-Crunching

Paul J. Nahin
Number Crunching Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 406 pages
File Size : 55,8 Mb
Release : 2011-08-08
Category : Mathematics
ISBN : 9781400839582

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Number-Crunching by Paul J. Nahin Pdf

More stimulating mathematics puzzles from bestselling author Paul Nahin How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions. Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

Mrs. Perkins's Electric Quilt

Paul J. Nahin
Mrs Perkins s Electric Quilt Book PDF

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 424 pages
File Size : 51,6 Mb
Release : 2009-08-17
Category : Mathematics
ISBN : 9781400833467

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Mrs. Perkins's Electric Quilt by Paul J. Nahin Pdf

An incomparable collection of stimulating math puzzles from bestselling author Paul Nahin What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself. In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems—some three dozen in all—that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end. Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class—and anyone who enjoys popular math books.

Prime Obsession

John Derbyshire
Prime Obsession Book PDF

Author : John Derbyshire
Publisher : Joseph Henry Press
Page : 446 pages
File Size : 50,5 Mb
Release : 2003-04-15
Category : Science
ISBN : 9780309141253

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Prime Obsession by John Derbyshire Pdf

In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.

Do Not Erase

Jessica Wynne
Do Not Erase Book PDF

Author : Jessica Wynne
Publisher : Princeton University Press
Page : 248 pages
File Size : 40,9 Mb
Release : 2021-06-22
Category : Mathematics
ISBN : 9780691222820

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Do Not Erase by Jessica Wynne Pdf

A photographic exploration of mathematicians’ chalkboards “A mathematician, like a painter or poet, is a maker of patterns,” wrote the British mathematician G. H. Hardy. In Do Not Erase, photographer Jessica Wynne presents remarkable examples of this idea through images of mathematicians’ chalkboards. While other fields have replaced chalkboards with whiteboards and digital presentations, mathematicians remain loyal to chalk for puzzling out their ideas and communicating their research. Wynne offers more than one hundred stunning photographs of these chalkboards, gathered from a diverse group of mathematicians around the world. The photographs are accompanied by essays from each mathematician, reflecting on their work and processes. Together, pictures and words provide an illuminating meditation on the unique relationships among mathematics, art, and creativity. The mathematicians featured in this collection comprise exciting new voices alongside established figures, including Sun-Yung Alice Chang, Alain Connes, Misha Gromov, Andre Neves, Kasso Okoudjou, Peter Shor, Christina Sormani, Terence Tao, Claire Voisin, and many others. The companion essays give insights into how the chalkboard serves as a special medium for mathematical expression. The volume also includes an introduction by the author, an afterword by New Yorker writer Alec Wilkinson, and biographical information for each contributor. Do Not Erase is a testament to the myriad ways that mathematicians use their chalkboards to reveal the conceptual and visual beauty of their discipline—shapes, figures, formulas, and conjectures created through imagination, argument, and speculation.

Prime Numbers and the Riemann Hypothesis

Barry Mazur,William Stein
Prime Numbers and the Riemann Hypothesis Book PDF

Author : Barry Mazur,William Stein
Publisher : Cambridge University Press
Page : 155 pages
File Size : 55,8 Mb
Release : 2016-04-11
Category : Mathematics
ISBN : 9781107101920

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Prime Numbers and the Riemann Hypothesis by Barry Mazur,William Stein Pdf

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

The Riemann Hypothesis and the Distribution of Prime Numbers

Naji Arwashan, PhD, PE
The Riemann Hypothesis and the Distribution of Prime Numbers Book PDF

Author : Naji Arwashan, PhD, PE
Publisher : Nova Science Publishers
Page : 232 pages
File Size : 40,5 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9781536194227

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The Riemann Hypothesis and the Distribution of Prime Numbers by Naji Arwashan, PhD, PE Pdf

This book is an introductory and comprehensive presentation of the Riemann Hypothesis, one of the most important open questions in math today. It is introductory because it is written in an accessible and detailed format that makes it easy to read and understand. And it is comprehensive because it explains and proves all the mathematical ideas surrounding and leading to the formulation of the hypothesis.

(Almost) Impossible Integrals, Sums, and Series

Cornel Ioan Vălean
Almost Impossible Integrals Sums and Series Book PDF

Author : Cornel Ioan Vălean
Publisher : Springer
Page : 539 pages
File Size : 47,9 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9783030024628

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(Almost) Impossible Integrals, Sums, and Series by Cornel Ioan Vălean Pdf

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.

Gamma

Julian Havil
Gamma Book PDF

Author : Julian Havil
Publisher : Princeton University Press
Page : 292 pages
File Size : 49,9 Mb
Release : 2017-10-31
Category : Mathematics
ISBN : 9780691178103

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Gamma by Julian Havil Pdf

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this.

Time Machines

Paul J. Nahin
Time Machines Book PDF

Author : Paul J. Nahin
Publisher : Springer Science & Business Media
Page : 674 pages
File Size : 45,8 Mb
Release : 2001-04-20
Category : Science
ISBN : 0387985719

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Time Machines by Paul J. Nahin Pdf

This book explores the idea of time travel from the first account in English literature to the latest theories of physicists such as Kip Thorne and Igor Novikov. This very readable work covers a variety of topics including: the history of time travel in fiction; the fundamental scientific concepts of time, spacetime, and the fourth dimension; the speculations of Einstein, Richard Feynman, Kurt Goedel, and others; time travel paradoxes, and much more.

Introduction to Banach Spaces and Algebras

Graham Allan,Graham R. Allan,Harold G. Dales
Introduction to Banach Spaces and Algebras Book PDF

Author : Graham Allan,Graham R. Allan,Harold G. Dales
Publisher : Oxford University Press
Page : 380 pages
File Size : 48,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780199206537

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Introduction to Banach Spaces and Algebras by Graham Allan,Graham R. Allan,Harold G. Dales Pdf

The text begins by giving the basic theory of Banach spaces, in particular discussing dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and to operators on Hilbert spaces. --

The Enjoyment of Mathematics

Hans Rademacher,Otto Toeplitz
The Enjoyment of Mathematics Book PDF

Author : Hans Rademacher,Otto Toeplitz
Publisher : Courier Corporation
Page : 228 pages
File Size : 43,9 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0486262421

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The Enjoyment of Mathematics by Hans Rademacher,Otto Toeplitz Pdf

Requiring only a basic background in plane geometry and elementary algebra, this classic poses 28 problems that introduce the fundamental ideas that make mathematics truly exciting. "Excellent . . . a thoroughly enjoyable sampler of fascinating mathematical problems and their solutions"—Science Magazine.