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Prime Numbers The Holy Grail Of Mathematics
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Book Synopsis Prime Numbers: The Holy Grail Of Mathematics by : Thamer Naouech
Download or read book Prime Numbers: The Holy Grail Of Mathematics written by Thamer Naouech and published by Thamer Naouech. This book was released on 2020-10-20 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is undeniable how prime numbers are one of the most beautiful and fascinating topics in mathematics. But what are prime numbers? Are they only numbers that are divisible by 1 and themselves, or do they have another interesting hidden face?Throughout history, the mystery of prime numbers has challenged the greatest minds in mathematics starting from Euclid of Alexandria to Fermat, Euler, Gauss, and Erdős,… who attempted to solve the puzzling problem of primes. The achievements they realized and the secrets they revealed can only assert how deep the concept of prime numbers is. Starting from how prime numbers exist in nature, and how they are of great use in modern cryptography on which our daily life completely depends, the author travels in the holy kingdom of primes diving into some conjectures involving those special numbers. From the Riemann Hypothesis and the well-known zeta function, he explains how a note in the margin turned to be Fermat’s Last Theorem, one of the most important problems in the history of mathematics. From Mersenne Primes, he gets to the twin primes, those shining little stars in the blue sky of primes. And from Euclid’s proof of the infinite number of primes he gets to a hidden pattern in the distribution of primes discovered by Stanisław Ulam and called the Ulam Spiral. After this little trip, you will know, dear reader, why prime numbers deserve to be called "the holy grail of mathematics".
Book Synopsis Prime Obsession by : John Derbyshire
Download or read book Prime Obsession written by John Derbyshire and published by Joseph Henry Press. This book was released on 2003-04-15 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stalking the Riemann Hypothesis by : Dan Rockmore
Download or read book Stalking the Riemann Hypothesis written by Dan Rockmore and published by Vintage. This book was released on 2006-05-09 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
Book Synopsis The Riemann Hypothesis by : Peter B. Borwein
Download or read book The Riemann Hypothesis written by Peter B. Borwein and published by Springer Science & Business Media. This book was released on 2008 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.
Book Synopsis Entangling Primes and Zeros by : David R Ely
Download or read book Entangling Primes and Zeros written by David R Ely and published by David R Ely. This book was released on 2024-04-26 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: For over 150 years, the Riemann Hypothesis stood as perhaps the greatest unsolved problem in mathematics. Proposed in 1859 by Bernard Riemann, the conjecture provided a tantalizing connection between the distribution of prime numbers and the zeros of an analytic function. Riemann located all the non-trivial zeros of the zeta function along a straight line in the complex plane. This simple pattern pointed to hidden order in the chaos of prime numbers. Generations of mathematicians struggled in vain to prove Riemann's alluring claim. It became the holy grail of number theory, resisting the most powerful mathematical minds. The Riemann Hypothesis gained renown as the most important problem in all of mathematics. But despite intense effort, the problem seemed mired in insurmountable difficulty. In this book, we walk through the proof that could finally cracked Riemann's age-old enigma. By bringing together ideas from complex analysis, number theory, and topology, the proof provides a creative bridge between mathematics' disparate domains. Methods based on symmetry, contradiction, and strategic re-expression illuminate Riemann's magic at last. The book offers the first comprehensive guide to understanding and appreciating this watershed mathematical achievement. It provides deep mathematical insights, historical perspectives, and reflection on problem-solving philosophy. Most importantly, the work pays tribute to the human spirit embodied in mathematics’ unending quest to understand the mysteries of patterns that surround us.
Book Synopsis Prime Numbers and the Riemann Hypothesis by : Barry Mazur
Download or read book Prime Numbers and the Riemann Hypothesis written by Barry Mazur and published by Cambridge University Press. This book was released on 2016-04-11 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Book Synopsis The Book of Prime Number Records by : Paulo Ribenboim
Download or read book The Book of Prime Number Records written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A. J. Coleman and H. W. Ellis and to acknowledge their long-lasting interest in the quality of teaching undergraduate students. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book oj Records, reminded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will also include some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work. Paulo Ribenboim CONTENTS Preface vii Guiding the Reader xiii Index of Notations xv Introduction Chapter 1. How Many Prime Numbers Are There? 3 I. Euclid's Proof 3 II.
Book Synopsis Stalking the Riemann Hypothesis by : Dan Rockmore
Download or read book Stalking the Riemann Hypothesis written by Dan Rockmore and published by Vintage. This book was released on 2007-12-18 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.
Book Synopsis The Music of the Primes by : Marcus du Sautoy
Download or read book The Music of the Primes written by Marcus du Sautoy and published by Harper Collins. This book was released on 2004-04-27 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines German mathematician Bernhard Riemann's hypothesis on imaginary numbers, sine waves, and prime numbers and attempts to unravel the mystery surrounding it.
Book Synopsis The Music of the Primes by : Marcus du Sautoy
Download or read book The Music of the Primes written by Marcus du Sautoy and published by Harper Perennial. This book was released on 2012-08-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved—one that baffles mathematicians to this day. Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.
Book Synopsis The Prime Number Theorem by : G. J. O. Jameson
Download or read book The Prime Number Theorem written by G. J. O. Jameson and published by Cambridge University Press. This book was released on 2003-04-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Book Synopsis The Distribution of Prime Numbers by : Albert Edward Ingham
Download or read book The Distribution of Prime Numbers written by Albert Edward Ingham and published by Cambridge University Press. This book was released on 1990-09-28 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
Book Synopsis The Great Mathematical Problems by : Ian Stewart
Download or read book The Great Mathematical Problems written by Ian Stewart and published by Profile Books. This book was released on 2013-03-07 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.
Download or read book Prime Numbers written by Richard Crandall and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field
Book Synopsis Number Theory by : George E. Andrews
Download or read book Number Theory written by George E. Andrews and published by Courier Corporation. This book was released on 2012-04-30 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
Book Synopsis The Development of Prime Number Theory by : Wladyslaw Narkiewicz
Download or read book The Development of Prime Number Theory written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
Book Synopsis Irregularities in the Distribution of Prime Numbers by : János Pintz
Download or read book Irregularities in the Distribution of Prime Numbers written by János Pintz and published by Springer. This book was released on 2018-07-04 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.
