The Great Prime Number Race

The Great Prime Number Race PDF

Author: Roger Plymen

Publisher: American Mathematical Soc.

Published: 2020-08-13

Total Pages: 152

ISBN-13: 1470462575

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Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number. This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

The Great Race

The Great Race PDF

Author: Levi Tillemann

Publisher: Simon and Schuster

Published: 2016-01-19

Total Pages: 352

ISBN-13: 1476773505

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The Great Race recounts the exciting story of a century-long battle among automakers for market share, profit, and technological dominance—and the thrilling race to build the car of the future. The world’s great manufacturing juggernaut—the $3 trillion automotive industry—is in the throes of a revolution. Its future will include cars Henry Ford and Karl Benz could scarcely imagine. They will drive themselves, won’t consume oil, and will come in radical shapes and sizes. But the path to that future is fraught. The top contenders are two traditional manufacturing giants, the US and Japan, and a newcomer, China. Team America has a powerful and little-known weapon in its arsenal: a small group of technology buffs and regulators from California. The story of why and how these men and women could shape the future—how you move, how you work, how you live on Earth—is an unexpected tale filled with unforgettable characters: a scorned chemistry professor, a South African visionary who went for broke, an ambitious Chinese ex-pat, a quixotic Japanese nuclear engineer, and a string of billion-dollar wagers by governments and corporations. “To explain the scramble for the next-generation auto—and the roles played in that race by governments, auto makers, venture capitalists, environmentalists, and private inventors—comes Levi Tillemann’s The Great Race…Mr. Tillemann seems ideally cast to guide us through the big ideas percolating in the world’s far-flung workshops and labs” (The Wall Street Journal). His account is incisive and riveting, explaining how America bounced back in this global contest and what it will take to command the industrial future.

The Book of Prime Number Records

The Book of Prime Number Records PDF

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 492

ISBN-13: 1468499386

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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.

Prime Numbers: The Holy Grail Of Mathematics

Prime Numbers: The Holy Grail Of Mathematics PDF

Author: Thamer Naouech

Publisher: Thamer Naouech

Published: 2020-10-20

Total Pages: 46

ISBN-13:

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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".

The New Book of Prime Number Records

The New Book of Prime Number Records PDF

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 558

ISBN-13: 1461207592

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This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible 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 decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.

Numbers and Figures

Numbers and Figures PDF

Author: Giancarlo Travaglini

Publisher: American Mathematical Society

Published: 2023-05-31

Total Pages: 304

ISBN-13: 1470472562

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One of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their connections to geometry, calculus, and real-life problems such as COVID-19 vaccines or fiscal frauds. Each conversation is in two parts—an introductory essay which provides a gentle introduction to the topic and a second section that delves deeper and requires study by the reader. The topics themselves are extremely appealing and include, for example, Pick's theorem, Simpson's paradox, Farey sequences, the Frobenius problem, and Benford's Law. Numbers and Figures will be a useful resource for college faculty teaching Elementary Number Theory or Calculus. The chapters are largely independent and could make for nice course-ending projects or even lead-ins to high school or undergraduate research projects. The whole book would make for an enjoyable semester-long independent reading course. Faculty will find it entertaining bedtime reading and, last but not least, readers more generally will be interested in this book if they miss the accuracy and imagination found in their high school and college math courses.

Prime Numbers

Prime Numbers PDF

Author: Richard Crandall

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 558

ISBN-13: 1468493167

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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

Matrix Models for Population, Disease, and Evolutionary Dynamics

Matrix Models for Population, Disease, and Evolutionary Dynamics PDF

Author: J. M. Cushing

Publisher: American Mathematical Society

Published: 2024-02-29

Total Pages: 293

ISBN-13: 1470473348

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This book offers an introduction to the use of matrix theory and linear algebra in modeling the dynamics of biological populations. Matrix algebra has been used in population biology since the 1940s and continues to play a major role in theoretical and applied dynamics for populations structured by age, body size or weight, disease states, physiological and behavioral characteristics, life cycle stages, or any of many other possible classification schemes. With a focus on matrix models, the book requires only first courses in multivariable calculus and matrix theory or linear algebra as prerequisites. The reader will learn the basics of modeling methodology (i.e., how to set up a matrix model from biological underpinnings) and the fundamentals of the analysis of discrete time dynamical systems (equilibria, stability, bifurcations, etc.). A recurrent theme in all chapters concerns the problem of extinction versus survival of a population. In addition to numerous examples that illustrate these fundamentals, several applications appear at the end of each chapter that illustrate the full cycle of model setup, mathematical analysis, and interpretation. The author has used the material over many decades in a variety of teaching and mentoring settings, including special topics courses and seminars in mathematical modeling, mathematical biology, and dynamical systems.

Born to Run

Born to Run PDF

Author: Christopher McDougall

Publisher: Profile Books

Published: 2010-12-09

Total Pages: 296

ISBN-13: 184765228X

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A New York Times bestseller 'A sensation ... a rollicking tale well told' - The Times At the heart of Born to Run lies a mysterious tribe of Mexican Indians, the Tarahumara, who live quietly in canyons and are reputed to be the best distance runners in the world; in 1993, one of them, aged 57, came first in a prestigious 100-mile race wearing a toga and sandals. A small group of the world's top ultra-runners (and the awe-inspiring author) make the treacherous journey into the canyons to try to learn the tribe's secrets and then take them on over a course 50 miles long. With incredible energy and smart observation, McDougall tells this story while asking what the secrets are to being an incredible runner. Travelling to labs at Harvard, Nike, and elsewhere, he comes across an incredible cast of characters, including the woman who recently broke the world record for 100 miles and for her encore ran a 2:50 marathon in a bikini, pausing to down a beer at the 20 mile mark.