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Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

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Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This volume is the second collection of Sandifer's How Euler Did It columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context.

Leonhard Euler (1707-1783) was the most important mathematician of the 18th century. His collected works, which number more than 800 books and articles, fill over 70 large volumes. He revolutionised real analysis and mathematical physics, single-handedly established the field of analytic number theory, and made important contributions to almost every other branch of mathematics. A great pedagogue as well as a great researcher, his textbooks educated the next generation of mathematicians. This book compiles over 20 papers, based on some of the most memorable contributions from mathematicians and historians of mathematics at academic meetings across the USA and Canada, in the years approaching Leonhard Euler's tercentenary. These papers will appeal not only to those who already have an interest in the history of mathematics, but will also serve as a compelling introduction to the subject, focused on the accomplishments of one of the greatest mathematical minds of all time.

Leonhard Euler was one of the most prolific mathematicians that have ever lived. This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

Leonhard Euler (1707-1783) was the most important mathematician of the 18th century. His collected works, which number more than 800 books and articles, fill over 70 large volumes. He revolutionised real analysis and mathematical physics, single-handedly established the field of analytic number theory, and made important contributions to almost every other branch of mathematics. A great pedagogue as well as a great researcher, his textbooks educated the next generation of mathematicians. This book compiles over 20 papers, based on some of the most memorable contributions from mathematicians and historians of mathematics at academic meetings across the USA and Canada, in the years approaching Leonhard Euler's tercentenary. These papers will appeal not only to those who already have an interest in the history of mathematics, but will also serve as a compelling introduction to the subject, focused on the accomplishments of one of the greatest mathematical minds of all time.

Euler Products (Mathematical Monograph)

In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence." What is it that makes Euler's identity, e]iPi + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; Pi an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.

Sandifer has been studying Euler for decades and is one of the world's leading experts on his work. This volume is the second collection of Sandifer's How Euler Did It columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler's clever inventiveness and Sandifer's wonderful ability to explicate and put it all in context.

Celebrating the 300th birthday of Leonhard Euler (1707-1783), one of the brightest stars in the mathematical firmament, this book stands as a testimonial to a mathematician of unsurpassed insight, industry, and ingenuity. The collected articles, aimed at a mathematically literate audience, address aspects of Euler's life and work, from the biographical to the historical to the mathematical. The oldest of these was written in 1872, and the most recent dates to 2006. Some of the papers focus on Euler and his world, others describe a specific Eulerian achievement, and still others survey a branch of mathematics to which Euler contributed significantly. Among the 34 contributors are some of the most illustrious mathematicians and mathematics historians of the past century, e.g. Florian Cajori, Carl Boyer, George Pólya, Andre Weil, and Paul Erdös. And there are a few poems and a mnemonic just for fun.

This is the first full-scale biography of Leonhard Euler (1707–83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler’s massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler’s work in its multilayered context―personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler’s fundamental contributions to almost every area of pure and applied mathematics―especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics―to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory.The narrative takes the reader from Euler’s childhood and education in Basel through his first period in St. Petersburg, 1727–41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton’s dynamics, and published the best-selling Letters to a German Princess―all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment.

Print on Demand. This book examines the nature of knowledge, arguing that we can have certainty about the existence of external objects. The author, a respected philosopher, explores different sources of knowledge, including the senses, reason, and testimony, and argues that each can provide us with reliable information about the world around us. The book also delves into the nature of extension, arguing that it is infinitely divisible, and the nature of bodies, arguing that they are made up of indivisible particles. The author's insights on these topics are significant and have had a lasting impact on the field of philosophy. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

This is the first full-scale biography of Leonhard Euler (1707–83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler’s massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler’s work in its multilayered context―personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler’s fundamental contributions to almost every area of pure and applied mathematics―especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics―to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory.The narrative takes the reader from Euler’s childhood and education in Basel through his first period in St. Petersburg, 1727–41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton’s dynamics, and published the best-selling Letters to a German Princess―all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment.

Excerpt from Letters of Euler on Different Subjects in Natural Philosophy, Vol. 1 of 2: Addressed to a German Princess; With Notes, and a Life of EulerIndependently of the great popularity of this work, it possesses a particular interest at the present time, in consequence of its containing a popular view of the doctrine, that light consists in the undulations Of an ethereal medium, which is now generally adopted, in consequence of recent discoveries in optics.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

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.

Excerpt from Letters of Euler on Different Subjects in Physics and Philosophy, Vol. 2 of 2: Addressed to a German Princess; Translated From the FrenchWhy does the Magnetic Needle afi'efi, in every Place of the Earth, a certain Direct tlon, differing in difl'erent Places and for what Reafon does it change, with Time, at the fame Place?About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

An acclaimed biography of the Enlightenment's greatest mathematicianThis is the first full-scale biography of Leonhard Euler (1707–1783), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing on Euler's massive published works and correspondence, this biography sets Euler's work in its multilayered context―personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics in his time―especially calculus, mechanics, and optics―to his advances in shipbuilding, telescopes, acoustics, ballistics, cartography, chronology, and music theory.

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