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The title derives from Laplace's assessment of Euler (1707-83): "Read Euler ... He is the master of us all." For the mathematically literate, Dunham (mathematics, Muhlenberg College, Allentown, PA) introduces the visually impaired genius (whose picture graces 10 franc Swiss currency); places his contributions to number theory, infinite series, and other diverse areas in a historical context; and outlines his magnum opus, . Book News, Inc.®, Portland, OR


Choice
An ideal book for enlivening undergraduate mathematics...he {Dunham} has Euler dazzling us with cleverness, page after page.


Ronald Graham, Chief Scientist, AT&T
William Dunham has written a superb book about the life and amazing achievements of one of the greatest mathematicians of all time. Unlike earlier writings about Euler, Dunham gives crystal clear accounts of how Euler ingeniously proved his most significant results, and how later experts have stood on Euler's broad shoulders. Such a book has long been overdue. It will not need to be done again for a long, long time.Martin Gardner Dunham has done it again! In "Euler: The Master of Us All," he has produced a masterful portrait of one of the most fertile mathematicians of all time. With Dunham's beautiful clarity and wit, we can follow with amazement Euler's strokes of genius which laid the groundwork for most of the mathematics we have today.


Ron Graham, Chief Scientist, AT&T
William Dunham has done it again! In "Euler: the Master of Us All", he has produced a masterful portrait of one of the most fertile mathematicians of all time. With Dunham's beautiful clarity and wit, we can follow with amazement Euler's strokes of genius which laid the groundwork for most of the mathematics we have today.


Martin Gardner
Mathematician William Dunham has written a superb book about the life and amazing achievements of one of the greatest mathematicians of all time. Unlike earlier writings about Euler, Professor Dunham gives crystal clear accounts of how Euler ingeniously proved his most significant results, and how later experts have stood on Euler's broad shoulders. Such a book has long been overdue. It will not need to be done again for a long long time.


Book Description
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.


About the Author
William Dunham is the Truman Koehler Professor of Mathematics at Muhlenberg College in Allentown, Pennsylvania. He has won two awards for excellence in expository writing from The Mathematical Association of America: the 1993 George Plya Award, and in 1997, the Trevor Evans Award. His books Journey Through Genius: The Great Theorems of Mathematics, and The Mathematical Universe have both been selections of the Book-of-the-Month Club and the History Book Club. He has also been the recipient of several grants from the National Endowment for the Humanities to fund seminars on the great theorems of mathematics in historical context.

FROM THE PUBLISHER

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.

SYNOPSIS

Selected as an Outstanding Academic Book by Choice Magazine.   From the award winning author of Journey Through Genius: The Great Theorems of Mathematics and The Mathematical Universe. Without question, Leonhard Euler (1707-1783) ranks among history￯﾿ﾽs greatest mathematicians. Over six decades of unmatched productivity, and despite a visual impairment that grew ever worse, he charted the course of mathematics throughout the eighteenth century and beyond. His reputation is captured in Laplace￯﾿ﾽs famous admonition, ￯﾿ﾽRead Euler, read Euler. He is the master of us all.￯﾿ﾽ Written for the mathematically literate reader, this book provides a glimpse of Euler in action. Following an introductory biographical sketch are chapters describing his contributions to eight different topics￯﾿ﾽ￯﾿ﾽnumber theory, logarithms, infinite series, analytic number theory, complex variables, algebra, geometry, and combinatorics. Each chapter begins with a prologue to establish the historical context and then proceeds to a detailed consideration of one or more Eulerian theorems on the subject at hand. Each chapter concludes with an epilogue surveying subsequent developments or addressing related questions that remain unanswered to this day. At the end of the book is a brief outline of Euler￯﾿ﾽs collected works, the monumental Opera Omnia, for which 73 volumes are in print. Many volumes are yet to appear. In all, the book contains three dozen proofs from this remarkable individual. Yet this is merely the tip of the scholarly iceberg, for Euler produced over 30,000 pages of pure and applied mathematics during his lifetime. Euler: The Master of Us All samples the work of a mathematician whose influence, industry, and ingenuity are of the very highest order.

FROM THE CRITICS

Math Reviews

Dunham's fine book captures the spirit of Euler's achievements and enables the English reader with a solid background in calculus and school algebra to share the enjoyment.... The first six chapters are a carefully orchestrated examination of Euler's use of algebra and analysis to study perfect numbers, primes, series expansions of transcendental functions, sums of certain series of integer reciprocals and the theory of equations.

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