How Euler Did Even More
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How Euler Did Even More
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Author : C. Edward Sandifer
language : en
Publisher: The Mathematical Association of America
Release Date : 2014-11-19
How Euler Did Even More written by C. Edward Sandifer and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
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.
How Euler Did Even More
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Author : Charles Edward Sandifer
language : en
Publisher:
Release Date : 2015
How Euler Did Even More written by Charles Edward Sandifer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Leonhard Euler
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Author : Emil A. Fellmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05
Leonhard Euler written by Emil A. Fellmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-05 with Mathematics categories.
Euler was not only by far the most productive mathematician in the history of mankind, but also one of the greatest scholars of all time. He attained, like only a few scholars, a degree of popularity and fame which may well be compared with that of Galilei, Newton, or Einstein. Moreover he was a cosmopolitan in the truest sense of the word; he lived during his first twenty years in Basel, was active altogether for more than thirty years in Petersburg and for a quarter of a century in Berlin. Leonhard Euler’s unusually rich life and broadly diversified activity in the immediate vicinity of important personalities which have made history, may well justify an exposition. This book is based in part on unpublished sources and comes right out of the current research on Euler. It is entirely free of formulae as it has been written for a broad audience with interests in the history of culture and science.
Euler
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Author : William Dunham
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-13
Euler written by William Dunham and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-13 with Mathematics categories.
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.
Euler S Pioneering Equation
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Author : Robin Wilson
language : en
Publisher: Oxford University Press
Release Date : 2018-02-22
Euler S Pioneering Equation written by Robin Wilson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-22 with Mathematics categories.
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, eiπ + 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; π 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.
Euler Through Time
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Author : V. S. Varadarajan
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Euler Through Time written by V. S. Varadarajan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at the center of today's mathematics. It is of great interesttherefore to examine his work and its relation to current mathematics. This book attempts to do that. In number theory the discoveries he made empirically would require for their eventual understanding such sophisticated developments as the reciprocity laws and class field theory. His pioneering work onelliptic integrals is the precursor of the modern theory of abelian functions and abelian integrals. His evaluation of zeta and multizeta values is not only a fantastic and exciting story but very relevant to us, because they are at the confluence of much research in algebraic geometry and number theory today (Chapters 2 and 3 of the book). Anticipating his successors by more than a century, Euler created a theory of summation of series that do not converge in the traditional manner. Chapter 5of the book treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics. The last chapter contains a brief treatment of Euler products. Euler discovered the product formula over the primes for the zeta function as well as for a smallnumber of what are now called Dirichlet $L$-functions. Here the book goes into the development of the theory of such Euler products and the role they play in number theory, thus offering the reader a glimpse of current developments (the Langlands program).
Foundations Of Differential Calculus
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Author : Euler
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-23
Foundations Of Differential Calculus written by Euler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-23 with Mathematics categories.
What differential calculus, and, in general, analysis ofthe infinite, might be can hardly be explainedto those innocent ofany knowledge ofit. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood. Besides those ideas in common usage, there are also others from finite analysis that are much less common and are usually explained in the courseofthe development ofthe differential calculus. For this reason, it is not possible to understand a definition before its principles are sufficiently clearly seen. In the first place, this calculus is concerned with variable quantities. Although every quantity can naturally be increased or decreased without limit, still, since calculus is directed to a certain purpose, we think of some quantities as being constantly the same magnitude, while others change through all the .stages of increasing and decreasing. We note this distinc tion and call the former constant quantities and the latter variables. This characteristic difference is not required by the nature of things, but rather because of the special question addressed by the calculus.
Leonhard Euler
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Author : Emil A. Fellmann
language : en
Publisher: Birkhäuser
Release Date : 2009-09-03
Leonhard Euler written by Emil A. Fellmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 with Mathematics categories.
Euler was not only by far the most productive mathematician in the history of mankind, but also one of the greatest scholars of all time. He attained, like only a few scholars, a degree of popularity and fame which may well be compared with that of Galilei, Newton, or Einstein. Moreover he was a cosmopolitan in the truest sense of the word; he lived during his first twenty years in Basel, was active altogether for more than thirty years in Petersburg and for a quarter of a century in Berlin. Leonhard Euler’s unusually rich life and broadly diversified activity in the immediate vicinity of important personalities which have made history, may well justify an exposition. This book is based in part on unpublished sources and comes right out of the current research on Euler. It is entirely free of formulae as it has been written for a broad audience with interests in the history of culture and science.
How Euler Did It
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Author : G. Edward Sandifer
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-08-03
How Euler Did It written by G. Edward Sandifer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-03 with Mathematics categories.
Euler S Pioneering Equation
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Author : Robin Wilson
language : en
Publisher:
Release Date : 2019-07-17
Euler S Pioneering Equation written by Robin Wilson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-17 with Equations categories.
In just seven symbols, with profound and beautiful simplicity, Euler's Equation connects five of the most important numbers in mathematics. Robin Wilson explores each number in turn, then brings them together to consider the power of the equation as a whole.