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Author: Robin Wilson
Publisher: Oxford University Press
ISBN: 0192514067
Category : Mathematics
Languages : en
Pages : 200
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Book Description
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.
Author: Robin Wilson
Publisher: Oxford University Press
ISBN: 0192514067
Category : Mathematics
Languages : en
Pages : 200
Get Book Here
Book Description
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.
Author: David Stipp
Publisher: Hachette UK
ISBN: 0465093787
Category : Mathematics
Languages : en
Pages : 240
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Book Description
An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.
Author: Nicholas J. Higham
Publisher: Princeton University Press
ISBN: 0691150397
Category : Mathematics
Languages : en
Pages : 1014
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Book Description
The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
Author: Graham Farmelo
Publisher: Granta Books (Uk)
ISBN:
Category : Mathematics
Languages : en
Pages : 312
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Book Description
A stunning and unique look at the great equations that lie at the heart of many of the most successful scientific theories.
Author: Robert P. Crease
Publisher: W. W. Norton & Company
ISBN: 0393345769
Category : Science
Languages : en
Pages : 318
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Book Description
"Any reader who aspires to be scientifically literate will find this a good starting place." —Publishers Weekly While we may be familiar with some of science’s greatest equations, we may not know that each and every equation emerged not in "Eureka!" moments but in years of cultural developments and scientific knowledge. With vignettes full of humor, drama, and eccentricity, philosopher and science historian Robert P. Crease shares the stories behind ten of history’s greatest equations, from the "first equation," 1 + 1 = 2, which promises a rational, well-ordered world, to Heisenberg’s uncertainty principle, which reveals the limitations of human knowledge. For every equation, Crease provides a brief account of who discovered it, what dissatisfactions lay behind its discovery, and what the equation says about the nature of our world.
Author: Ian Stewart
Publisher: Basic Books
ISBN: 0465029744
Category : Mathematics
Languages : en
Pages : 225
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Book Description
The seventeen equations that form the basis for life as we know it. Most people are familiar with history's great equations: Newton's Law of Gravity, for instance, or Einstein's theory of relativity. But the way these mathematical breakthroughs have contributed to human progress is seldom appreciated. In In Pursuit of the Unknown, celebrated mathematician Ian Stewart untangles the roots of our most important mathematical statements to show that equations have long been a driving force behind nearly every aspect of our lives. Using seventeen of our most crucial equations -- including the Wave Equation that allowed engineers to measure a building's response to earthquakes, saving countless lives, and the Black-Scholes model, used by bankers to track the price of financial derivatives over time -- Stewart illustrates that many of the advances we now take for granted were made possible by mathematical discoveries. An approachable, lively, and informative guide to the mathematical building blocks of modern life, In Pursuit of the Unknown is a penetrating exploration of how we have also used equations to make sense of, and in turn influence, our world.
Author: Stephen Ornes
Publisher: Sterling New York
ISBN: 9781454930440
Category : MATHEMATICS
Languages : en
Pages : 0
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Book Description
The worlds of visual art and mathematics beautifully unite in this spectacular volume by award-winning writer Stephen Ornes. He explores the growing sensation of math art, presenting such pieces as a colorful crocheted representation of non-Euclidian geometry that looks like sea coral and a 65-ton, 28-foot-tall bronze sculpture covered in a space-filling curve. We learn the artist's story for every work, plus the mathematical concepts and equations behind the art.
Author: Hermann Sohr
Publisher: Springer Science & Business Media
ISBN: 3034805519
Category : Mathematics
Languages : en
Pages : 376
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Book Description
The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.
Author: Robert Crease
Publisher: Hachette UK
ISBN: 1472100174
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Here are the stories of the ten most popular equations of all time as voted for by readers of Physics World, including - accessibly described here for the first time - the favourite equation of all, Euler's equation. Each is an equation that captures with beautiful simplicity what can only be described clumsily in words. Euler's equation [eip + 1 = 0] was described by respondents as 'the most profound mathematic statement ever written', 'uncanny and sublime', 'filled with cosmic beauty' and 'mind-blowing'. Collectively these equations also amount to the world's most concise and reliable body of knowledge. Many scientists and those with a mathematical bent have a soft spot for equations. This book explains both why these ten equations are so beautiful and significant, and the human stories behind them.
Author: J. David Logan
Publisher: Springer Science & Business Media
ISBN: 0387299300
Category : Mathematics
Languages : en
Pages : 297
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Book Description
Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying di?erential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts.
