how euler did it spectrum

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How Euler Did Even More

Author : C. Edward Sandifer
ISBN : 9780883855843
Genre : Mathematics
File Size : 37. 79 MB
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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.

The Early Mathematics Of Leonhard Euler

Author : C. Edward Sandifer
ISBN : 0883855593
Genre : Mathematics
File Size : 79. 57 MB
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A portrait of Euler's early mathematics between 1725 and 1741, rich in technical detail.

Sophie S Diary A Mathematical Novel

Author : Dora Musielak
ISBN : 9780883855775
Genre : Fiction
File Size : 26. 75 MB
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Sophie Germain, the first and only woman in history to make a substantial contribution to the proof of Fermat's Last Theorem, grew up during the most turbulent years of the French Revolution. Her mathematical genius was discovered by Lagrange around 1797. Published research about Germain focuses on her achievements, noting that she assumed a man's name at the École Polytechnique in Paris, to submit her own work to Lagrange. Yet, no biography has explained how Germain learned mathematics before that time to become so sure of her analytical skills to carry out such a daring act. Sophie's Diary is an attempt to answer this question: How did Germain learn enough mathematics to enter the world of Lagrange's analysis in the first place? In Sophie's Diary, Germain comes to life through a fictionalized journal that intertwines mathematics with history of mathematics plus historically-accurate accounts of the brutal events that took place in Paris between 1789 and 1793. This format provides a plausible perspective of how a young Sophie could have learned mathematics on her own—both fascinated by numbers and eager to master tough subjects without a tutor's guidance. Her passion for mathematics is integrated into her personal life as an escape from societal outrage. Sophie's Diary is suitable for a variety of readers?both students and teachers, mathematicians and novices?who will be inspired and enlightened on a field of study made easy as is told through the intellectual and personal struggles of an exceptional young woman.

Nonplussed

Author : Julian Havil
ISBN : 1400837383
Genre : Mathematics
File Size : 58. 79 MB
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Math--the application of reasonable logic to reasonable assumptions--usually produces reasonable results. But sometimes math generates astonishing paradoxes--conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than any other day? Or that cones can roll unaided uphill? In Nonplussed!--a delightfully eclectic collection of paradoxes from many different areas of math--popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas. Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs. Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.

Music And The Making Of Modern Science

Author : Peter Pesic
ISBN : 9780262027274
Genre : Music
File Size : 90. 94 MB
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In the natural science of ancient Greece, music formed the meeting place between numbers and perception; for the next two millennia, Pesic tells us in Music and the Making of Modern Science, "liberal education" connected music with arithmetic, geometry, and astronomy within a fourfold study, the quadrivium. Peter Pesic argues provocatively that music has had a formative effect on the development of modern science -- that music has been not just a charming accompaniment to thought but a conceptual force in its own right. Pesic explores a series of episodes in which music influenced science, moments in which prior developments in music arguably affected subsequent aspects of natural science. He describes encounters between harmony and fifteenth-century cosmological controversies, between musical initiatives and irrational numbers, between vibrating bodies and the emergent electromagnetism. He offers lively accounts of how Newton applied the musical scale to define the colors in the spectrum; how Euler and others applied musical ideas to develop the wave theory of light; and how a harmonium prepared Max Planck to find a quantum theory that reengaged the mathematics of vibration. Taken together, these cases document the peculiar power of music -- its autonomous force as a stream of experience, capable of stimulating insights different from those mediated by the verbal and the visual. An innovative e-book edition available for iOS devices will allow sound examples to be played by a touch and shows the score in a moving line.

Walter Gautschi Volume 3

Author : Claude Brezinski
ISBN : 9781461471325
Genre : Mathematics
File Size : 64. 62 MB
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Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

Iciam 07

Author : Rolf Jeltsch
ISBN : 3037190566
Genre : Mathematics
File Size : 81. 57 MB
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The International Council for Industrial and Applied Mathematics (ICIAM) is the worldwide organisation of societies which are dedicated primarily of significantly to applied and/or industrial mathematics. The ICIAM Congresses, held every 4 years, are run under the auspices of the Council with the aim to advance the applications of mathematics in all parts of the world. The 6th ICIAM Congress was held in Zurich, Switzerland, 16-20 July 2007, and was attended by more than 3000 scientists from 47 countries. This volume collects the invited lectures of this Congress, the appreciations of the ICIAM Prize winners' achievements and the Euler Lecture celebrating the 300th anniversary of Euler. The authors of these papers are leading researchers of their fields, rigorously selected by a distinguished international program committee. The book presents an overview of contemporary applications of mathematics, new perspectives and open problems.

Dr Euler S Fabulous Formula

Author : Paul J. Nahin
ISBN : 1400838479
Genre : Mathematics
File Size : 35. 4 MB
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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.

The Mathematical Mechanic

Author : Mark Levi
ISBN : 9780691154565
Genre : Science
File Size : 64. 98 MB
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In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.

Is Mathematics Inevitable

Author : Underwood Dudley
ISBN : 0883855666
Genre : Mathematics
File Size : 76. 70 MB
Format : PDF
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This is a collection of gems from the literature of mathematics that shine as brightly today as when they first appeared in print. They deserve to be seen and admired.The selections include two opposing views on the purpose of mathematics, The Strong Law of Small Numbers, the treatment of calculus in the 1771 Encyclopaedia Britannica, several proofs that the number of legs on a horse is infinite, a deserved refutation of the ridiculous Euler-Diderot anecdote, the real story of p and the Indiana Legislature, the reason why Theodorus stopped proving that square roots were irrational when he to the square root of 17, an excerpt from Mathematics Made Difficult, a glimpse into the mind of a calculating prodigy.There will be something of interest here for almost anyone interested in mathematics.Underwood Dudley is the bestselling author of several MAA books: Mathematical Cranks, Numerology, and the Trisectors. He has an Erdos number of 1.

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