How Euler Did Even More

Author: C. Edward Sandifer
Publisher: The Mathematical Association of America
ISBN: 0883855844
Category: Mathematics
Page: 240
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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.

Walter Gautschi, Volume 3

Selected Works with Commentaries
Author: Claude Brezinski,Ahmed Sameh
Publisher: Springer Science & Business Media
ISBN: 146147132X
Category: Mathematics
Page: 767
View: 1346

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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


Author: Rolf Jeltsch,Gerhard Wanner
Publisher: European Mathematical Society
ISBN: 9783037190562
Category: Mathematics
Page: 483
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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

Cures Many Mathematical Ills
Author: Paul J. Nahin
Publisher: Princeton University Press
ISBN: 9781400838479
Category: Mathematics
Page: 416
View: 7061

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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.

Sophie's Diary: A Mathematical Novel

Author: Dora Musielak
Publisher: MAA
ISBN: 0883855771
Category: Fiction
Page: 292
View: 5406

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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.

Speech Spectrum Analysis

Author: Sean Fulop
Publisher: Springer Science & Business Media
ISBN: 9783642174780
Category: Technology & Engineering
Page: 206
View: 7544

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The accurate determination of the speech spectrum, particularly for short frames, is commonly pursued in diverse areas including speech processing, recognition, and acoustic phonetics. With this book the author makes the subject of spectrum analysis understandable to a wide audience, including those with a solid background in general signal processing and those without such background. In keeping with these goals, this is not a book that replaces or attempts to cover the material found in a general signal processing textbook. Some essential signal processing concepts are presented in the first chapter, but even there the concepts are presented in a generally understandable fashion as far as is possible. Throughout the book, the focus is on applications to speech analysis; mathematical theory is provided for completeness, but these developments are set off in boxes for the benefit of those readers with sufficient background. Other readers may proceed through the main text, where the key results and applications will be presented in general heuristic terms, and illustrated with software routines and practical "show-and-tell" discussions of the results. At some points, the book refers to and uses the implementations in the Praat speech analysis software package, which has the advantages that it is used by many scientists around the world, and it is free and open source software. At other points, special software routines have been developed and made available to complement the book, and these are provided in the Matlab programming language. If the reader has the basic Matlab package, he/she will be able to immediately implement the programs in that platform---no extra "toolboxes" are required.

Euler as Physicist

Author: Dieter Suisky
Publisher: Springer Science & Business Media
ISBN: 3540748652
Category: Science
Page: 338
View: 800

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The subject of the book is the development of physics in the 18th century centered upon the fundamental contributions of Leonhard Euler to physics and mathematics. This is the first book devoted to Euler as a physicist. Classical mechanics are reconstructed in terms of the program initiated by Euler in 1736 and its completion over the following decades until 1760. The book examines how Euler coordinated his progress in mathematics with his progress in physics.

Prime Numbers and the Riemann Hypothesis

Author: Barry Mazur,William Stein
Publisher: Cambridge University Press
ISBN: 1107101921
Category: Mathematics
Page: 150
View: 447

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This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

An Episodic History of Mathematics

Mathematical Culture Through Problem Solving
Author: Steven G. Krantz
Publisher: MAA
ISBN: 0883857669
Category: Mathematics
Page: 381
View: 4704

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An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematicsboth classical and modern.Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincar, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists.This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practicalgetting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on.This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process.

Is mathematics inevitable?

a miscellany
Author: Underwood Dudley,Gerald L. Alexanderson,Nathan Altshiller-Court,John Aubry,Girolamo Cardano,Lewis Carroll,Patricia Cline Cohen,Jean Dieudonné,Leonard F. Klosinski,Joseph A. Gallian,Richard J. Gillings,Richard K. Guy,Arthur Edward Hallerberg,Paul Richard Halmos,David Hemenway,Morris Kline,Carl E. Linderholm,Robert L. McCabe,Edward Rothstein,Marlow Sholander,David Eugene Smith,John Lighton Synge,James Smith,Richard J. Trudeau,Steven Bradley Smith,Wong Ngai Ying
Publisher: The Mathematical Association of America
ISBN: 9780883855669
Category: Mathematics
Page: 325
View: 3422

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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.


The Master of Us All
Author: William Dunham
Publisher: MAA
ISBN: 9780883853283
Category: Mathematics
Page: 185
View: 528

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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.

The Discrepancy Method

Randomness and Complexity
Author: Bernard Chazelle
Publisher: Cambridge University Press
ISBN: 9780521003575
Category: Computers
Page: 475
View: 7652

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The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal to students and researchers in computer science, operations research, pure and applied mathematics, and engineering.


Mathematical Proof of Implausible Ideas
Author: Julian Havil
Publisher: Princeton University Press
ISBN: 9781400837380
Category: Mathematics
Page: 216
View: 562

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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.

The Mathematical Mechanic

Using Physical Reasoning to Solve Problems
Author: Mark Levi
Publisher: Princeton University Press
ISBN: 0691154562
Category: Science
Page: 186
View: 3285

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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.

Concrete Mathematics

A Foundation for Computer Science
Author: Ronald L. Graham,Donald Ervin Knuth,Oren Patashnik
Publisher: Addison-Wesley Professional
ISBN: 9780201558029
Category: Computers
Page: 657
View: 3385

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This book, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every discipline.

Gödel, Escher, Bach

An Eternal Golden Braid
Author: Douglas R. Hofstadter
Publisher: N.A
ISBN: 9780140179972
Category: Artificial intelligence
Page: 777
View: 5769

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