How Euler Did It


Author: C. Edward Sandifer
Publisher: MAA
ISBN: 9780883855638
Category: Mathematics
Page: 237
View: 2916

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How Euler Did It is a collection of 40 monthly columns that appeared on MAA Online between November 2003 and February 2007 about the mathematical and scientific work of the great 18th century Swiss mathematician Leonhard Euler. Almost every column is self-contained and gives the context, significance and some of the details of a particular facet of his work. First we find interesting stories about Euler's work in geometry. In a discussion of the Euler polyhedral formula the author speculates about whether Descartes had a role in Euler's discovery and analyzes the flaw in Euler's proof. We also learn of Euler's solution to Cramer's paradox and its role in the early days of linear algebra. Number theory is well-represented. We see Euler's first proof of Fermat's little theorem for which he used mathematical induction, as well as his discovery of over a hundred pairs of amicable numbers, and his work on odd perfect numbers, about which little is known even today. Elsewhere in the book we learn of the development of what we now call Venn diagrams, what Euler knew about orthogonal matrices, Euler's ideas on the foundations of calculus (before the days of limits, epsilons and deltas), and his proof that mixed partial derivatives are equal.Professor Sandifer based his columns on Euler's own words in the original language in which they were written. In this way, the author was able to uncover many details that are not found in other sources. For example, we see how Euler used differential equations and continued fractions to prove that the constant e is irrational, several years before Lambert, who is usually credited with this discovery. Euler also made an observation equivalent to saying that the number of primes less than a number x is approximately x/Inx, an observation usually attributed to Gauss some 15 years after Euler died.The collection ends with a somewhat playful, but factual, account of Euler's role in the discovery on America.

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: 9508

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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,Gerhard Wanner
Publisher: European Mathematical Society
ISBN: 9783037190562
Category: Mathematics
Page: 483
View: 7671

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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.

Speech Spectrum Analysis


Author: Sean A. Fulop
Publisher: Springer Science & Business Media
ISBN: 9783642174780
Category: Technology & Engineering
Page: 206
View: 312

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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.

Proof and Other Dilemmas

Mathematics and Philosophy
Author: Roger Simons
Publisher: MAA
ISBN: 9780883855676
Category: Mathematics
Page: 346
View: 8786

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For the majority of the twentieth century, philosophers of mathematics focused their attention on foundational questions. However, in the last quarter of the century they began to return to basics, and two new schools of thought were created: social constructivism and structuralism. The advent of the computer also led to proofs and development of mathematics assisted by computer, and to questions concerning the role of the computer in mathematics. This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers have not yet discussed. The other half, written by philosophers of mathematics, summarise the discussion in that community during the last 35 years. A connection is made in each case to issues relevant to the teaching of mathematics.

Euler as Physicist


Author: Dieter Suisky
Publisher: Springer Science & Business Media
ISBN: 3540748652
Category: Science
Page: 338
View: 6899

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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.

The Encyclopaedia Britannica

Or, Dictionary of Arts, Sciences, and General Literature
Author: Thomas Stewart Traill
Publisher: N.A
ISBN: N.A
Category: Encyclopedias and dictionaries
Page: N.A
View: 6959

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Signal Conditioning

An Introduction to Continuous Wave Communication and Signal Processing
Author: Apurba Das
Publisher: Springer Science & Business Media
ISBN: 3642288189
Category: Technology & Engineering
Page: 312
View: 9114

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“Signal Conditioning” is a comprehensive introduction to electronic signal processing. The book presents the mathematical basics including the implications of various transformed domain representations in signal synthesis and analysis in an understandable and lucid fashion and illustrates the theory through many applications and examples from communication systems. The ease to learn is supported by well-chosen exercises which give readers the flavor of the subject. Supplementary electronic material is available on http://extras.springer.com including MATLAB codes illuminating applications in the domain of one dimensional electrical signal processing, image processing, and speech processing. The book is an introduction for students with a basic understanding in engineering or natural sciences.

GAMMA

Eulers Konstante, Primzahlstrände und die Riemannsche Vermutung
Author: Julian Havil
Publisher: Springer-Verlag
ISBN: 3540484965
Category: Mathematics
Page: 302
View: 3576

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Jeder kennt p = 3,14159..., viele kennen e = 2,71828..., einige i. Und dann? Die "viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156... - benannt nach dem genialen Leonhard Euler (1707-1783). Bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet die "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identität, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wörterbüchern, elende mathematische Würmer und Jeeps in der Wüste. Besser kann man nicht über Mathematik schreiben. Was Julian Havil dazu zu sagen hat, ist spektakulär.

Optical Anecdotes


Author: D. J. Lovell
Publisher: SPIE Press
ISBN: 9780819455055
Category: Technology & Engineering
Page: 134
View: 3956

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This new printing of D.J. Lovell's popular 1981 text is a collection of stories about the attempts since the beginnings of history to answer the question: What is light? Lovell's introduction sets the stage: The history of man's investigations of the nature of light is fascinating. It encompasses a large cast of characters who interact with all facets of the history of mankind. The anecdotes presented here describe a few of the events that took place in man's search for the nature of light -- a search which included drama, adventure, humor, political and religious entanglements, pestilence, and the many foibles of men. The resulting compilation is sure to motivate readers in their own explorations of this age-old question.

History of Science


Author: Alistair Cameron Crombie,Michael A. Hoskin
Publisher: N.A
ISBN: N.A
Category: Science
Page: N.A
View: 9045

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A review of literature and research in the history of science, medicine and technology in its intellectual and social context.

Color Vision

Perspectives from Different Disciplines
Author: Werner G. K. Backhaus,Reinhold Kliegl,John S. Werner
Publisher: Walter de Gruyter
ISBN: 3110806983
Category: Science
Page: 358
View: 8880

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