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基本説明
Chronicles the life and mathematics of the man whose published works fill more than 70 hefty volumes. Contains papers from a variety of authors, including the three editors of the book, Ed Sandifer, Lawrence D'Antonio, and Robert Bradley, as well as pieces by Stacy Langton, Rüdiger Thiele, Mark McKinzie, and other noted scholars. Topics covered in the book include analysis, geometry, algebra, probability, astronomy, and mechanics.
Full Description
When an important mathematician celebrates a landmark birthday, other mathematicians sometimes gather together to give papers in appreciation of the life and work of the great person. When a mathematician as influential and productive as Euler celebrates an anniversary as important as the 300th, a single meeting isn't sufficient to present all of the contributions. Leonhard Euler (1707-1783) was the most important mathematician of the 18th century. His collected works, with 800 books and articles, fill over 70 large volumes. He revolutionized real analysis and mathematical physics, single-handedly established the field of analytic number theory, and made important contributions to almost every other branch of mathematics. A great pedagogue as well as a great researcher, his textbooks educated the next generation of mathematicians. During the years leading up to Leonhard Euler's tercentenary, at more than a dozen academic meetings across the USA and Canada, mathematicians and historians of mathematics honored Euler in papers detailing his life and work. This book collects more than 20 papers based on some of the most memorable of these contributions. These papers are accessible to a broad mathematical audience. They will appeal to those who already have an interest in the history of mathematics. For those who don't, they will serve as a compelling introduction to the subject, focused on the accomplishments of one of the great mathematical minds of all time. Topics include analysis - especially Euler's fearless and masterful manipulation of power series - geometry, algebra, probability, astronomy and mechanics.
Contents
Introduction; Leonhard Euler, the decade 1750-1760 Rüdiger Thiele; Euler's fourteen problems C. Edward Sandifer; The Euler archive: giving Euler to the world Dominic Klyve and Lee Stemkoski; The Euler-Bernoulli proof of the fundamental theorem of algebra Christopher Baltus; The quadrature of Lunes, from Hippocrates to Euler Stacy G. Langton; What is a function? Rüdiger Thiele; Enter, stage center: the early drama of the hyperbolic functions Janet Heine Barnett; Euler's solution of the Basel problem - the longer story C. Edward Sandifer; Euler and elliptic integrals Lawrence D'Antonio; Euler's observations on harmonic progressions Mark McKinzie; Origins of a classic formalist argument: power series expansions of the logarithmic and exponential functions Mark McKinzie; Taylor and Euler: linking the discrete and continuous Dick Jardine; Dances between continuous and discrete: Euler's summation formula David J. Pengelley; Some combinatorics in Jacob Bernoulli's Ars Conjectandi Stacy G. Langton; The Genoese lottery and the partition function Robert E. Bradley; Parallels in the work of Leonhard Euler and Thomas Clausen Carolyn Lathrop and Lee Stemkoski; Three bodies? Why not four? The motion of the Lunar Apsides Robert E. Bradley; 'The fabric of the universe is most perfect': Euler's research on elastic curves Lawrence D'Antonio; The Euler advection equation Roger Godard; Euler rows the boa C. Edward Sandifer; Lambert, Euler, and Lagrange as map makers George W. Heine, III; Index.
