Download or read book Correspondence of Leonhard Euler with Christian Goldbach written by Leonhard Euler and published by Birkhäuser. This book was released on 2015-09-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When Leonhard Euler first arrived at the Russian Academy of Sciences, at the age of 20, his career was supported and promoted by the Academy’s secretary, the Prussian jurist and amateur mathematician Christian Goldbach (1690-1764). Their encounter would grow into a lifelong friendship, as evinced by nearly 200 letters sent over 35 years. This exchange – Euler’s most substantial long-term correspondence – has now been edited for the first time with an English translation, ample commentary and documentary indices. These present an overview of 18th-century number theory, its sources and repercussions, many details of the protagonists’ biographies, and a wealth of insights into academic life in St. Petersburg and Berlin between 1725 and 1765. Part I includes an introduction and the original texts of the Euler-Goldbach letters, while Part II presents the English translations and documentary indices.
Download or read book The Early Mathematics of Leonhard Euler written by C. Edward Sandifer and published by American Mathematical Soc.. This book was released on 2020-07-14 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Early Mathematics of Leonhard Euler gives an article-by-article description of Leonhard Euler's early mathematical works; the 50 or so mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These early pieces contain some of Euler's greatest work, the Konigsberg bridge problem, his solution to the Basel problem, and his first proof of the Euler-Fermat theorem. It also presents important results that we seldom realize are due to Euler; that mixed partial derivatives are (usually) equal, our f(x) f(x) notation, and the integrating factor in differential equations. The books shows how contributions in diverse fields are related, how number theory relates to series, which, in turn, relate to elliptic integrals and then to differential equations. There are dozens of such strands in this beautiful web of mathematics. At the same time, we see Euler grow in power and sophistication, from a young student when at 18 he published his first work on differential equations (a paper with a serious flaw) to the most celebrated mathematician and scientist of his time. It is a portrait of the world's most exciting mathematics between 1725 and 1741, rich in technical detail, woven with connections within Euler's work and with the work of other mathematicians in other times and places, laced with historical context.
Download or read book Mathematical Correspondences and Critical Editions written by Maria Teresa Borgato and published by Birkhäuser. This book was released on 2019-03-22 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical correspondence offers a rich heritage for the history of mathematics and science, as well as cultural history and other areas. It naturally covers a vast range of topics, and not only of a scientific nature; it includes letters between mathematicians, but also between mathematicians and politicians, publishers, and men or women of culture. Wallis, Leibniz, the Bernoullis, D'Alembert, Condorcet, Lagrange, Gauss, Hermite, Betti, Cremona, Poincaré and van der Waerden are undoubtedly authors of great interest and their letters are valuable documents, but the correspondence of less well-known authors, too, can often make an equally important contribution to our understanding of developments in the history of science. Mathematical correspondences also play an important role in the editions of collected works, contributing to the reconstruction of scientific biographies, as well as the genesis of scientific ideas, and in the correct dating and interpretation of scientific writings. This volume is based on the symposium “Mathematical Correspondences and Critical Editions,” held at the 6th International Conference of the ESHS in Lisbon, Portugal in 2014. In the context of the more than fifteen major and minor editions of mathematical correspondences and collected works presented in detail, the volume discusses issues such as • History and prospects of past and ongoing edition projects, • Critical aspects of past editions, • The complementary role of printed and digital editions, • Integral and partial editions of correspondence, • Reproduction techniques for manuscripts, images and formulae, and the editorial challenges and opportunities presented by digital technology.
Download or read book Leonhard Euler written by Robert E. Bradley and published by Elsevier. This book was released on 2007-03-20 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler's life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler's philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler's innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.- Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century
Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Leonhard Euler written by Ronald Calinger and published by Princeton University Press. This book was released on 2019-12-03 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment."--Publisher's description.
Download or read book Leonhard Euler s Letters to a German Princess written by Ronald S Calinger and published by Morgan & Claypool Publishers. This book was released on 2019-06-28 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leonhard Euler's Letters to a German Princess: A Milestone in the History of Physics Textbooks and More is a milestone in the history of physics textbooks and the instruction of women in the sciences. It also covers views of its author on epistemology, religion, and innovations in scientific equipment, including telescopes and microscopes. Today, 250 years later, we study this work of Euler's as a foundation for the history of physics teaching and analyze the letters from an historical and pedagogical point of view.
Download or read book Reciprocity Laws written by Franz Lemmermeyer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.
Download or read book Leonhard Euler written by Emil A. Fellmann and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euler was not only by far the most productive mathematician in the history of mankind, but also one of the greatest scholars of all time. He attained, like only a few scholars, a degree of popularity and fame which may well be compared with that of Galilei, Newton, or Einstein. Moreover he was a cosmopolitan in the truest sense of the word; he lived during his first twenty years in Basel, was active altogether for more than thirty years in Petersburg and for a quarter of a century in Berlin. Leonhard Euler’s unusually rich life and broadly diversified activity in the immediate vicinity of important personalities which have made history, may well justify an exposition. This book is based in part on unpublished sources and comes right out of the current research on Euler. It is entirely free of formulae as it has been written for a broad audience with interests in the history of culture and science.
Download or read book The Legacy of Leonhard Euler written by Lokenath Debnath and published by World Scientific. This book was released on 2010 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler''s works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler''s personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author''s historically motivated method of teaching, special attention is given to demonstrate that Euler''s work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler''s extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research. Erratum. Sample Chapter(s). Chapter 1: Mathematics Before Leonhard Euler (434 KB). Contents: Mathematics Before Leonhard Euler; Brief Biographical Sketch and Career of Leonhard Euler; Euler''s Contributions to Number Theory and Algebra; Euler''s Contributions to Geometry and Spherical Trigonometry; Euler''s Formula for Polyhedra, Topology and Graph Theory; Euler''s Contributions to Calculus and Analysis; Euler''s Contributions to the Infinite Series and the Zeta Function; Euler''s Beta and Gamma Functions and Infinite Products; Euler and Differential Equations; The Euler Equations of Motion in Fluid Mechanics; Euler''s Contributions to Mechanics and Elasticity; Euler''s Work on the Probability Theory; Euler''s Contributions to Ballistics; Euler and His Work on Astronomy and Physics. Readership: Undergraduate and graduate students of mathematics, mathematics education, physics, engineering and science. As well as professionals and prospective mathematical scientists.
Download or read book Resources for Teaching Discrete Mathematics written by Brian Hopkins and published by MAA. This book was released on 2009 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopkins collects the work of 35 instructors who share their innovations and insights about teaching discrete mathematics at the high school and college level. The book's 9 classroom-tested projects, including building a geodesic dome, come with student handouts, solutions, and notes for the instructor. The 11 history modules presented draw on original sources, such as Pascal's "Treatise on the Arithmetical Triangle," allowing students to explore topics in their original contexts. Three articles address extensions of standard discrete mathematics content. Two other articles explore pedagogy specifically related to discrete mathematics courses: adapting a group discovery method to larger classes, and using logic in encouraging students to construct proofs.
Download or read book Elements of Algebra written by Leonhard Euler and published by . This book was released on 1810 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vita Mathematica written by Ronald Calinger and published by Cambridge University Press. This book was released on 1996 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enables teachers to learn the history of mathematics and then incorporate it in undergraduate teaching.
Download or read book Problem Solved written by Robert Snedden and published by Arcturus Publishing. This book was released on 2018-11-15 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: From early humans carving notches in bones to the discovery of quantum mechanics and chaos theory - mathematics has certainly come a long way. Fully illustrated and augmented with helpful timelines and diagrams, Problem Solved! explores some of history's greatest mathematical breakthroughs. Covering topics from Ancient Egyptian geometry to chaos theory, readers will learn about Euclid of Alexandria, Brahmagupta, Sir Isaac Newton, Alan Turing and more. Whether solving practical or abstract problems, these mathematicians have each sought to improve our lives, and have bought us to the world we know today. With each concept explained in easy-to-understand language, there's no need to be a calculus genius to marvel at these incredible feats of problem-solving brilliance.
Download or read book Euler written by William Dunham and published by American Mathematical Society. This book was released on 2022-01-13 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Pythagoras Legacy written by Marcel Danesi and published by Oxford University Press. This book was released on 2020-02-04 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the famous Pythagorean statement reads, 'Number rules the universe', and its veracity is proven in the many mathematical discoveries that have accelerated the development of science, engineering, and even philosophy. A so called "art of the mind", mathematics has guided and stimulated many aspects of human innovation down through the centuries. In this book, Marcel Danesi presents a historical overview of the ten greatest achievements in mathematics, and dynamically explores their importance and effects on our daily lives. Considered as a chain of events rather than isolated incidents, Danesi takes us from the beginnings of modern day mathematics with Pythagoras, through the concept of zero, right the way up to modern computational algorithms. Loaded with thought-provoking practical exercises and puzzles, Pythagoras' Legacy allows the reader to apply their knowledge and discover the significance of mathematics in their everyday lives.
Download or read book Leonhard Euler and the Foundations of Celestial Mechanics written by Dora Musielak and published by Springer Nature. This book was released on 2022-11-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this book is to shine a bright light on the intellectual context of Euler’s contributions to physics and mathematical astronomy. Leonhard Euler is one of the most important figures in the history of science, a blind genius who introduced mathematical concepts and many analytical tools to help us understand and describe the universe. Euler also made a monumental contribution to astronomy and orbital mechanics, developing what he called astronomia mechanica. Orbital mechanics of artificial satellites and spacecraft is based on Euler’s analysis of astromechanics. However, previous books have often neglected many of his discoveries in this field. For example, orbital mechanics texts refer to the five equilibrium points in the Sun-Earth-Moon system as Lagrange points, failing to credit Euler who first derived the differential equations for the general n-body problem and who discovered the three collinear points in the three-body problem of celestial mechanics. These equilibrium points are essential today in space exploration; the James Webb Space Telescope (successor to the Hubble), for example, now orbits the Sun near L2, one of the collinear points of the Sun-Earth-Moon system, while future missions to study the universe will place observatories in orbit around Sun-Earth and Earth-Moon equilibrium points that should be properly called Euler-Lagrange points. In this book, the author uses Euler’s memoirs, correspondence, and other scholarly sources to explore how he established the mathematical groundwork for the rigorous study of motion in our Solar System. The reader will learn how he studied comets and eclipses, derived planetary orbits, and pioneered the study of planetary perturbations, and how, old and blind, Euler put forward the most advanced lunar theory of his time.
