Turning Points In The History Of Mathematics
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Turning Points In The History Of Mathematics
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Author : Hardy Grant
language : en
Publisher: Birkhäuser
Release Date : 2016-04-15
Turning Points In The History Of Mathematics written by Hardy Grant and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-15 with Mathematics categories.
This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.
Bernhard Riemann 1826 1866
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Author : Detlef Laugwitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-08
Bernhard Riemann 1826 1866 written by Detlef Laugwitz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-08 with Mathematics categories.
The name of Bernard Riemann is well known to mathematicians and physicists around the world. His name is indelibly stamped on the literature of mathematics and physics. This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.
Bernhard Riemann 1826 1866
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Author : Detlef Laugwitz
language : en
Publisher:
Release Date : 1999
Bernhard Riemann 1826 1866 written by Detlef Laugwitz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematicians categories.
This book, originally written in German and presented here in an English-language translation, is the first attempt to examine Riemann's scientific work from a single unifying perspective. Laugwitz describes Riemann's development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hilbert gave prominence to the Riemannian principle of utilizing thought, not calculation, to achieve proofs. Hermann Weyl interpreted the Riemann principle - for mathematics and physics alike - to be a matter of "understanding the world through its behavior in the infinitely small." This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann's work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.
History Of Mathematics
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Author : Craig Smorynski
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-03
History Of Mathematics written by Craig Smorynski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-03 with Mathematics categories.
General textbooks, attempting to cover three thousand or so years of mathematical history, must necessarily oversimplify just about everything, the practice of which can scarcely promote a critical approach to the subject. To counter this, History of Mathematics offers deeper coverage of key select topics, providing students with material that could encourage more critical thinking. It also includes the proofs of important results which are typically neglected in the modern history of mathematics curriculum.
Classics In The History Of Greek Mathematics
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Author : Jean Christianidis
language : de
Publisher: Springer
Release Date : 2004-09-16
Classics In The History Of Greek Mathematics written by Jean Christianidis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-16 with Mathematics categories.
This volume includes a selection of 19 classic papers on the history of Greek mathematics that were published during the 20th century and affected significantly the state of the art of this field. It is divided into six thematic sections and covers all the major issues of the Greek mathematical production. First, the inclusion in one volume of a considerable number of papers that had been published for the first time in old, and in certain cases hard to find, scientific journals representing turning-points in the history of the field, constitutes a particularly useful aid for all those working on the history of mathematics. Second, by means of the selected papers and the introductory texts of six well-known modern historians of ancient mathematics that accompany them, the reader can follow the ways the historiography of Greek mathematics developed. Finally, the introductory texts that precede each chapter help the reader to approach critically the selected papers and at the same time to get an idea of the issues being further clarified by the new historiographical approaches. The audience of the book includes scholars from history and philosophy of mathematics and mathematical sciences, scholars from history of science, students in the field of history of mathematics and history of sciences.
A History Of Non Euclidean Geometry
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Author : Boris A. Rosenfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-08
A History Of Non Euclidean Geometry written by Boris A. Rosenfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-08 with Mathematics categories.
The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
A History In Sum
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Author : Steve Nadis
language : en
Publisher: Harvard University Press
Release Date : 2013-11-01
A History In Sum written by Steve Nadis and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with Mathematics categories.
In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard's mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry, complex analysis, and other esoteric subdisciplines that are rarely written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics--an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce's successors transformed the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Influential figures soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
A Station Favorable To The Pursuits Of Science Primary Materials In The History Of Mathematics At The United States Military Academy
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Author : Joe Albree
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
A Station Favorable To The Pursuits Of Science Primary Materials In The History Of Mathematics At The United States Military Academy written by Joe Albree and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book reveals the rich collection of mathematical works located at the nation's first military school, the U.S. Military Academy at West Point. It outlines the relevant history of the Academy, discusses the mathematics department and curriculum, and describes the development of the library during the nineteenth century. A major part of this book is an annotated catalog of the more than 1300 works published between 1496 and 1915 found in the West Point library. Mathematics and its instruction greatly influenced the development of the Academy, the technological growth of America's army, and the standards of the military profession. These events, in turn, were crucial to the overall development of mathematics, mechanics, and engineering during the nineteenth century in the United States. Three individuals played a prominent role in this chronicle: Sylvanus Thayer, Charles Davies, and Albert Church. Listed are rare and historically valuable works in a broad range of mathematical subjects. The collection clearly shows the strong European influence on the early Academy. Also listed are numerous textbooks by West Point faculty and graduates; significant contributions were made by these writers to algebra, geometry, calculus, descriptive geometry, mechanics, surveying, and mathematics education. This book provides an important resource for the general audience as well as for those in pursuit of more scholarly information. It contains many interesting photographs and valuable details about the West Point collection. It is a must-have for anyone interested in mathematical books and collections.
Essays In The History Of Mathematics
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Author : Arthur Schlissel
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Essays In The History Of Mathematics written by Arthur Schlissel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Mathematics And Its History
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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-27
Mathematics And Its History written by John Stillwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-27 with Mathematics categories.
This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added as well as commentary that helps place the exercises in context.