[PDF] Turning Points In The History Of Mathematics eBook

Author : Hardy Grant
Publisher : Birkhäuser
Page : 112 pages
File Size : 17,38 MB
Release : 2016-04-15
Category : Mathematics
ISBN : 1493932640

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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.

Author : Detlef Laugwitz
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 15,74 MB
Release : 2009-06-08
Category : Mathematics
ISBN : 0817647775

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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.

Author : Joseph W. Dauben
Publisher : Springer Science & Business Media
Page : 776 pages
File Size : 37,55 MB
Release : 2002-09-23
Category : Mathematics
ISBN : 9783764361679

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As an historiographic monograph, this book offers a detailed survey of the professional evolution and significance of an entire discipline devoted to the history of science. It provides both an intellectual and a social history of the development of the subject from the first such effort written by the ancient Greek author Eudemus in the Fourth Century BC, to the founding of the international journal, Historia Mathematica, by Kenneth O. May in the early 1970s.

Author : Detlef Laugwitz
Publisher :
Page : 357 pages
File Size : 32,37 MB
Release : 1999
Category : Mathematicians
ISBN : 9783764340407

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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.

Author : S.G. Shanker
Publisher : Routledge
Page : 571 pages
File Size : 48,27 MB
Release : 2013-12-19
Category : Philosophy
ISBN : 1317832035

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First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

Author : David E. Smith
Publisher : Courier Corporation
Page : 756 pages
File Size : 31,8 MB
Release : 1958-06-01
Category : Mathematics
ISBN : 9780486204307

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Within this two-volume edition, Professor Smith covers the entire history of mathematics in the Near and Far East and the West, from primitive number concepts to the calculus. His account is distinguished by impeccable scholarship combined with unusual clarity and readability. Footnotes add many technical points outside the book's actual line of development and direct the reader to disputed matters and source readings. Hundreds of illustrations from Egyptian papyri, Hindu, Chinese, and Japanese manuscripts, Greek and Roman texts, Medieval treatises, maps, portraits, etc. are used along with modern graphs and diagrams. Every major figure from Euclid to Descartes, Gauss, and Riemann and hundreds of lesser-known figures — Theon of Smyrna, Rabbi ben Ezra, Radulph of Laon, Mersenns, Benedetti, and more — are considered both with respect to specific problems and with an awareness of their overall influence on mathematics. Volume II: Special Topics, considering mathematics in terms of arithmetic geometry, algebra, trig, calculus, calculating machines, and other specific fields and problems. 192 Topics for Discussion. 195 illustrations. Index.

Author : Roger L. Cooke
Publisher : John Wiley & Sons
Page : 630 pages
File Size : 16,17 MB
Release : 2011-02-14
Category : Mathematics
ISBN : 1118030249

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This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Author : Steven G. Krantz
Publisher : MAA
Page : 395 pages
File Size : 25,34 MB
Release : 2010-04
Category : Mathematics
ISBN : 0883857669

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A series of snapshots of the history of mathematics from ancient times to the twentieth century.