Turning Points In The History Of Mathematics

Author : Hardy Grant,Israel Kleiner
Publisher : Birkhäuser
Page : 109 pages
File Size : 53,5 Mb
Release : 2016-04-15
Category : Mathematics
ISBN : 9781493932641

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Turning Points in the History of Mathematics by Hardy Grant,Israel Kleiner Pdf

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 : 50,9 Mb
Release : 2009-06-08
Category : Mathematics
ISBN : 9780817647773

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Bernhard Riemann 1826–1866 by Detlef Laugwitz Pdf

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 : Detlef Laugwitz
Publisher : Unknown
Page : 357 pages
File Size : 42,7 Mb
Release : 1999
Category : Mathematicians
ISBN : 3764340401

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Bernhard Riemann, 1826-1866 by Detlef Laugwitz Pdf

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 : Craig Smorynski
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 48,9 Mb
Release : 2007-12-03
Category : Mathematics
ISBN : 9780387754819

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History of Mathematics by Craig Smorynski Pdf

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.

Author : Arthur Schlissel
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 41,9 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821822982

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Essays in the History of Mathematics by Arthur Schlissel Pdf

Author : Luke Heaton
Publisher : Oxford University Press
Page : 337 pages
File Size : 46,9 Mb
Release : 2017
Category : History
ISBN : 9780190621766

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A Brief History of Mathematical Thought by Luke Heaton Pdf

Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, -no mathematical knowledge required.- Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. --

Author : Angela Lynn Evans Walmsley
Publisher : University Press of America
Page : 92 pages
File Size : 43,7 Mb
Release : 2007-05-22
Category : Education
ISBN : 9781461676218

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A History of Mathematics Education during the Twentieth Century by Angela Lynn Evans Walmsley Pdf

A History of Mathematics Education during the Twentieth Century describes the history of mathematics education in the United States with conceptual themes concerning philosophy, mathematics content, teacher education, pedagogy, and assessment.

Author : Niccol- Guicciardini
Publisher : Cambridge University Press
Page : 393 pages
File Size : 45,6 Mb
Release : 2021-07-22
Category : History
ISBN : 9781108834964

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Anachronisms in the History of Mathematics by Niccol- Guicciardini Pdf

Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.

Author : Luke Hodgkin
Publisher : OUP Oxford
Page : 296 pages
File Size : 43,7 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9780191664366

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A History of Mathematics by Luke Hodgkin Pdf

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

Author : Steven G. Krantz
Publisher : MAA
Page : 395 pages
File Size : 44,7 Mb
Release : 2010-04
Category : Mathematics
ISBN : 9780883857663

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An Episodic History of Mathematics by Steven G. Krantz Pdf

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

Author : Steve Nadis
Publisher : Harvard University Press
Page : 128 pages
File Size : 45,5 Mb
Release : 2013-11-01
Category : Mathematics
ISBN : 9780674727892

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A History in Sum by Steve Nadis Pdf

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.

Author : A.N. Kolmogorov,A.P. Yushkevich
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 50,6 Mb
Release : 1998-03-24
Category : Mathematics
ISBN : 3764358459

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Mathematics of the 19th Century by A.N. Kolmogorov,A.P. Yushkevich Pdf

The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.

Author : Jean Christianidis
Publisher : Springer
Page : 492 pages
File Size : 44,6 Mb
Release : 2004-09-16
Category : Mathematics
ISBN : STANFORD:36105119804206

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Classics in the History of Greek Mathematics by Jean Christianidis Pdf

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.

Author : Walter William Rouse Ball
Publisher : Unknown
Page : 576 pages
File Size : 52,6 Mb
Release : 1908
Category : Mathematicians
ISBN : UOM:39015065517024

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A Short Account of the History of Mathematics by Walter William Rouse Ball Pdf

Author : James R. Newman
Publisher : Рипол Классик
Page : 2535 pages
File Size : 48,8 Mb
Release : 1960
Category : History
ISBN : 9785881361617

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The World of Mathematics by James R. Newman Pdf