The Search For Mathematical Roots 1870 1940
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The Search For Mathematical Roots 1870 1940
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Author : I. Grattan-Guinness
language : en
Publisher: Princeton University Press
Release Date : 2011-02-11
The Search For Mathematical Roots 1870 1940 written by I. Grattan-Guinness and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-11 with Mathematics categories.
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). ? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
The Search For Mathematical Roots 1870 1940
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Author : I. Grattan-Guinness
language : en
Publisher:
Release Date : 2011
The Search For Mathematical Roots 1870 1940 written by I. Grattan-Guinness and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A.N. Whitehead in their Principia mathematica (1910-1913).? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E.H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
The Search For Mathematical Roots 1870 1940
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Author : I. Grattan-Guinness
language : en
Publisher:
Release Date : 2000
The Search For Mathematical Roots 1870 1940 written by I. Grattan-Guinness and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913). This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
From The Calculus To Set Theory 1630 1910
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Author : I. Grattan-Guinness
language : en
Publisher: Princeton University Press
Release Date : 2020-10-06
From The Calculus To Set Theory 1630 1910 written by I. Grattan-Guinness and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Mathematics categories.
From the Calculus to Set Theory traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and the foundations of mathematics in the early twentieth century. It chronicles the work of mathematicians from Descartes and Newton to Russell and Hilbert and many, many others while emphasizing foundational questions and underlining the continuity of developments in higher mathematics. The other contributors to this volume are H. J. M. Bos, R. Bunn, J. W. Dauben, T. W. Hawkins, and K. Møller-Pedersen.
New Perspectives On Mathematical Practices
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Author : Bart van Kerkhove
language : en
Publisher: World Scientific
Release Date : 2009
New Perspectives On Mathematical Practices written by Bart van Kerkhove and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
The New Era In American Mathematics 1920 1950
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Author : Karen Hunger Parshall
language : en
Publisher: Princeton University Press
Release Date : 2022-02-22
The New Era In American Mathematics 1920 1950 written by Karen Hunger Parshall and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-22 with History categories.
"The 1920s witnessed the birth of a serious mathematical research community in America. Prior to this, mathematical research was dominated by scholars based in Europe-but World War I had made the importance of scientific and technological development clear to the American research community, resulting in the establishment of new scientific initiatives and infrastructure. Physics and chemistry were the beneficiaries of this renewed scientific focus, but the mathematical community also benefitted, and over time, began to flourish. Over the course of the next two decades, despite significant obstacles, this constellation of mathematical researchers, programs, and government infrastructure would become one of the strongest in the world. In this meticulously-researched book, Karen Parshall documents the uncertain, but ultimately successful, rise of American mathematics during this time. Drawing on research carried out in archives around the country and around the world, as well as on the secondary literature, she reveals how geopolitical circumstances shifted the course of international mathematics. She provides surveys of the mathematical research landscape in the 1920s, 30s, and 40s, introduces the key players and institutions in mathematics at that time, and documents the effect of the Great Depression and the second world war on the international mathematical community. The result is a comprehensive account of the shift of mathematics' "center of gravity" to the American stage"--
The History Of Mathematics
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Author : Roger L. Cooke
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-14
The History Of Mathematics written by Roger L. Cooke and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-14 with Mathematics categories.
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.
A History Of Mathematics In The United States And Canada
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Author : David E. Zitarelli
language : en
Publisher: American Mathematical Society
Release Date : 2022-10-25
A History Of Mathematics In The United States And Canada written by David E. Zitarelli and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-25 with Mathematics categories.
This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of a research community the United States in the last quarter of the nineteenth. In the story of the colonial period, particular emphasis is given to several prominent colonial figures—Jefferson, Franklin, and Rittenhouse—and four important early colleges—Harvard, Québec, William & Mary, and Yale. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins in 1876 the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians including especially Klein, Hilbert, and Sylvester. Klein's visit to the US and his Evanston Colloquium are extensively detailed. The founding of the American Mathematical Society is thoroughly discussed. David Zitarelli was emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he was one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this was his magnum opus—sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.
A History Of Mathematics In The United States And Canada Volume 1 1492 1900
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Author : David E. Zitarelli
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-10-21
A History Of Mathematics In The United States And Canada Volume 1 1492 1900 written by David E. Zitarelli 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 2019-10-21 with Education categories.
This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of a research community the United States in the last quarter of the nineteenth. In the story of the colonial period, particular emphasis is given to several prominent colonial figures—Jefferson, Franklin, and Rittenhouse—and four important early colleges—Harvard, Québec, William & Mary, and Yale. During the first three-quarters of the nineteenth century, mathematics in North America was largely the occupation of scattered individual pioneers: Bowditch, Farrar, Adrain, B. Peirce. This period is given a fuller treatment here than previously in the literature, including the creation of the first PhD programs and attempts to form organizations and found journals. With the founding of Johns Hopkins in 1876 the American mathematical research community was finally, and firmly, founded. The programs at Hopkins, Chicago, and Clark are detailed as are the influence of major European mathematicians including especially Klein, Hilbert, and Sylvester. Klein's visit to the US and his Evanston Colloquium are extensively detailed. The founding of the American Mathematical Society is thoroughly discussed. David Zitarelli is emeritus Professor of Mathematics at Temple University. A decorated and acclaimed teacher, scholar, and expositor, he is one of the world's leading experts on the development of American mathematics. Author or co-author of over a dozen books, this is his magnum opus—sure to become the leading reference on the topic and essential reading, not just for historians. In clear and compelling prose Zitarelli spins a tale accessible to experts, generalists, and anyone interested in the history of science in North America.
Philosophy Of Mathematics
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Author :
language : en
Publisher: Elsevier
Release Date : 2009-07-08
Philosophy Of Mathematics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-08 with Philosophy categories.
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included