Description: Conflicts Between Generalization, Rigor, and Intuition by Gert Schubring This volume is, as may be readily apparent, the fruit of many years labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International GraÃÿmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811-precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites-significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic met FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This book deals with the development of the terms of analysis in the 18th and 19th centuries, the two main concepts being negative numbers and infinitesimals. Schubring studies often overlooked texts, in particular German and French textbooks, and reveals a much richer history than previously thought while throwing new light on major figures, such as Cauchy. Back Cover Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there. This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization (in particular, algebraization as an agent for generalizing) and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor. The study focuses on the 18th and the 19th centuries, with a detailed analysis of Lazare Carnots and A. L. Cauchys foundational ideas. By researching the development of the concept of negative and infinitely small numbers, the book provides a productive unity to a large number of historical sources. This approach permits a nuanced analysis of the meaning of mathematical ideas as conceived of by 18th and 19th century scientists, while illustrating the authors actions within the context of their respective cultural and scientific communities. The result is a highly readable study of conceptual history and a new model for the cultural history of mathematics. Table of Contents Question and Method.- Paths Toward Algebraization — Development to the Eighteenth Century. The Number Field.- Paths toward Algebraization — The Field of Limits: The Development of Infinitely Small Quantities.- Culmination of Algebraization and Retour du Refoulé.- Le Retour du Refoulé: From the Perspective of Mathematical Concepts.- Cauchys Compromise Concept.- Development of Pure Mathematics in Prussia/Germany.- Conflicts Between Confinement to Geometry and Algebraization in France.- Summary and Outlook. Review From the reviews:"This is a very ambitious book, both in its methodology and in the amount of material it addresses. … The topic is of major interest, focusing on two concepts that extended the idea of what was meant by number … . this book remains a major contribution. The rich and detailed account of textbooks and educational institutions, and the key passages and events Schubring highlights … add greatly to our understanding of the history of mathematics in one of its most exciting periods." (Judith V. Grabiner, SIAM Review, Vol. 48 (2), 2006)"The present book is a voluminous and detailed study of the conceptual developments of negative numbers and infinitesimals from the prehistory of the calculus to the end of the nineteenth century. ... It stands out as special by treating many primary mathematical sources that are rarely subjected to historical study … . this volume presents an important new contextualised perspective on the history of negative numbers and infinitesimals. It includes a rich variety of institutional and philosophical discussions … ." (Henrik Kragh SØrenson, Zentralblatt MATH, Vol. 1086, 2006)"This deep and important epistemological study analyses the evolution of concepts fundamental to mathematical analysis up to the nineteenth century. … The author examines how concepts were generalized and differentiated and pays particular attention to the role of symbolism. He critically reviews the work of other authors who have treated the same historical periods." (E. J. Barbeau, Mathematical Reviews, Issue 2006 d) Long Description This volume is, as may be readily apparent, the fruit of many years labor in archives and libraries, unearthing rare books, researching Nachl Review Quote From the reviews:"This is a very ambitious book, both in its methodology and in the amount of material it addresses. The topic is of major interest, focusing on two concepts that extended the idea of what was meant by number " . this book remains a major contribution. The rich and detailed account of textbooks and educational institutions, and the key passages and events Schubring highlights add greatly to our understanding of the history of mathematics in one of its most exciting periods." (Judith V. Grabiner, SIAM Review, Vol. 48 (2), 2006)"The present book is a voluminous and detailed study of the conceptual developments of negative numbers and infinitesimals from the prehistory of the calculus to the end of the nineteenth century. ... It stands out as special by treating many primary mathematical sources that are rarely subjected to historical study . this volume presents an important new contextualised perspective on the history of negative numbers and infinitesimals. It includes a rich variety of institutional and philosophical discussions ." (Henrik Kragh S renson, Zentralblatt MATH, Vol. 1086, 2006)"This deep and important epistemological study analyses the evolution of concepts fundamental to mathematical analysis up to the nineteenth century. The author examines how concepts were generalized and differentiated and pays particular attention to the role of symbolism. He critically reviews the work of other authors who have treated the same historical periods." (E. J. Barbeau, Mathematical Reviews, Issue 2006 d) Feature Includes supplementary material: sn.pub/extras Details ISBN1441919872 Author Gert Schubring Publisher Springer-Verlag New York Inc. Series Sources and Studies in the History of Mathematics and Physical Sciences Year 2010 ISBN-10 1441919872 ISBN-13 9781441919878 Format Paperback Imprint Springer-Verlag New York Inc. Subtitle Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany Place of Publication New York, NY Country of Publication United States DEWEY 510 Short Title CONFLICTS BETWEEN GENERALIZATI Language English Media Book Pages 678 Publication Date 2010-12-01 AU Release Date 2010-12-01 NZ Release Date 2010-12-01 US Release Date 2010-12-01 UK Release Date 2010-12-01 Illustrations XIV, 678 p. Edition Description Softcover reprint of hardcover 1st ed. 2005 Alternative 9780387228365 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96237515;
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ISBN-13: 9781441919878
Book Title: Conflicts Between Generalization, Rigor, and Intuition
Number of Pages: 678 Pages
Publication Name: Conflicts Between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany
Language: English
Publisher: Springer-Verlag New York Inc.
Item Height: 235 mm
Subject: Mathematics
Publication Year: 2010
Type: Textbook
Item Weight: 1044 g
Author: Gert Schubring
Item Width: 155 mm
Format: Paperback
