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Author: Gert Schubring
Publisher: Springer
ISBN: 303001617X
Category : Education
Languages : en
Pages : 201
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Book Description
This contributed volume investigates the active role of the different contexts of mathematics teaching on the evolution of the practices of mathematical concepts, with particular focus on their foundations. The book aims to deconstruct the strong and generally wide-held conviction that research in mathematics constitutes the only driving force for any progress in the development of mathematics as a field. In compelling and convincing contrast, these chapters aim to show the productive function of teaching, showcasing investigations from countries and regions throughout various eras, from Old Babylonia through the 20th Century. In so doing, they provide a critical reflection on the foundations of mathematics, as well as instigate new research questions, and explore the interfaces between teaching and research.
Author: Gert Schubring
Publisher: Springer
ISBN: 303001617X
Category : Education
Languages : en
Pages : 201
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Book Description
This contributed volume investigates the active role of the different contexts of mathematics teaching on the evolution of the practices of mathematical concepts, with particular focus on their foundations. The book aims to deconstruct the strong and generally wide-held conviction that research in mathematics constitutes the only driving force for any progress in the development of mathematics as a field. In compelling and convincing contrast, these chapters aim to show the productive function of teaching, showcasing investigations from countries and regions throughout various eras, from Old Babylonia through the 20th Century. In so doing, they provide a critical reflection on the foundations of mathematics, as well as instigate new research questions, and explore the interfaces between teaching and research.
Author: Catherine Goldstein
Publisher: Springer Science & Business Media
ISBN: 3540347208
Category : Mathematics
Languages : en
Pages : 579
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Book Description
Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication.
Author: Giora Hon
Publisher: Springer Science & Business Media
ISBN: 140208448X
Category : Science
Languages : en
Pages : 337
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Book Description
Many literary critics seem to think that an hypothesis about obscure and remote questions of history can be refuted by a simple demand for the production of more evidence than in fact exists. The demand is as easy to make as it is impossible to satisfy. But the true test of an hypothesis, if it cannot be shown to con?ict with known truths, is the number of facts that it correlates and explains. Francis M. Cornford [1914] 1934, 220. It was in the autumn of 1997 that the research project leading to this publication began. One of us [GH], while a visiting fellow at the Center for Philosophy of Science (University of Pittsburgh), gave a talk entitled, “Proportions and Identity: The Aesthetic Aspect of Symmetry”. The presentation focused on a confusion s- rounding the concept of symmetry: it exhibits unity, yet it is often claimed to reveal a form of beauty, namely, harmony, which requires a variety of elements. In the audience was the co-author of this book [BRG] who responded with enthusiasm, seeking to extend the discussion of this issue to historical sources in earlier periods. A preliminary search of the literature persuaded us that the history of symmetry was rich in possibilities for new insights into the making of concepts. John Roche’s brief essay (1987), in which he sketched the broad outlines of the history of this concept, was particularly helpful, and led us to conclude that the subject was worthy of monographic treatment.
Author: Carl Friedrich Gauss
Publisher: Springer
ISBN: 1493975609
Category : Mathematics
Languages : en
Pages : 491
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Book Description
Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
Author: Claude Brezinski
Publisher: Springer Science & Business Media
ISBN: 3642581692
Category : Mathematics
Languages : en
Pages : 556
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Book Description
The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...
Author: Scott B. Guthery
Publisher: Docent Press
ISBN: 1453810579
Category : Mathematics
Languages : en
Pages : 266
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Book Description
The curious property that John Farey observed in one of Henry Goodwyn's tables has enduring pratical and theoretic interest. This book traces the curious property, the mediant, from its initial sighting by Nicolas Chuquet and Charles Haros to its connection to the Riemann hypothesis by Jerome Franel.
Author: Rózsa Péter
Publisher:
ISBN:
Category : Recursive functions
Languages : en
Pages : 308
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Book Description
Author: Kostas Gavroglu
Publisher: Springer Science & Business Media
ISBN: 9780792365631
Category : History
Languages : en
Pages : 248
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Book Description
The articles in this volume of ARCHIMEDES examine particular cases of `reception' in ways that emphasize pressing historiographical and methodological issues. Such issues arise in any consideration of the transmission and appropriation of scientific concepts and practices that originated in the several `centers' of European learning, subsequently to appear (often in considerably altered guise) in regions at the European periphery. They discuss the transfer of new scientific ideas, the mechanisms of their introduction, and the processes of their appropriation at the periphery. The themes that frame the discussions of the complex relationship between the origination of ideas and their reception include the ways in which the ideas of the Scientific Revolution were introduced, the particularities of their expression in each place, the specific forms of resistance encountered by these new ideas, the extent to which such expression and resistance displays national characteristics, the procedures through which new ways of dealing with nature were made legitimate, and the commonalities and differences between the methods developed by scholars for handling scientific issues.
Author: A. Rosenberg
Publisher: Springer Science & Business Media
ISBN: 9401027552
Category : History
Languages : en
Pages : 318
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Book Description
Although the novel, V oyages el avantures de] aques Masse, caused some thing of a stir during the first half of the eighteenth century, its author, Simon Tyssot de Patot (1655-1738), remained largely unknown in his lifetime, and it is only in this century that he has been recognized as one of the countless soldiers in the vast army of philosophes that assaulted the bastions of religious, political and sodallife in Europe of the late seven 1 teenth and early eighteenth centuries. Tyssot was a Huguenot who lived most of his life in Holland where he pursued a career as professor of mathematics in the sodal and cultural 1 Tyssot and his work seem to have been first brought to the attention of modem writers by the German critics during their investigation of the type of desert island or robinsonade literature that preceded and followed Defoe's Robinson Crusoe. The earliest reference I have found occurs in A. Kippenberg, Robinson in Deutschland bis zur Insel Felsenburg (1713-43), Hanover, 1892, pp. 66-67. Tyssot's name and work appear to have been first linked with the development of socialism in A. Lichtenberger, Le Socialisme au XVIIIe siecle, Paris, 1895, p. 44. Tyssot's Voyages et avantures de]aques Masse was discussed for its literary merits in A. LeBreton, Le Roman au dix huitieme siecle, Paris, 1898. LeBreton did not know that Tyssot was the author.
Author: Frédéric Bastiat
Publisher: Jazzybee Verlag
ISBN: 3849648788
Category : Business & Economics
Languages : en
Pages : 770
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Book Description
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