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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 Graßmann 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 method.
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field
This book is about the creation and production of textbooks for learning and teaching mathematics. It covers a period from Antiquity to Modern Times. The analysis begins by assessing principal cultures with a practice of mathematics. The tension between the role of the teacher and his oral mode, on the one hand, and the use of a written (printed) text, in their respective relation with the student, is one of the dimensions of the comparative analysis, conceived of as the ‘textbook triangle’. The changes in this tension with the introduction of the printing press are discussed. The book presents various national case studies (France, Germany, Italy) as well as analyses of the internationalisation of textbooks via transmission processes. As this topic has not been sufficiently explored in the literature, it will be very well received by scholars of mathematics education, mathematics teacher educators and anyone with an interest in the field.
Thomas Kuhn and Karl Popper are believed by many who study science to be the two key thinkers of the twentieth century. Each addressed the question of how scientific theories change, but they came to different conclusions. By turning our attention to ambiguity and indecision in science, Menachem Fisch, in Creatively Undecided, offers a new way to look at how scientific understandings change. Following Kuhn, Fisch argues that scientific practice depends on the framework in which it is conducted, but he also shows that those frameworks can be understood as the possible outcomes of the rational deliberation that Popper viewed as central to theory change. How can a scientist subject her standards to rational appraisal if that very act requires the use of those standards? The way out, Fisch argues, is by looking at the incentives scientists have to create alternative frameworks in the first place. Fisch argues that while science can only be transformed from within, by people who have standing in the field, criticism from the outside is essential. We may not be able to be sufficiently self-critical on our own, but trusted criticism from outside, even if resisted, can begin to change our perspective—at which point transformative self-criticism becomes a real option.