Conflicts Between Generalization Rigor And Intuition
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| Author | : Gert Schubring |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 689 |
| Release | : 2006-06-10 |
| Genre | : Mathematics |
| ISBN | : 0387282734 |
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.
| Author | : Gert Schubring |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 700 |
| Release | : 2005-06-14 |
| Genre | : Mathematics |
| ISBN | : 9780387228365 |
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.
| Author | : Sung Je Cho |
| Publisher | : Springer |
| Total Pages | : 917 |
| Release | : 2015-07-16 |
| Genre | : Education |
| ISBN | : 3319171879 |
This book comprises the full selected Regular Lectures from the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 4700 experts from 100 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. These selected Regular Lectures present the work of fifty-one prominent mathematics educators from all over the globe. The Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.
| Author | : Jeffrey M. Binder |
| Publisher | : University of Chicago Press |
| Total Pages | : 328 |
| Release | : 2022-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 0226822540 |
A wide-ranging history of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians well before the computer age: How do you draw the line between computational rules and the complexities of making systems comprehensible to people? By attending to this question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz’s calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole’s nineteenth-century logic system; and the early programming language ALGOL, short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. Machine learning, in its increasing dependence on words, erodes the line between technical and everyday language, revealing the urgent stakes underlying this boundary. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction.
| Author | : Michael Friedman |
| Publisher | : Springer Nature |
| Total Pages | : 258 |
| Release | : 2022-09-26 |
| Genre | : Mathematics |
| ISBN | : 3031057201 |
The book offers an extensive study on the convoluted history of the research of algebraic surfaces, focusing for the first time on one of its characterizing curves: the branch curve. Starting with separate beginnings during the 19th century with descriptive geometry as well as knot theory, the book focuses on the 20th century, covering the rise of the Italian school of algebraic geometry between the 1900s till the 1930s (with Federigo Enriques, Oscar Zariski and Beniamino Segre, among others), the decline of its classical approach during the 1940s and the 1950s (with Oscar Chisini and his students), and the emergence of new approaches with Boris Moishezon’s program of braid monodromy factorization. By focusing on how the research on one specific curve changed during the 20th century, the author provides insights concerning the dynamics of epistemic objects and configurations of mathematical research. It is in this sense that the book offers to take the branch curve as a cross-section through the history of algebraic geometry of the 20th century, considering this curve as an intersection of several research approaches and methods. Researchers in the history of science and of mathematics as well as mathematicians will certainly find this book interesting and appealing, contributing to the growing research on the history of algebraic geometry and its changing images.
| Author | : Nerida Ellerton |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 230 |
| Release | : 2012-01-18 |
| Genre | : Education |
| ISBN | : 9400726392 |
The focus of this book is the fundamental influence of the cyphering tradition on mathematics education in North American colleges, schools, and apprenticeship training classes between 1607 and 1861. It is the first book on the history of North American mathematics education to be written from that perspective. The principal data source is a set of 207 handwritten cyphering books that have never previously been subjected to careful historical analysis.
| Author | : Michela Massimi |
| Publisher | : Springer |
| Total Pages | : 351 |
| Release | : 2017-04-26 |
| Genre | : Science |
| ISBN | : 331953730X |
This edited collection showcases some of the best recent research in the philosophy of science. It comprises of thematically arranged papers presented at the 5th conference of the European Philosophy of Science Association (EPSA15), covering a broad variety of topics within general philosophy of science, and philosophical issues pertaining to specific sciences. The collection will appeal to researchers with an interest in the philosophical underpinnings of their own discipline, and to philosophers who wish to study the latest work on the themes discussed.
| Author | : Jesper Lützen |
| Publisher | : Oxford University Press |
| Total Pages | : 305 |
| Release | : 2023-01-26 |
| Genre | : Mathematical analysis |
| ISBN | : 0192867393 |
Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat's last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. Lützen argues that the role of impossibility results have changed over time. At first, they were considered rather unimportant meta-statements concerning mathematics but gradually they obtained the role of important proper mathematical results that can and should be proved. While mathematical impossibility proofs are more rigorous than impossibility arguments in other areas of life, mathematicians have employed great ingenuity to circumvent impossibilities by changing the rules of the game. For example, complex numbers were invented in order to make impossible equations solvable. In this way, impossibilities have been a strong creative force in the development of mathematics, mathematical physics, and social science.
| Author | : Philip Beeley |
| Publisher | : Routledge |
| Total Pages | : 389 |
| Release | : 2020-10-20 |
| Genre | : Literary Criticism |
| ISBN | : 1000207471 |
Libraries and archives contain many thousands of early modern mathematical books, of which almost equally many bear readers’ marks, ranging from deliberate annotations and accidental blots to corrections and underlinings. Such evidence provides us with the material and intellectual tools for exploring the nature of mathematical reading and the ways in which mathematics was disseminated and assimilated across different social milieus in the early centuries of print culture. Other evidence is important, too, as the case studies collected in the volume document. Scholarly correspondence can help us understand the motives and difficulties in producing new printed texts, library catalogues can illuminate collection practices, while manuscripts can teach us more about textual traditions. By defining and illuminating the distinctive world of early modern mathematical reading, the volume seeks to close the gap between the history of mathematics as a history of texts and history of mathematics as part of the broader history of human culture.
| Author | : Évelyne Barbin |
| Publisher | : Springer |
| Total Pages | : 446 |
| Release | : 2019-07-01 |
| Genre | : Mathematics |
| ISBN | : 3030148084 |
This book seeks to explore the history of descriptive geometry in relation to its circulation in the 19th century, which had been favoured by the transfers of the model of the École Polytechnique to other countries. The book also covers the diffusion of its teaching from higher instruction to technical and secondary teaching. In relation to that, there is analysis of the role of the institution – similar but definitely not identical in the different countries – in the field under consideration. The book contains chapters focused on different countries, areas, and institutions, written by specialists of the history of the field. Insights on descriptive geometry are provided in the context of the mathematical aspect, the aspect of teaching in particular to non-mathematicians, and the institutions themselves.
