John Fauvel - Böcker

August Möbius was one of the nineteenth century's most influential mathematicians and astronomers. Written by six distinguished contributors, this book explores the work of Möbius and his fellow-German scholars, in particular the achievements which act as a mirror for the work being undertaken by his contemporaries around the world.The background to Möbius's life and labours is provided by John Fauvel. Gert Schubring examines the mathematical community in nineteenth-century Germany, while Allan Chapman describes the revolution in astronomy that took place during the period. Jeremy Gray analyses Möbius's contribution to geometrical mechanics and Norman Biggs traces his role in the development of topological ideas. Finally, Ian Stewart explores the legacy Möbius left to mathematics in our own century.

This is the story of the intellectual and social life of a community, and of its interactions with the wider world. For eight centuries mathematics has been researched and studied at Oxford, and the subject and its teaching have undergone profound changes during that time. This highly readable and beautifully illustrated book reveals the richness and influence of Oxford's mathematical tradition and the fascinating characters that helped to shape it. The story begins with the founding of the University of Oxford and the establishing of the medieval curriculum, in which mathematics had an important role. The Black Death, the advent of printing, the Civil War, and the Newtonian revolution all had a great influence on the development of mathematics at Oxford. So too did many well-known figures: Roger Bacon, Henry Savile, Robert Hooke, Christopher Wren, Edmond Halley, Florence Nightingale, Charles Dodgson (Lewis Carroll), and G. H. Hardy, to name but a few. Later chapters bring us to the 20th century, with some entertaining reminiscences by Sir Michael Atiyah of the thirty years he spent as an Oxford mathematician.In this second edition the story is brought right up to the opening of the new Mathematical Institute in 2013 with a foreword from Marcus du Sautoy and recent developments from Peter M. Neumann.

A number of significant contributions have been made, both to specific intellectual disciplines and on the broader philosophical front. by researches into the nature of inquiry. The papers in this collection illustrate a number of such areas of debate in mathematics. natural science. social studies and history. allowing an appraisal of their importance in their own context as well as comparisons across disciplinary frontiers. Some extracts are undoubtedly classic - Plato on mathematics. Newton on physics and J.S. Mill on social science. However. most contributions are more contemporary - work by theorists such as Foucault and Hofstadter. and by practitioners such as Bondi and Einstein. Mathematics is considered under a number of headings. from Plato's 'eternal truth' to Hodgkin's 'social practice'. Its relation to the 'real world' is discussed in a number of essays. In the section on natural science various strands of the Popper-Kuhn debate can be followed. including the questions of progress. rationality and the demarcation of science as opposed to 'pseudo­science'. A similar set of problems is presented in the sections on social inquiry. Here the scientific status of sociology, anthro­pology, history and the like is at issue. Some writers argue that social inquiry is quite distinct from science. whilst others. in­cluding Hempel, deny that there is any essential difference between the human and the natural sciences. The final sections are devoted to more general problems. Extracts from Hume, Hirst and Foucault discuss the isolation and definition of forms of knowledge; the prevailing views of the objectivity of science are challenged by Hanson and Kuhn; and the role of values in social inquiry is debated by Weber, Gouldner and Hesse.

This text investigates how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment, and curricula. Most of the leading specialists in the field have contributed to this book, whose topics include the integration of history in the classroom, its value in the training of teachers, and historical support for particular subjects and for students with diverse educational requirements. Resulting from an international study on behalf of ICMI (the International Commission of Mathematics Instruction), the text draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. Together with its 300-item annotated bibliography of recent work in the field in eight languages, the book provides firm foundations for future developments.Focusing on such issues as the many different ways in which the history of mathematics might be useful, on scientific studies of its effectiveness as a classroom resource, and on the political process of spreading awareness of these benefits through curriculum design, the book will be of particular interest to teachers, mathematics educators, decision-makers, and concerned parents across the world.

A number of significant contributions have been made, both to specific intellectual disciplines and on the broader philosophical front. by researches into the nature of inquiry. The papers in this collection illustrate a number of such areas of debate in mathematics. natural science. social studies and history. allowing an appraisal of their importance in their own context as well as comparisons across disciplinary frontiers. Some extracts are undoubtedly classic - Plato on mathematics. Newton on physics and J.S. Mill on social science. However. most contributions are more contemporary - work by theorists such as Foucault and Hofstadter. and by practitioners such as Bondi and Einstein. Mathematics is considered under a number of headings. from Plato's 'eternal truth' to Hodgkin's 'social practice'. Its relation to the 'real world' is discussed in a number of essays. In the section on natural science various strands of the Popper-Kuhn debate can be followed. including the questions of progress. rationality and the demarcation of science as opposed to 'pseudo­science'. A similar set of problems is presented in the sections on social inquiry. Here the scientific status of sociology, anthro­pology, history and the like is at issue. Some writers argue that social inquiry is quite distinct from science. whilst others. in­cluding Hempel, deny that there is any essential difference between the human and the natural sciences. The final sections are devoted to more general problems. Extracts from Hume, Hirst and Foucault discuss the isolation and definition of forms of knowledge; the prevailing views of the objectivity of science are challenged by Hanson and Kuhn; and the role of values in social inquiry is debated by Weber, Gouldner and Hesse.

An investigation into how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment and curricula. Most of the leading specialists in the field have contributed to this book, whose topics include the integration of history in the classroom, its value in the training of teachers, historical support for particular subjects and for students with diverse educational requirements, the use of original texts written by great mathematicians of the past, the epistemological backgrounds to choose for history, and non-standard media and other resources, from drama to the Internet. Resulting from an international study on behalf of ICMI (the International Commission of Mathematics Instruction), the book draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. Together with its 300-item annotated bibliography of recent work in the field in eight languages, the book provides firm foundations for future developments.Focusing on such issues as the many different ways in which the history of mathematics might be useful, on scientific studies of its effectiveness as a classroom resource, and on the political process of spreading awareness of these benefits through curriculum design, the book should be of particular interest to teachers, mathematics educators, decision-makers and concerned parents across the world.