Man and Nature in the Renaissance offers an introduction to science and medicine during the earlier phases of the scientific revolution, from the mid-fifteenth century to the mid-seventeenth century. Renaissance science has frequently been approached in terms of the progress of the exact sciences of mathematics and astronomy, to the neglect of the broader intellectual context of the period. Conversely, those authors who have emphasized the latter frequently play down the importance of the technical scientific developments. In this book, Professor Debus amalgamates these approaches: The exact sciences of the period are discussed in detail, but reference is constantly made to religious and philosophical concepts that play little part in the science of our own time. Thus, the renewed interest in mystical texts and the subsequent impact of alchemy, astrology, and natural magic on the development of modern science and medicine are central to the account. Major themes that are followed throu
This volume examines a variety of biological and medical problems using mathematical models to understand complex system dynamics. Featured topics include autism spectrum disorder, ectoparasites and a
This book introduces readers to the financial markets, derivatives, structured products and how the products are modelled and implemented by practitioners. In addition, it equips readers with the nece
This book identifies three of the exceptionally fruitful periods of the millennia-long history of the mathematical tradition of India: the very beginning of that tradition in the construction of the n
The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is kno
This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972–1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy o
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
The Culture of the Mathematics Classroom is becoming an increasingly salient topic of discussion in mathematics education. Studying and changing what happens in the classroom allows researchers and educators to recognize the social character of mathematical pedagogy and the relationship between the classroom and culture at large. The volume is divided into three sections, reporting findings gained both in research and in practice. The first presents several attempts to change classroom culture by focusing on the education of mathematics teachers and on teacher-researcher collaboration. The second section shifts to the interactive processes of the mathematics classroom and to the communal nature of learning. The third section discusses the means of constructing, filtering, and establishing mathematical knowledge that are characteristic of the classroom culture. As an examination of the social nature of mathematical teaching and learning, the volume should appeal both to educational psyc
This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.
In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
An Introduction to Mathematics for Economics introduces quantitative methods to students of economics and finance in a succinct and accessible style. The introductory nature of this textbook means a background in economics is not essential, as it aims to help students appreciate that learning mathematics is relevant to their overall understanding of the subject. Economic and financial applications are explained in detail before students learn how mathematics can be used, enabling students to learn how to put mathematics into practice. Starting with a revision of basic mathematical principles the second half of the book introduces calculus, emphasising economic applications throughout. Appendices on matrix algebra and difference/differential equations are included for the benefit of more advanced students. Other features, including worked examples and exercises, help to underpin the readers' knowledge and learning. Akihito Asano has drawn upon his own extensive teaching experience to cr
It appears to us that the universe is structured in a deeply mathematical way. Falling bodies fall with predictable accelerations. Eclipses can be accurately forecast centuries in advance. Nuclear pow
The Culture of the Mathematics Classroom is becoming an increasingly salient topic of discussion in mathematics education. Studying and changing what happens in the classroom allows researchers and educators to recognize the social character of mathematical pedagogy and the relationship between the classroom and culture at large. The volume is divided into three sections, reporting findings gained both in research and in practice. The first presents several attempts to change classroom culture by focusing on the education of mathematics teachers and on teacher-researcher collaboration. The second section shifts to the interactive processes of the mathematics classroom and to the communal nature of learning. The third section discusses the means of constructing, filtering, and establishing mathematical knowledge that are characteristic of the classroom culture. As an examination of the social nature of mathematical teaching and learning, the volume should appeal both to educational psyc
This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern techn
"An Introduction to Mathematics for Economics introduces quantitative methods to students of economics and finance in a succinct and accessible style. The introductory nature of this textbook means a
