A Primer of Infinitesimal Analysis by John L Bell
One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this book, basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal - that is, a quantity so small that its square and all higher powers can be set, literally, to zero. As we show, the systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the 'infinitesimal' methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. The book also contains a historical and philosophical introduction, a chapter describing the logical features of the infinitesimal framework, and an appendix sketching the developments in the mathematical discipline of category theory that have made the refounding of infinitesimals possible.John L. Bell has been Professor of Philosophy and Adjunct Professor of Mathematics at the University of Western Ontario since 1989. From 1968-89 he was Lecturer and Senior Lecturer in Mathematics, and Reader in Mathematical Logic, at the London School of Economics. In 1975 he was a Visiting Fellow at the Polish Academy of Sciences, and in 1980 and 1982 at the Mathematics Department of the National University of Singapore. In 1991 he was a Visiting Professor at the Department of Mathematics of the University of Padova, and in 2007 he was a Visiting Directeur de Recherche, CNRS at the Ecole Polytechnique, Paris. In 2009 he was elected a Fellow of the Royal Society of Canada. In 2011 his biography appeared in Canadian Who's Who. That same year saw the publication by Springer of his Festschrift Vintage Enthusiasms: Essays in Honour of John L. Bell.
He is a member of the Editorial Boards of Philosophia Mathematica, Axiomathes, and the Western Ontario Series in Philosophy of Science.
He has published 11 books and more than 70 papers. The books are with such presses as Oxford, Cambridge, Springer, and North-Holland: five of these books are in second, third, or fourth printings or editions; two of them have been republished by Dover. They include titles on model theory, mathematical logic, Boolean-valued models of set theory, topos theory, smooth infinitesimal analysis, the axiom of choice, the evolution of mathematical concepts, the continuous and the infinitesimal, intuitionistic set theory, and oppositions and paradoxes His technical papers include titles on model theory, set theory, first and second-order logic, infinitary languages, large cardinals, incompleteness, Hilbert's epsilon calculus, the axiom of choice, Zorn's lemma, Boolean algebras, lattice theory, category and topos theory, type theory, constructive mathematics, quantum logic, and space-time theory, His work of a more philosophical nature includes papers on category theory in the foundations of mathematics, quantum logic and empiricism, mereology in mathematics, the concept of the infinitesimal, the nature of elementary propositions, the cohesiveness of the continuum, sets and classes as many, the philosophical outlook of Hermann Weyl, Russell's paradox, the nature of cosmological theories, the infinity of the past and aesthetics in mathematics.
| SKU | Unavailable |
| ISBN 13 | 9780521624015 |
| ISBN 10 | 0521624010 |
| Title | A Primer of Infinitesimal Analysis |
| Author | John L Bell |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 1998-07-28 |
| Number of pages | 136 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |