Author | : John L. Bell |
Publisher | : Cambridge University Press |
Total Pages | : 7 |
Release | : 2008-04-07 |
Genre | : Mathematics |
ISBN | : 0521887186 |
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Author | : John L. Bell |
Publisher | : Cambridge University Press |
Total Pages | : 7 |
Release | : 2008-04-07 |
Genre | : Mathematics |
ISBN | : 0521887186 |
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Author | : James M. Henle |
Publisher | : Courier Corporation |
Total Pages | : 146 |
Release | : 2014-01-15 |
Genre | : Mathematics |
ISBN | : 0486151018 |
Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.
Author | : F. William Lawvere |
Publisher | : Cambridge University Press |
Total Pages | : 409 |
Release | : 2009-07-30 |
Genre | : Mathematics |
ISBN | : 0521894859 |
This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.
Author | : Nader Vakil |
Publisher | : Cambridge University Press |
Total Pages | : 587 |
Release | : 2011-02-17 |
Genre | : Mathematics |
ISBN | : 1107002028 |
A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.
Author | : Stewart Shapiro |
Publisher | : |
Total Pages | : 235 |
Release | : 2014 |
Genre | : Logic |
ISBN | : 0199696527 |
Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like "valid" and "logical consequence" are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the "debates" in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.
Author | : Henry C. Foley |
Publisher | : Academic Press |
Total Pages | : 954 |
Release | : 2021-06-16 |
Genre | : Technology & Engineering |
ISBN | : 0128200529 |
Introduction to Chemical Engineering Analysis Using Mathematica, Second Edition reviews the processes and designs used to manufacture, use, and dispose of chemical products using Mathematica, one of the most powerful mathematical software tools available for symbolic, numerical, and graphical computing. Analysis and computation are explained simultaneously. The book covers the core concepts of chemical engineering, ranging from the conservation of mass and energy to chemical kinetics. The text also shows how to use the latest version of Mathematica, from the basics of writing a few lines of code through developing entire analysis programs. This second edition has been fully revised and updated, and includes analyses of the conservation of energy, whereas the first edition focused on the conservation of mass and ordinary differential equations. - Offers a fully revised and updated new edition, extended with conservation of energy - Covers a large number of topics in chemical engineering analysis, particularly for applications to reaction systems - Includes many detailed examples - Contains updated and new worked problems at the end of the book - Written by a prominent scientist in the field
Author | : John L. Bell |
Publisher | : Springer Nature |
Total Pages | : 320 |
Release | : 2019-09-09 |
Genre | : Mathematics |
ISBN | : 3030187071 |
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Author | : Charles Chapman Pugh |
Publisher | : Springer Science & Business Media |
Total Pages | : 445 |
Release | : 2013-03-19 |
Genre | : Mathematics |
ISBN | : 0387216847 |
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.