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A Primer of Infinitesimal Analysisby John L. Bell
Cambridge University Press 2008; US$ 52.00A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal. more...
The Strength of Nonstandard Analysisby Imme van den Berg; Vitor Neves
Springer 2007; US$ 129.00Nonstandard Analysis enhances mathematical reasoning by introducing new ways of expression and deduction. Distinguishing between standard and nonstandard mathematical objects, its inventor, the eminent mathematician Abraham Robinson, settled in 1961 the centuries-old problem of how to use infinitesimals correctly in analysis. Having also worked as an engineer, he saw not only that his method greatly simplified mathematically proving and teaching, but also served as a powerful tool in modelling, analyzing and solving problems in the applied sciences, among others by effective rescaling and by infinitesimal discretizations. This book reflects the progress made in the forty years since the appearance of Robinson??'s revolutionary book Nonstandard... more...
An Introduction to Nonstandard Real Analysisby Albert E. Hurd; Peter A. Loeb
Elsevier 1985; US$ 121.00The aim of this book is to make Robinson's discovery, and some of the subsequent research, available to students with a background in undergraduate mathematics. In its various forms, the manuscript was used by the second author in several graduate courses at the University of Illinois at Urbana-Champaign. The first chapter and parts of the rest of the book can be used in an advanced undergraduate course. Research mathematicians who want a quick introduction to nonstandard analysis will also find it useful. The main addition of this book to the contributions of previous textbooks on nonstandard analysis (12,37,42,46) is the first chapter, which eases the reader into the subject with an elementary model suitable for the calculus, and the... more...
Introduction to the Theory of infiniteseimalsby K. D. Stroyan; W. A. J. Luxemburg
Elsevier 1976; US$ 121.00Introduction to the Theory of infiniteseimals more...
The Philosophy of Mathematical Practiceby Paolo Mancosu
Oxford University Press, UK 2008; US$ 100.00There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment. - ;Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with contemporary philosophy of mathematics will be aware of the need... more...
The Foundations of Analysis, Book 1by K. G. Binmore
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