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About this book
There are good reasons to believe that nonstandard analysis, in some ver sion or other, will be the analysis of the future. KURT GODEL This book is a compilation and development of lecture notes written for a course on nonstandard analysis that I have now taught several times. Students taking the course have typically received previous introductions to standard real analysis and abstract algebra, but few have studied formal logic. Most of the notes have been used several times in class and revised in the light of that experience. The earlier chapters could be used as the basis of a course at the upper undergraduate level, but the work as a whole, including the later applications, may be more suited to a beginning graduate course. This prefacedescribes my motivationsand objectives in writingthe book. For the most part, these remarks are addressed to the potential instructor. Mathematical understanding develops by a mysterious interplay between intuitive insight and symbolic manipulation. Nonstandard analysis requires an enhanced sensitivity to the particular symbolic form that is used to ex press our intuitions, and so the subject poses some unique and challenging pedagogical issues. The most fundamental ofthese is how to turn the trans fer principle into a working tool of mathematical practice. I have found it vi Preface unproductive to try to give a proof of this principle by introducing the formal Tarskian semantics for first-order languages and working through the proofofLos's theorem.
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Table of contents (20 chapters)
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Front Matter
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Basic Analysis
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Front Matter
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Internal and External Entities
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Front Matter
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Nonstandard Frameworks
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Front Matter
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Reviews
R. Goldblatt
Lectures on the Hyperreals
An Introduction to Nonstandard Analysis
"Suitable for a graduate course . . . could be covered in an advanced undergraduate course . . . The author’s ideas on how to achieve both intelligibility and rigor . . . will be useful reading for anyone intending to teach nonstandard analysis."—AMERICAN MATHEMATICAL SOCIETY
Authors and Affiliations
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Bibliographic Information
Book Title: Lectures on the Hyperreals
Book Subtitle: An Introduction to Nonstandard Analysis
Authors: Robert Goldblatt
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-0615-6
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1998
Hardcover ISBN: 978-0-387-98464-3Published: 01 October 1998
Softcover ISBN: 978-1-4612-6841-3Published: 03 October 2012
eBook ISBN: 978-1-4612-0615-6Published: 06 December 2012
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XIV, 293
Topics: Real Functions