Graduate Texts in Mathematics

Lectures on the Hyperreals

An Introduction to Nonstandard Analysis

Authors: Goldblatt, Robert

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About this Textbook

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.

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


Table of contents (20 chapters)

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-1-4612-0615-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-0-387-98464-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $84.95
price for USA
  • ISBN 978-1-4612-6841-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on the Hyperreals
Book Subtitle
An Introduction to Nonstandard Analysis
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
188
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-1-4612-0615-6
DOI
10.1007/978-1-4612-0615-6
Hardcover ISBN
978-0-387-98464-3
Softcover ISBN
978-1-4612-6841-3
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIV, 293
Topics