Nonstandard Analysis (Paperback)

Alain M. Robert

ISBN 10: 0486432793 / ISBN 13: 9780486432793

Published by Dover Publications Inc., New York, 2003

About this Item

Paperback. This introduction to nonstandard analysis is based on the axiomatic internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises, hints, and solutions. This wonderful little book by Alain Robert should bring about a complete change in the learning of NSA. The author has accomplished a rare feat in the educational literature. He has succeeded in writing a book which is simple and brilliant, deep and witty, short and far-ranging. This is mathematics teaching at its best." - J.-M. Levy-Leblond, European Journal of Physics Brief and readable, this introduction to nonstandard analysis is based on the axiomatic IST (internal set theory) approach. The two-part treatment starts with a clear, rigorous exposition of theory, followed by self-contained chapters on applications. Exercises appear at the conclusion of each chapter, with hints in addition to full solutions. Theoretical topics include idealization, standardization and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Chapters involving applications cover invariant means, approximation of functions, differential equations, perturbation of a Green function, and an invariant subspaces problem. This introduction to nonstandard analysis is based on the axiomatic internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises, hints, and solutions. 1988 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780486432793

Bibliographic Details

• Title: Nonstandard Analysis (Paperback)
• Publisher: Dover Publications Inc., New York
• Publication Date: 2003
• Language: English
• ISBN 10: 0486432793
• ISBN 13: 9780486432793
• Binding: Paperback
• Condition: new

About this title

Synopsis

This wonderful little book by Alain Robert should bring about a complete change in the learning of NSA. The author has accomplished a rare feat in the educational literature. He has succeeded in writing a book which is simple and brilliant, deep and witty, short and far-ranging. This is mathematics teaching at its best." — J.-M. Lévy-Leblond, European Journal of Physics
Brief and readable, this introduction to nonstandard analysis is based on the axiomatic IST (internal set theory) approach. The two-part treatment starts with a clear, rigorous exposition of theory, followed by self-contained chapters on applications. Exercises appear at the conclusion of each chapter, with hints in addition to full solutions. Theoretical topics include idealization, standardization and transfer, real numbers and numerical functions, continuity, differentiability, and integration. Chapters involving applications cover invariant means, approximation of functions, differential equations, perturbation of a Green function, and an invariant subspaces problem.

About the Author

Alain M. Robert is an active Professor of Mathematics at the University of Neuchatel in Switzerland.