| Applied Nonstandard Analysis Contributor(s): Davis, Martin (Author) |
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ISBN: 0486442292 ISBN-13: 9780486442297 Publisher: Dover Publications OUR PRICE: $13.46 Product Type: Paperback - Other Formats Published: July 2005 Annotation: This text assumes no knowledge of mathematical logic. Beginning with a nonstandard construction of the real number system, it leads students thorough the basic topics of elementary real analysis, topological spaces, and Hilbert space. Includes nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. 1977 edition. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis |
| Dewey: 515 |
| LCCN: 2005045425 |
| Series: Dover Books on Mathematics |
| Physical Information: 0.43" H x 5.42" W x 8.5" (0.48 lbs) 208 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Geared toward upper-level undergraduates and graduate students, this text explores the applications of nonstandard analysis without assuming any knowledge of mathematical logic. It develops the key techniques of nonstandard analysis at the outset from a single, powerful construction; then, beginning with a nonstandard construction of the real number system, it leads students through a nonstandard treatment of the basic topics of elementary real analysis, topological spaces, and Hilbert space. Important topics include nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. The focus on compact operators on a Hilbert space includes the Bernstein-Robinson theorem on invariant subspaces, which was first proved with nonstandard methods. Ever mindful of the needs of readers with little background in these subjects, the text offers a straightforward treatment that provides a strong foundation for advanced studies of analysis |