Beginning Functional Analysis (Undergraduate Texts in Mathematics) - Hardcover

Saxe, Karen

Hardcover

ISBN 10: 0387952241 ISBN 13: 9780387952246

Publisher: Springer, 2001

Synopsis

This book is designed as a text for a first course on functional analysis for ad­ vanced undergraduates or for beginning graduate students. It can be used in the undergraduate curriculum for an honors seminar, or for a "capstone" course. It can also be used for self-study or independent study. The course prerequisites are few, but a certain degree of mathematical sophistication is required. A reader must have had the equivalent of a first real analysis course, as might be taught using [25] or [109], and a first linear algebra course. Knowledge of the Lebesgue integral is not a prerequisite. Throughout the book we use elementary facts about the complex numbers; these are gathered in Appendix A. In one spe­ cific place (Section 5.3) we require a few properties of analytic functions. These are usually taught in the first half of an undergraduate complex analysis course. Because we want this book to be accessible to students who have not taken a course on complex function theory, a complete description of the needed results is given. However, we do not prove these results.

About this title

From the Back Cover

The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators relating these points as linear transformations on these spaces. The author presents the basics of functional analysis with attention paid to both expository style and technical detail, while getting to interesting results as quickly as possible. The book is accessible to students who have completed first courses in linear algebra and real analysis. Topics are developed in their historical context, with accounts of the past - including biographies - appearing throughout the text. The book offers suggestions and references for further study, and many exercises.

Karen Saxe is Associate Professor of Mathematics at Macalester College in St. Paul, Minnesota. She received her Ph.D. from the University of Oregon. Before joining the faculty at Macalester, she held a two-year FIPSE post-doctoral position at St. Olaf College in Northfield, Minnesota. She currently serves on the editorial board of the MAA's College Mathematics Journal. This is her first book.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 0387952241
• ISBN 13: 9780387952246
• Binding: Hardcover
• Number of pages: 208