Frames for Undergraduates (Student Mathematical Library) (Student Mathematical Library, 40) - Softcover

Deguang Han; Keri Kornelson; David Larson; Eric Weber

Softcover

ISBN 10: 0821842129 ISBN 13: 9780821842126

Publisher: American Mathematical Society, 2007

Synopsis

Frames for Undergraduates is an undergraduate-level introduction to the theory of frames in a Hilbert space. This book can serve as a text for a special-topics course in frame theory, but it could also be used to teach a second semester of linear algebra, using frames as an application of the theoretical concepts. It can also provide a complete and helpful resource for students doing undergraduate research projects using frames. The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students.

About this title

Review

"This incredibly readable book is an enticing introduction to frames. It contains the perfect combination of fundamental ideas from linear algebra and operator theory, and foundational examples and applications of finite frames. My students and I have found it to be an all-around pleasure to read." ---- Michael Orrison, Harvey Mudd College

"I used this book in an undergraduate special topics course on frame theory. With the prerequisite being a standard linear algebra course, I appreciated the comprehensive yet economical background on the necessary ideas from linear algebra and finite dimensional operator theory. The chapters on frame theory cover a nice range of topics, from sampling theory and image reconstruction to frames arising from unitary representations of a group to more recent developments like frame potential, which has interesting connections to physics and platonic solids. My students were inspired not only by these topics but also by the final chapter on anecdotes; many of them had never entertained the possibility that they could do original mathematical research as undergraduates." ---- Fumiko Futamura, Ph.D., Southwestern University

"The result (of this book) is a concise and accessible treatment that serves well as a semester's text." ---- Mathematical Horizon

Edition details

• Publisher: American Mathematical Society
• Publication date: 2007
• ISBN 10: 0821842129
• ISBN 13: 9780821842126
• Binding: Paperback
• Language: English
• Number of pages: 295