- Gebundene Ausgabe: 280 Seiten
- Verlag: Springer; Auflage: 2006 (17. Oktober 2006)
- Sprache: Englisch
- ISBN-10: 0387295194
- ISBN-13: 978-0387295190
- Größe und/oder Gewicht: 15,6 x 1,9 x 23,4 cm
- Durchschnittliche Kundenbewertung: 1 Kundenrezension
Nr. 1.236.945 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
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Analysis and Probability: Wavelets, Signals, Fractals (Graduate Texts in Mathematics) (Englisch) Gebundene Ausgabe – 17. Oktober 2006
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them that are described in this book mean that there is something for everyone." (Judith A. Packer, Mathematical Reviews, Issue 2008 a)
This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals. The book brings together tools from engineering and math, especially from signal and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications.Key features are: a hands-on approach for students, including tutorials and numerous exercises; excellent motivation throughout; new pedagogical features: glossary of terms, their use in mathematics and in engineering, help for cross-audiences, image processing, visual presentation of key algorithms, structure and geometry of big matrix computations, explanation of uses of the theory in applications outside of mathematics; includes more than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions of algorithms, and separate illustrations; separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers; and each chapter concludes with a helpful guide to the literature allowing students to follow up on the topics in the book. Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa. This book is based in part on interdisciplinary courses that he has taught over the last several years, and on his work with his current and former students. His most recent book was written jointly with Ola Bratteli and is entitled "Wavelets Through a Looking Glass", 2002 Birkhauser Boston. Alle Produktbeschreibungen
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It is not written in the proper and systematic way. The author for example uses the "." notation for a variable without stating what it means. He introduces # notation as cardinality of a set without telling you right there that # stands for cardinality (it is in the list of symbols but it is not referred to where it must) Chapters are likewise disorganized and sections do not build up understanding.
The author wants to be creative and introduce ideas from multiple directions. This is an advantage for a workshop or class environment but don't waste your time and money if you are interested in fractals, or probability or wavelets or signal processing or harmonic analysis.... instead buy the standard focused texts. There is no royal road to mathematics but there are good textbooks and this is not one of them. I did not give it one star because if you already know all of these subjects, perhaps this book is good essay in how they relate to each other. The author should have simply put these notes on his webpage for free rather than create a textbook out of them. It is now days a custom to make a textbook out of poorly developed notes; it is unfortunate.
jpeg-format to store photographs. Millions of people employ such wavelet-based
technology every day. In sharp contrast to that, only a few thousand people on
the planet have a detailed understanding of the mathematics concerning the
C*-algebras O_n even though (as the book under review shows) there is a
strong relationship between the two.
This book entertains and educates the reader with a high-precision tour
connecting very current technological advances such as high-tech filters and
compression methods, classical mathematics such as wavelets and probability
theory and advanced, new mathematical methods such as non-commutative Hilbert
space operator algebra applications. This book distinguishes itself by placing
modern mathematics close to modern technology and by showing (again) that pure
mathematics is not necessarily only for mathematics' sake. The author Palle
E.T. Jorgensen is a world-class mathematician with a distinguished publication
record. This is a book that *every* student of mathematics should read in
order to be guided and motivated what courses to take, what other more basic
books to read, and what research to pursue. This is a book that computer
scientists, physicists and engineers should read. In my opinion, it could
spawn new innovation, maybe no patents, but benefits for all of mankind.
For a book apparently aimed at promoting the applied mathematics point of view, it actually gives very little context locally, meaning in each chapter or section or remark. It deviates from the usual math textbook pattern (motivation/context/special cases -> general definitions of main objects -> theorems and proofs -> references and further results) and does not do it well. The prerequisites listed in the beginning of each chapter can be somewhat frivolous.
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