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The authors have been beguiled and entranced by mathematics all of their lives, and both believe it is the highest expression of pure thought and an essential component-one might say the quintessence-of nature. How else can one ex plain the remarkable effectiveness of mathematics in describing and predicting the physical world? The projection of the mathematical method onto the subspace of human endeav 1 ors has long been a source of societal progress and commercial technology. The invention of the electronic digital computer (not the mechanical digital computer of Babbage) has made the role of mathematics in civilization even more central by making mathematics active in the operation of products. The writing of this book was intertwined with the development of a start-up company, Aware, Inc. Aware was founded in 1987 by one of the authors (H.L.R.), and the second author (R.O.W.) put his shoulder to the wheel as a consultant soon after.
List of contents
I. The Scalable Structure of Information.- 1 The New Mathematical Engineering.- 2 Good Approximations.- 3 Wavelets: A Positional Notation for Functions.- II Wavelet Theory.- 4 Algebra and Geometry of Wavelet Matrices.- 5 One-Dimensional Wavelet Systems.- 6 Examples of One-Dimensional Wavelet Systems.- 7 Higher-Dimensional Wavelet Systems.- III Wavelet Approximation and Algorithms.- 8 The Mallat Algorithm.- 9 Wavelet Approximation.- 10 Wavelet Calculus and Connection Coefficients.- 11 Multiscale Representation of Geometry.- 12 Wavelet-Galerkin Solutions of Partial Differential Equations.- IV Wavelet Applications.- 14 Modulation and Channel Coding.- References.
