The world according to wavelets : the story of a mathematical technique in the making

This book, lovingly written and highly accessible, embraces the often unheralded notion that mathematics contains ideas that can, and deserve, to be communicated to a wider public - even if what is communicated is at the level of appreciation rather that practical knowledge. Put simply, it is a book about the wavelet transform, that strange and scientifically intriguing new method of encoding information with an abundance of practical applications. Drawing on interviews with leading wavelet researchers in the United States and France, it tells the story of the meteoric rise of this new field from its scattered beginnings a decade ago to its current status as a hot topic cutting across traditional scientific boundaries. But more than that, this book is a wonderfully successful attempt to entice the non-mathematical reader into formerly uncharted territory without sacrificing precision. The material is masterfully organized so mathematical details can be assimilated at one's own pace; the main text is devoid of formulas and relates a story of people and ideas, while separate boxes and appendices contain intricate discussions for the more mathematically adventurous. Read more... The World According to Wavelets -- Ch. 1. Fourier Analysis: A Poem Transforms Our World -- Ch. 2. Seeking New Tools -- Ch. 3. A New Language Acquires a Grammar -- Ch. 4. Applications -- Ch. 5. Beyond Wavelets -- Beyond Plain English Barbara Burke Hubbard begins her examination of wavelets with the story of the development of Fourier analysis, the essential underpinning for telephones, x-ray machines, and computers. Without any dizzying technical or mathematical detail she describes the more recent, meteoric rise of wavelet analysis and its many practical applications. The second half of the book lucidly presents the mathematical formulas and details of wavelet analysis for those seeking a deeper understanding. In this second edition she includes a discussion of new medical and genetic applications such as mammography, heart disease, and fingerprints; recent technical developments; a more in-depth look at wavelet history and wavelet researchers; and an updated bibliography and list of software and web sites. I own the very first (French) edition of Mrs. Barbara's book. It is nice reading, but not so fun as some would say. It has some advanced calculus level math ( Fourier transform ) and treats mainly Haar wavelets. As an introduction to the subject it is quite adequate, but if you need/want something more go elsewhere. Drawing on interviews with leading wavelet researchers in the USA and France, this book tells the story of the rise of the field. It attempts to make the subject accessible to the non-mathematical reader, without sacrificing precision. Although wavelets represent a departure from Fourier analysis, they are also natural extension of it: the two languages clearly belong to the same family.