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Applied Mathematics

Data Compression, Spectral Methods, Fourier Analysis, Wavelets, and Applications

  • Textbook
  • © 2013

Overview

  • A comprehensive Applied Mathematics Textbook on the theory and methods with the central theme of information data processing, manipulation, and compression
  • Self-contained with minimum prerequisites from elementary linear algebra and calculus
  • A Text book for teaching at both undergraduate and beginning graduate levels
  • Self-study for researchers in all disciplines of science and engineering

Part of the book series: Mathematics Textbooks for Science and Engineering (MTSE, volume 2)

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Table of contents (10 chapters)

Keywords

About this book

This textbook, apart from introducing the basic aspects of applied mathematics, focuses on recent topics such as information data manipulation, information coding, data approximation, data dimensionality reduction, data compression, time-frequency and time scale bases, image manipulation, and image noise removal. The methods treated in more detail include spectral representation and “frequency” of the data, providing valuable information for, e.g. data compression and noise removal. Furthermore, a special emphasis is also put on the concept of “wavelets” in connection with the “multi-scale” structure of data-sets. The presentation of the book is elementary and easily accessible, requiring only some knowledge of elementary linear algebra and calculus. All important concepts are illustrated with examples, and each section contains between 10 an 25 exercises. A teaching guide, depending on the level and discipline of instructions is included for classroom teaching and self-study.

Reviews

From the book reviews:

“The work under review is an elementary textbook on several contemporary topics in applied mathematics that should appeal to mathematics, science, and engineering students. It is written in a modular form that makes it suitable for a variety of courses or seminars in applied mathematics.” (Marcin M. Bownik, Mathematical Reviews, December, 2014)

Authors and Affiliations

  • Department of Statistics, Stanford University, Stanford, USA

    Charles K. Chui

  • University of Missouri, Department of Mathematics and Computer Science, St. Louis, USA

    Qingtang Jiang

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