TTU-CR Mathematics

This volume is a celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the book was born as part of the activities of World Mathematical Year 2000. It consists of 28 articles written by influential mathematicians. Authors of 14 contributions were recognized in various years by the IMU as recipients of the Fields Medal, from K.F. Roth (Fields Medalist, 1958) to W.T. Gowers (Fields Medalist, 1998).

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 timescale 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.

In this accessible and illuminating study of how the science of mathematics developed, a veteran math researcher and educator looks at the ways in which our evolutionary makeup is both a help and a hindrance to the study of math.