matrices and eigenvalue problems, large scale linear systems, harmonic analysis, data analysis, quadrature and power expansions...illustrated by numerical examples worked out in detail." The contents of the book are stylized "parexic analysis lies between classical analysis and numerical analysis: it is roughly the theory of approximation by finite (or truncated infinite) algorithms." Research Lanczos did pioneering work along with G. C. Danielson on what is now called the fast Fourier transform (FFT, 1940), but the significance of his discovery was not appreciated at the time, and today the FFT is credited to Cooley and Tukey (1965). (As a matter of fact, similar claims can be made for several other mathematicians, including Carl Friedrich Gauss.). Lanczos was the one who introduced Chebyshev polynomials to numerical computing. He discovered the diagonalizable matrix. Working in Washington DC at the U.S. National Bureau of Standards after 1949, Lanczos developed a number of techniques for mathematical calculations using digital computers, including: the Lanczos algorithm for finding eigenvalues of large symmetric matrices, the Lanczos approximation for the gamma function, the conjugate gradient method for solving systems of linear equations. In 1962, Lanczos showed that the Weyl tensor, which plays a fundamental role in general relativity, can be obtained from a tensor potential that is now called the Lanczos potential. Lanczos resampling is based on a windowed sinc function as a practical upsampling filter approximating the ideal sinc function. Lanczos resampling is widely used in video up-sampling for digital zoom applications and image scaling. Books such as The Variational Principles of Mechanics (1949) is a classic graduate text on mechanics. He shows his explanatory ability and enthusiasm as a physics teacher: in the preface of the first edition he says it is taught for a two-semester graduate course of three hours weekly. Publications Books 1949: The Variational Principles of Mechanics (dedicated to Albert Einstein), University of Toronto Press , followed by 1962, 1966, 1970 editions. 1956: Applied Analysis, Prentice Hall 1961: Linear Differential Operators, Van Nostrand Company, (1962: The Variational Principles of Mechanics, 2nd ed.) (1966: The Variational Principles of Mechanics, 3rd ed.) 1966: Albert Einstein and the cosmic world order: six lectures delivered at the University of Michigan in the Spring of 1962, Interscience Publishers 1966: Discourse on Fourier Series, Oliver & Boyd 1968: Numbers without End, Edinburgh: Oliver & Boyd (1970: The Variational Principles of Mechanics, 4th ed.) 1970: Judaism and Science, Leeds University Press