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Elements of Pure and Applied Mathematics

Harry Lass
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
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This is a Dover reprint of a book first published in 1957. Written by an engineer working in jet propulsion at Cal Tech, it is a fairly standard survey of "applicable analysis" as it was at the time. The chapters are mostly independent of each other, though most chapters depend on the last, which attempts to lay the foundations of real analysis.

In his review of the book for the Mathematical Gazette, T. A. A. Broadbent says that the standard criticism of books of this type is that they deal with 50-year-old mathematics using 100-year-old methods. Broadbent argued that Lass's book did not live up to that stereotype. I'm not sure he was right. Almost a century after Weierstrass, for example, Lass was still using Cauchy's definition of an "infinitesimal" (from his Cours d'Analyse, 1821). On the other hand, this appears in chapter 10, and most students of the book would have ignored the theory presented in that chapter anyway.

Fifty-plus years later, I'm afraid one would have to say that the book comes much closer to the stereotype. Engineering mathematics has progressed a lot. I suspect that Elements of Pure and Applied Mathematics would today be of most interest to historians or to those looking for unusual (and old-fashioned) examples.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.

1. Linear Equations, Determinants, and Matrices
2. Vector Analysis
3. Tensor Analysis
4. Complex-variable Theory
5. Differential Equations
6. Orthogonal Polynomials, Fourier Series, and Fourier Integrals
7. The Stieltjes Integral, Laplace Transform, and Calculus of Variations
8. Group Theory and Algebraic Equations
9. Probability Theory and Statistics
10. Real-variable Theory