This book brings together 27 classic articles by Gilbert Strang on linear algebra, computational science, applied mathematics, and calculus, each introduced by a new essay. The essays present historical background, the current state, and unsolved problems.

The topics, each central in the teaching and use of mathematics, include: the four fundamental subspaces and perfect bases; an effective way to introduce the exponential ex; the finite element method and its accuracy; wavelets and signal processing; the Fundamental Theorem of Calculus; the joint spectral radius; and a great variety of matrices (Toeplitz, circulant, banded, incidence, graph Laplacian, and Pascal matrices).

Gilbert Strang is Professor of Mathematics at the Massachusetts Institute of Technology and an Honorary Fellow of Balliol College. He was an undergraduate at MIT and a Rhodes Scholar at Oxford. His doctorate was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. Professor Strang has published a monograph with George Fix, "An Analysis of the Finite Element Method", and has authored six widely used textbooks. He served as President of SIAM during 1999 and 2000 and he is Chair of the U.S. National Committee on Mathematics for 2003-2004.