The papers were elicited primarily from Mathematics for Industry: Challenges and Frontiers, a conference sponsored by SIAM in October, 2003. This collection of papers is a forum for leading industrial and government scientists and engineers to describe their work and what they hope to accomplish over the next decade. The goal is to focus the mathematical community on research that will both advance mathematics and provide immediate benefits to industry. The papers focus on describing the needs of industry and government and on highlighting mathematics that may play a role in providing solutions.