This report describes the Applied Mathematics Laboratory (AML) operated by the Department of Mathematics at Towson State University, Maryland. AML is actually a course offered to selected undergraduates who are given the opportunity to apply their skills in investigating industrial and governmental problems. By agreement with sponsoring organizations, AML undertakes research projects of a mathematical nature whose analysis, solution, and exposition require the substantial involvement of a team of students and faculty members for an academic year. Evidence of program effectiveness includes the following facts: AML is recognized in the business community in the Baltimore metropolitan area; corporate responses have been uniformly favorable; and AML received the Distinguished Program Award from the Maryland Association of Higher Education in 1984. Recommendations considered when setting up such a project included: contract all year-long projects in the spring for the next academic year; assess the same fee for each project; have a tenured and self-confident faculty member as the primary director; and have an administrator who can interact well with industrial and business people. An appendix lists AML projects from 1980 through 1989. Contains 3 references. (Author/SM)