The purpose of this monograph is to provide a concise introduction to the theory of generalized inverses of matrices that is accessible to undergraduate mathematics majors. Although results from this active area of research have appeared in a number of excellent graduate level text books since 1971, material for use at the undergraduate level remains fragmented. The basic ideas are so fundamental, however, that they can be used to unify various topics that an undergraduate has seen but perhaps not related. Material in this monograph was first assembled by the author as lecture notes for the...

The text of this monograph represents the author's lecture notes from a course taught in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook in the Spring of 1977. On account of its origin as lecture notes, some sections of the text are telegraphic in style while other portions are overly detailed. This stylistic foible has not been modified as it does not appear to detract seriously from the readability and it does help to indicate which topics were stressed. The audience for the course at Stony Brook was composed almost entirely of fourth...

The material discussed in this monograph should be accessible to upper level undergraduates in the mathemati cal sciences. Formal prerequisites include a solid intro duction to calculus and one semester of probability. Although differential equations are employed, these are all linear, constant coefficient, ordinary differential equa tions which are solved either by separation of variables or by introduction of an integrating factor. These techniques can be taught in a few minutes to students who have studied calculus. The models developed to describe an epidemic outbreak of smallpox are...

It would be difficult to overestimate the importance of stochastic independence in both the theoretical development and the practical appli- cations of mathematical probability. The concept is grounded in the idea that one event does not "condition" another, in the sense that occurrence of one does not affect the likelihood of the occurrence of the other. This leads to a formulation of the independence condition in terms of a simple "product rule," which is amazingly successful in capturing the essential ideas of independence. However, there are many patterns of "conditioning" encountered in...