This book is the outcome of the 1983 American Mathematical Society Short Course given at
Computer communications is one of the fastest growing areas of the communications and
computer industry. This area is characterized by rapid technological advances and problems of a
theoretical nature that are often very difficult to solve. These problems range from those that arise
on a single chip where communication among thousands of elements on a chip is influenced by
electrical properties to those that arise when humans communicate with data bases where the
logical aspects of communications play a more important role.
A variety of mathematical methods is needed to attempt to solve such problems. Therefore,
they vary from partial differential equations to temporal or modal logic. Thus, a short course or
even a long one cannot give an exhaustive treatment of the role of mathematics in computer
We therefore have included in this course and in this book a sample of the work that involves
mathematics and can give those interested in the area a flavor of the field. The hope is that this
material can be used as a starting point and, with the help of some of the references can aid in
other educational or research efforts.
The authors come from varied organizations and are themselves more mathematically inclined
than the typical computer communications engineer, so it must be emphasized that these papers
reflect the work only of practicing theoreticians. The models given in these papers are, however, a
good starting point for applied mathematicians.
I wish to thank all the authors for their cooperation both in the short course and in work
leading to the completion of this manuscript. Responsibility for the delay in the publication of this
book is solely mine, and I extend my apologies both to the readers and to the authors.
All of us would like to thank Brenda Douglas, Susan Pope and Geraldine Moore for their
patient efforts at putting the different manuscripts together in a single format during a
time of organizational chaos. I would like to especially thank Barbara Wicklund for editing and
managing the production of this book.