# An Introduction to the Mathematics of Biology

## Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

This text in mathematical biology contains the following:
• the use of mathematics for constructing biological models.
• an in depth treatment of connections in biology and mathematics.
• the use of a computer algebra system to examine the models. The authors of this textbook have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another, but has a unity of its own. The biology and mathematics are equal; they are complete and flow smoothly into and out of one another. Students' responses to the approach have been exhilarating to watch as they are invited to modify the construction of models of contemporary interest - models for HIV, for the ingestion of environmental contamination, or for genetics and aging. The book has several important features which the authors have developed from their classroom experience. First and foremost, the book is designed to be understandable to students of biology as well as to students of mathematics and related physical sciences. No prior study of biology is necessary and only the concepts of first year calculus are required. The mathematics proceeds from simple concepts to more complex ones; the biology proceeds from the population level down to the molecular level. This arrangement makes the material accessible to most biology majors and to most students near the beginning of their mathematical studies. A unique feature of this book is the use of a computer algebra system in parts of every chapter. This allows a hands-on approach to computation, which provides a rich source of information through the use of "what-if" scenarios. The result is that students grasp important biological and mathematical concepts in a way that is nearly impossible without such technology. For students who do not have access to the computer algebra system, each topic is complete without the use of either numerical or symbolic equations. Graphical visualization are provided for all the mathematical results. The syntax in the book is written as appropriate for Maple V, release 3. However, all the syntax of the book has now been revised for Maple V, release 4 and presented as files accessible from this WEB page as revised Maple code. For readers who have Maple and Netscape on their computers, directions for configuring Netscape Navigator, Version 3, to launch Maple V, Release 4 are contained in a file accessible above. Thereafter, appropriate syntax for each chapter can be obtained with no typing by the reader. The text has extensive exercises, problems, and examples, along with references for further study. The book will be of interest to any mathematics department that teaches mathematical biology or mathematical modeling. It also lends itself to self-study for more advanced mathematicians and scientists who wish to explore further this most exciting frontier in the applications of mathematics and computers to the natural sciences. To contact the authors, send electronic messages or address correspondence through the U. S. mail:
Edward Yeargers (send e-mail) School of Biology, Georgia Tech, Atlanta, GA, 30332-0230
Ron Shonkwiler (send e-mail)School of Mathematics, Georgia Tech, Atlanta, GA, 30332-0160
Jim Herod (send e-mail)School of Mathematics, Georgia Tech, Atlanta, GA, 30332-0160
A list of errors known as of July 1, 1997 are listed in this errata file.