Preface
The justification for a concept lies exclusively in its clear and
unambiguous relation to facts that can be experienced.
- Albert Einstein
Useful, straightforward, thought-provoking, and fun: qualities college
students rarely ascribe to mathematics. But this text presents just
such mathematics, for students who have studied some algebra and want
to know more, either to pursue one of the social or life sciences or
to satisfy their pure intellectual curiosity.
The book consists entirely of problems in which mathematics models
familiar phenomena, like automobile fuel consumption, depreciation,
population growth, inflation, and the spread of epidemics. To
investigate such problems requires algebra: a thorough study of linear
equations, unit calculations, the estimation of large
numbers. logarithms, e, and the trigonometry of right triangles.
Throughout the book the nature of the problems studied dictates the
approach to the mathematics-setting up models and drawing inferences,
but little formal manipulation and no proofs identified as such. I
believe that the abstract truths that make mathematics beautiful and
useful are best left implicit at this level. I have found that
students tend to agree.
To master real data, the book teaches the use of the scientific
calculator in parallel with the mathematics. Features are introduced
as their need is felt. The calculator builds confidence because it
frees the user to concentrate on mathematics without worrying about
arithmetic. Students learn a new skill while enjoying concrete
approaches to some traditionally troublesome abstractions like inverse
functions and the rounding of answers to the appropriate number of
significant digits.
On pace and coverage: When I teach real problems at a reasonable rate
students find the mathematics clearly helpful in solving those
problems-they learn more, remember more, and enjoy more than they do
when I hurry. If I try to cover too much material I revert to
teaching algorithms rather than how to think about problems. Then
student interest flags and less is learned more painfully. My right
pace for a one-semester course allows me to cover all of Parts I and
II, on Linear Algebra and Exponential Models (treating Chapters 6, 7,
14, and 15 somewhat skimpily), and either Part III (Quadratic Models)
or Part IV (Trigonometry).
In the five years since I first taught a course based on these ideas I
ave learned from both students and colleagues exposed to this growing
text. Particular thanks go to Peter Ash, Bernice Auslander, Don
Babcock, Valerie Collins, Dan Comenetz, Pamela Dodds, Marilyn
Frankenstein, Matt Gaffney, Paul Mason, Michael Monette, Betty O'Neil,
Earl Porter, Barbara Ruth, Geza Schay, Robert Seeley, Mary Shaner,
Lorraine Turner, Tan VoVan, and Wing Aero. Students who suggested
problems may find those problems here, with their names attached.
Andrew Gleason added a thoughtful reading of an early draft this
material to years of talk about mathematics and its philosophy,
pedagogy, and exposition. Alex Greene's editorial enthusiasm was just
e spur I needed to turn rough notes and ambitious ideas into this
finished book. Bob Morris kept UNIX running and answered formatting
questions while Benjamin Bolker typed the manuscript. Little, Brown's
reviewers, Dan Kemp (South Dakota State University), E. James Peake Iowa
State University of Science and Technology), Shirley Sorensen
University of Maryland), and, particularly, Charles Jepsen (Grinnell
College), were receptive and helpful. Ian Irvine and Dave Lynch at
Little, Brown managed the editing and production with open-minded
or. My wife Joan was there through some hard times-I'm glad we share
this good one. My children, Jessica and Benjamin, were there, too.
Growing and learning and laughing with them have shaped me and hence
this book. They are part of why I enjoyed writing it so much, so for
them.