1. Overview; 2. Sequences and difference equations; 3. Arithmetic growth; 4. Linear graphs, functions and equations; 5. Quadratic growth models; 6. Quadratic graphs, functions and equations; 7. Polynomial and rational functions; 8. Fitting a line to data; 9. Geometric growth; 10. Exponential functions; 11. More on logarithms; 12. Geometric sums and mixed models; 13. Logistic growth; 14. Chaos in logistic models.
Explains the relevance and importance of mathematical modelling for a non-technical audience.
Kalman uses basic growth models...not only to convey the power of
mathematics in solving real-world problems, but also to motivate
the study of the elementary functions usually encountered in
college algebra courses. There is a natural evolution from a simple
hypotheses to difference equations, to their solutions, to the
study of the elementary functions associated with the solutions.
There is an emphasis on the ""why"" of algebra and on manipulation
associated with applications rather than for its own
sake.Numerical, graphical, and symbolic approaches are used
throughout, and the numerous exercises include reading
comprehension exercises and group selected exercises...Aimed at
students at the college algebra or liberals arts mathematics level,
the slow careful development should be clear even to those with a
weak algebraic background. Highly recommended."" - Choice
""An innovative alternative to introductory college mathematics
intended for any student not headed for calculus. Uses discrete and
continuous models of growth to introduce increasingly sophisticated
algebraic patterns...An effective blend of narrative, motivation,
calculation, and graphical representation that introduces algebraic
thinking with a minimum of algebraic formalisms."" - The American
Mathematical Monthly
""The book is well balanced and succeeds in introducing the use of
discrete models to students who might view a mathematics class with
a weary eye...the author does a superb job of addressing a
difficult audience. This is especially true of the problem sets. An
excellent mix of reading, simple/short answer, and word problems of
varying difficulties are given. Furthermore, complete answers to
some of the problems are given in the same chapter, rather than in
an appendix."" - Kelly Black, University of New Hampshire
""This book can be described as the protocol of the ultimate (and
apparently successful) teaching experiment, namely to lead students
with hardly any mathematical background at all, to a respectable
level in the fundamentals of mathematics in such a way, that they
will always have positive thoughts about it. ...The expert reader
may use this book as a rich source of growth problems."" -
Springer-Verlag, Zentallblatt fur Mathematik
""I found the book a refreshing alternative to college algebra
textbooks and would recommend it to instructors who are seeking
changes."" - The Mathematics Teacher
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