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For All Practical Purposes (FAPP)

Solomon Garfunkel (Project Director), et al.; W.H. Freeman (for COMAP), 3rd Ed., 1994 (4th Ed., 1997); $45.

Although written for a college-level audience, the material in this book has been used successfully at many grade levels. It is a great reference that is fun to read; everyone should have this book on their shelf. It has a wealth of contemporary topics, and each edition has added new topics. Of special interest are Spotlights--profiles of mathematicians or computer scientists who have contributed substantially to the solutions of problems mentioned in the book. There is an accompanying series of 26 half-hour video tapes which give overviews and applications of the topics; text supplements and an instructor's guide are available.

Content. This book is packed with topics and problems; there is enough material for a year-long course on the uses of mathematics. Many different semester courses could also be designed around this book. The third edition has five parts, as follows:
Management Science: graph models and problems (Eulerian paths, Traveling Salesman Problem, spanning trees, and scheduling), linear programming;
Statistics/Data: data collection and representation, probability and statistics;
Coding Information: identification and error-correcting codes;
Social Choice: voting, fair division, apportionment, game theory;
Size and Shape: growth models, measurement, astronomy, fractals, symmetry, tilings.

The focus is on real-world problems and models. Note that a number of standard discrete mathematics topics are not covered, such as shortest path problems, graph coloring, and permutations, and some of the mathematics used is continuous rather than discrete.

Classroom Use. This book was intended for introductory college courses, but teachers have reported using it successfully with a wide range of younger students, from gifted 7th- and 8th-graders in an enrichment program, to 11th- and 12th-graders (including non-college-bound students). Most high school teachers find the reading level too high for their students; instead, they use it as a resource for themselves, adapting the problems for their classes. Specific examples of the use of the text are given in this volume [17,34].

Comments. The following is an excerpt from a review of the first edition (1988), by Anthony Piccolino, on the mathematics faculty at Montclair State University, who used the book for three years in teaching an elective mathematics course to high school seniors [28].

[This is] a textbook which addresses real-life situations, emphasizes mathematical modeling, encourages students to make mathematical connections, and devotes extraordinary efforts to changing students' narrow view of mathematics. ...

I found this book to be most effective when used in conjunction with the 26-program video series of the same name. The animation and the delivery style are wonderfully motivating and give students an excellent sense of the ``big picture'' for each chapter before having students delve into various detailed aspects of the chapter. ...

I recommend this book with great enthusiasm!

Joseph Malkevitch, on the mathematics faculty of York College of CUNY, and one of the authors of the section on Management Science, believes the text has played a key role in the evolution of college ``mathematics-for-liberal-arts'' courses [24]. He wrote,

[Its] approach underlines the importance for students of analyzing and understanding real-world situations and building mathematical models rather than gaining facility with solving exercises based on the models.

[Texts like this can] show how the ideas being developed in discrete mathematics are essential for emerging new technologies such as robotics, computer vision, data compression, and medical imaging.

next up previous
Next: Excursions in Modern Mathematics Up: Discrete Mathematics Textbooks Previous: Mathematics, a Human Endeavor