Excursions in Modern Mathematics

  (9-College)
Peter Tannenbaum and Robert Arnold; Prentice-Hall, 2nd Ed., 1995; $57.

This book, first published in 1992, was evidently inspired by For All Practical Purposes (FAPP), and, like FAPP, is intended for an introductory college-level course. The title conveys its goal of providing interesting ``trips'' through the realm of contemporary mathematics. The style is less cluttered than FAPP, and many find that it makes a better textbook than FAPP (which is a better reference, however). Many high school teachers use it as a resource for themselves, finding the reading level too high for their students (as with FAPP). The publisher also offers a supplement of New York Times articles connected to the text topics. The following description and comments are based on the first (1992) edition.

Content. Excursions covers a subset of the topics of FAPP (there is no section on codes, and fewer topics in each section), and introduces topics in a different order. The topics covered are divided into four parts, as follows:

1.

Social Choice: voting theory, fair division, apportionment;

2.

Management Science: Eulerian tours, traveling salesman problem, minimum-cost spanning trees, scheduling;

3.

Growth and Symmetry: Fibonacci numbers and sequences, population growth, transformation geometry, fractals;

4.

Statistics: collecting and describing data, probability, and the normal distribution.

Classroom Use. Teachers have reported using this as a text for a discrete mathematics elective at the 12th-grade level, and as a resource or supplement for discrete mathematics courses for grades 9-10 and 10-11. It has also been used to introduce discrete topics in calculus at grade 12.

Comments. One teacher, who used the book as supplementary reading and as a resource for herself, felt it was the most useful of the four books in terms of the topic coverage and quantity of material. She found the material on fair division and voting very strong, but was disappointed that graph coloring and codes were not included.

The following comments are taken from a review [2] by high school teacher and mathematics supervisor, Ethel Breuche LP `91, who used the book as a resource.

I feel that this text is wonderfully rich. It is rich with examples and simple and thorough explanations. It is rich in discussion and explorations. Most of all it is rich in exercises at the end of each chapter ..., which increase in level of difficulty and creative problem solving.

Some chapters are followed by an additional appendix. ... For example, in the voting theory section, the voting scheme for the nominations for the Academy Awards is described in detail. Every chapter offers references for further research and readings. The text is written with deliberate thoughtfulness with regard to racial and gender equity. ...

Whether using the book as a resource or as a classroom text, I cannot praise it enough. Although written for a college-level liberal-arts math course, [college-bound high-school] juniors and seniors whose reading ability is average or above can use this text as well.