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The Saga of Mathematics
The Saga of Mathematics: A Brief History, Lewinter, Marty and Widulski, William, pb, 2002,302pp., $ 23, Prentice-Hall, Upper Saddle River, NJ 07458 http://www.prenhall.com/
My first impression of The Saga of Mathematics: A Brief History was that the book was not very technical, yet contained a variety of exercises from the spectrum of mathematical history. It is written in a very casual style and contains thirteen chapters on mathematics from the accomplishments of the Egyptians to those of the 20th Century.
There are three to five pages of exercises at the end of each chapter. Most topics include at least two exercises so that one can be done in class and the other assigned for homework. Additional exercises and answers to many of the chapter exercises are contained in the appendices.
By omitting important topics, writers often give a somewhat biased view of the development of mathematics. Saga is such a book. The authors avoid detailed discussion of Asian mathematics by saying: "little is known about the mathematics of ancient China ... [the emperor] had all the manuscripts... burned. Fortunately ... Nine Sections survived." Several Chinese problems and others from India are relegated to an appendix. This approach is not only unacceptable; it can only lead to false conclusions. The title of the next chapter "Those Incredible Greeks" clearly asserts the chauvinistic view of the superiority of western mathematics.
There are several other problems with the book. Ideas are often cited out of place. When the Egyptian division problem was relegated to an appendix, the authors missed a great chance at motivating the use of unit fractions. Parallel lines are discussed in the section on Thales. In general, the authors' approach to geometry is sparse and disorderly. Music and figurate numbers are first discussed half-way through the book and not as part of the Pythagorean tradition. Modular arithmetic is discussed without reference to Karl Friedrich Gauss who is not even mentioned in Saga. Ten pages are devoted to graph theory and the last two chapters are not really historical at all. In fact, the general impression that I get is that the authors are dropping names solely to introduce the mathematics that they feel "general education" students can handle without presenting a fair overview of the history involved. I think that I may use this book to teach the critical reading of history to my students.
Jim Kiernan, Adjunct Professor, Brooklyn College, CUNY