Math through the Ages: A Gentle History for Teachers and Others (Expanded Edition)

MATH THROUGH THE AGES: A GENTLE HISTORY FOR TEACHERS AND OTHERS (EXPANDED EDITION) by William P. Berlinghoff and Fernando Q. Gouvea Oxton House Publishers and The Mathematical Association of America 2004, 273 pp. As I write this review, I have just finished the last class meeting of my history of mathematics course and am eagerly awaiting term papers from my 30 students. The text I used this semester was Math Through the Ages: A Gentle History for Teachers and Others. It is a text I am happy to recommend to teachers of the history of mathematics whose course is populated with prospective teachers of mathematics, prospective elementary school teachers, liberal arts students, and mathematics majors. Math Through the Ages (MTA) is built around twenty-five historical sketches covering selected ideas in basic mathematics. Each sketch is a blend of mathematics and history. The reader sees how the mathematical topic fits into the larger mathematical scene, learns of the major figures in its development, and investigates certain technical details about the topic. The sketches range from a brief look at numeration systems to Cantorian set theory. Each sketch is followed by questions and projects that were, in the words of the authors, "constructed ... with several distinct reader objectives in mind: * to learn more about the mathematical ideas in the sketch; * to do or express mathematics in historical ways; * to learn more about the mathematical history of the topic; and * to see how and where the mathematical history fits in with broader historical perspectives." (p. x) I assigned at least one of the questions in each sketch and was pleased to see that they challenged the students to reach beyond the text for factual information and mathematical technique. I also found that the level of mathematics required by the questions varied greatly, giving every student some things they could do easily and some things they found difficult. Preceding the twenty-five sketches in MTA is a 55-page digest of the history of mathematics. This "History of Mathematics in a Large Nutshell" previews the topics in the sketches, offers up topics not found in the sketches, and helps tie diverse topics into a nice whole. I assigned this "nutshell" at the beginning of the course and then again at the end to give the students a preview of where they were going and a post view of where they had been. …