The following review appeared in the September 1996 issue of the National Council of Teachers of Mathematics' Mathematics Teacher, pp 516 - 517.

Who is Fourier? A Mathematical Adventure

This mathematics book is unique and most interesting. It was originally written by Japanese students studying language - including the sounds of language - at the Japanese Transnational College of LEX. The students were motivated to study Fourier analysis as they learned of its usefulness for sound-wave analysis. The LEX students drafted learning modules and presented them to one another. Selected modules were then combined to create the book.

Thirteen chapters are arranged in three units. The four chapters in Part 1 introduce Fourier analysis by describing the students' desire to study sound-wave patterns. The chapters consider graphs of trigonometric functions and their addition and subtraction. Fourier coefficients, and Fourier expansion, form a discrete perspective. Throughout the development, the context for study is wave forms for the sounds of Japanese vowels.

Part 2 presents background information on differentiation, integration, and vectors, in preparation for more work in Fourier analysis. These four chapters could stand alone as material in a first-year calculus course, although the methods focus primarily on trigonometric functions. After conceptualizing the values of 'e' and 'i', as well as Euler's formula, the five chapters of Part 3 bring readers back to Fourier analysis through Fourier transforms and fast Fourier transforms. Again, the material unfolds through the LEX students' focus on sound-wave analysis.

This brief content description of sound and accurate mathematics tells only part of the story of this unique publication. The rest of the story lies in the book's format and presentation. The content is presented in an informal, conversational style that is appealing and motivational. Pages are not filled with paragraphs of dense text; graphs, pictures, tables, reminders, icons, and other visual cues complement the written presentation. An appendix contains patterns for cut-out manipulatives used in several sections of development, and an answers section is included.

Who might use this book? Teachers who want to expand their own understanding of Fourier analysis can benefit from working through this material, especially Parts 1 and 3. Teachers might use parts of the book in their secondary school or college courses, or perhaps give the materials to students engaged in independent study. Although the books may not be appropriate as the primary textbook for typical courses in the secondary school or undergraduate mathematics curriculum, both its content and style make it appealing as a resource or reference work.

- Roger Day, Illinois State University, Normal, IL 61790-4520

Reprinted with permission from Mathematics Teacher, copyright September 1996 by the National Council of Teachers of Mathematics.