99i:01005 01A05
Laubenbacher, Reinhard(1-NMS); Pengelley, David(1-NMS)
Mathematical expeditions. (English. English summary)
Chronicles by the explorers. Undergraduate Texts in Mathematics. Readings in Mathematics.
Springer-Verlag, New York, 1999. x+275 pp. $32.00. ISBN 0-387-98433-X

Born of a freshman honors course, this book reflects the belief of the authors that students should
experience mathematics through the words of its creators. The five independent chapters treat (1)
the parallel postulate and non-Euclidean geometry; (2) set theory and infinity (Bolzano, Cantor,
Zermelo); (3) infinitesimal analysis (quadratures of Archimedes and Cavalieri, calculus of Leibniz and
Cauchy, Robinson nonstandard analysis); (4) Fermat's last theorem (Euclid to Euler, Germain and
Kummer); and (5) solvability by radicals (culminating in Galois). Following an overview giving the
historical and mathematical setting, each chapter contains annotated historical excerpts interspersed
with exercises to encourage further exploration. There is a large bibliography. This book is suitable
for a general mathematical reader and would be an excellent text for a history-based undergraduate
course, although some items, while not technical, require considerable mathematical maturity.

                           Reviewed by E. J. Barbeau