Andrew M. Bruckner, Brian S. Thomson,
  Judith B. Bruckner

Digital versions PDF
Source available No
Problems Yes
Solutions Yes
License Copyright by authors
  • Text for discovery based course for students with little mathematical background
  • Printed versions available for $40 (color) and $15 (black and white)
  • Most problems have solutions at the end of the chapter
  • For more information and to download

This book does a very good job conveying what it is like to “do” mathematics as a creative activity. Each of the four chapters presents a topic as a sequence of problems, conjectures, explorations, heuristic approaches, and rigorous justification. Because the number of topics is small there is time for students to explore without being rushed to “learn” the material. Courses that would use this book are not pre-requisite courses and so there is not the pressure to cover the content. Although written for students with minimal background, this book could profitably be used in an upper level course for advanced students or for independent study courses or for senior project/thesis ideas.

The four chapters deal with tilings, Pick’s formula, Nim, and links. An appendix reprints the original 1901 paper from the Annals of Mathematics by Charles Bouton giving the complete solution to the game of Nim.