Mathematical Gems III is part of the MAA’s Dolciani Mathematical Expositions series. As would be expected from a book in this series, it is very easy to read and filled with interesting mathematics. This book is accessible to an undergraduate but it is enjoyable for mathematicians.
In this volume, you will find many gems from combinatorics, graph theory, geometry, and elementary number theory. A wide selection of problems from national and international Olympiads is included. Problems involving probability, stochastic processes and series can also be found. All of the problems are clearly presented and often there is a short description of how they came to the author’s attention. Solutions and explanations are given in an engaging manner that is likely encouraging to an undergraduate but at the same time allows a more experienced mathematician to quickly and easily see the direction of the argument.
For someone focused on teaching undergraduates this book could be a great and easy resource for supplemental problems for a course in combinatorics, graph theory or geometry. There are few problems appropriate for a calculus course, but it would be a great source for a wide variety of proof and problem solving techniques for a bridge course. Problems of the week for undergraduates would be easily found in this book. It could also be useful for preparation for Olympiads or other math competitions for undergraduates or talented high school students. Almost any mathematician involved with students will find this book useful.
Aside from its utility, this is a very enjoyable book that can help broaden one’s mathematical horizons with interesting little tidbits about Helly’s Theorem, Lucas Numbers, or Katona’s problem on families of separating subsets, among other things. It’s definitely a book that is worth checking out and it might inspire you or one of your students to find your own mathematical gem.
Suzanne Caulk is an assistant professor of mathematics at Regis University in Denver, CO. She is very interested in modular forms. You can email her at firstname.lastname@example.org.