This book is an outgrowth of a collection of sixty-two problems
offered in the The American Mathematical Monthly (AMM) the author
has worked over the last two decades. Each selected problem has a
central theme, contains gems of sophisticated ideas connected to
important current research, and opens new vistas in the
understanding of mathematics. The AMM problem section provides one
of the most challenging and interesting problem sections among the
various journals and online sources currently available. The
published problems and solutions have become a treasure trove rife
with mathematical gems. The author presents either his published
solution in the AMM or an alternative solution to the published one
to present and develop problem-solving techniques. A rich glossary
of important theorems and formulas is included for easy reference.
The reader may regard this book as a starter set for AMM problems,
providing a jumping of point to new ideas, and extending their
personal lexicon of problems and solutions. This collection is
intended to encourage the reader to move away from routine
exercises toward creative solutions, as well as offering the reader
a systematic illustration of how to organize the transition from
problem solving to exploring, investigating and discovering new
results.
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