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The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to translate verbal discussions into analytical data; learn problem-solving methods for attacking collections of analytical questions or data; build a personal arsenal of solutions and internalized problem-solving techniques; and become "armed problem solvers", ready to battle with a variety of puzzles in different areas of life. Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a "Challenge Problem" is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. A Solutions Manual to most end-of-chapter exercises is available.
Preface
Acknowledgements
Basic Concepts
Introductory Remarks
A First Problem
How to Count
The Use of Induction
Problems of Logic
Issues of Parity
Exercises
A Deeper Look at Geometry
Classical Planar Geometry
Analytic Geometry
Miscellaneous and Exotic Geometry Problems
Solid Geometry
Exercises
Problems Involving Counting
Elementary Problems in Probability
More Sophisticated Problems in Probability
More on Counting
The Classical Marriage Problem and Related Ideas
Exercises
Problems of Logic
Straight Logic
Games
Tracing Routes, and Learning from Parity
Mysterious Arithmetic Problems
Surprises
Exercises
Recreational Math
Magic Squares and Related Ideas
Problems Involving Weighings
Exercises
Algebra and Analysis
A Little Algebra
Inequalities
Trigonometry and Related Ideas
Exercises
A Miscellany
Crossing the River and Similar Exercises
Things That Are Impossible
Exercises
Real Life
Introductory Remarks
Everyday Objects
Some Case Studies
Statistics
Exercises
Bibliography
Index
Solutions to odd-numbered problems