Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact,using recreational mathematics--problems, puzzles and games--to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them.
Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire games and puzzles, and much more. Sample problems (solved in the text) whet readers' appetites and motivate discussions; practice problems solidify their grasp of mathematical ideas; and exercises challenge them, fostering problem-solving ability. Appendixes contain information on basic algebraic techniques and mathematical inductions,and other helpful addenda include hints and solutions, plus answers to selecteda
problems. An extensive appendix on probability is new to this Dover edition.
Problem solving through recreational mathematics 趣味数学问题求解
内容提要 ：
目录 ：
Preface
To the Reader Acknowledgments 1 Following the Clues Sample Problems Which Chart or Diagram to Choose Presenting a Solution Some Steps in Problem Solving Tree Diagrams The Multiplication Principle Simplification The Chapter in Retrospect Exercises 2 Solve It With Logic Sample Problems Statements Variables and Connectives Negation "And- Conjunction "Or'- Disjunction Conditional and Biconditional Statements Drawing Conclusions Compound Statements Logical Implication and Equivalence Arguments and Validity The Chapter in Retrospect Exercises 3 From Words to Equations Algebraic Recreations Sample Problems Introducing Variables The Chapter in Retrospect Exercises 4 Solve It Wrth Integers, Some Topics From Number Theory Sample Problems Diophantine Equations Divisibility Prime Numbers The Infinitude of Primes The Sieve of Eratosthenes More About Primes Linear Diophantine Equations Division With Remainders Congruence Casting Out Nines Solving Linear Congruences …… 5 More About Numbers:Bases and Cryptarithmetic 6 Solve It with Networks;An Introduction to Graph Theory 7 Games of Stratedgy for Two Players 8 Solitaire Games and Puzzles 9 Potpourri Appendix Bibliography Hints and Solutions Answers to Selected Problems Index |
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