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Publisher:

Dover Publications

Publication Date:

2000

Number of Pages:

480

Format:

Paperback

Price:

14.95

ISBN:

0486409171

Category:

General

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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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 With 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; Solving Linear Diophantine Equations; The Chapter in Retrospect; Exercises | ||||||||

5. | More About Numbers: Bases and Cryptarithmetic; Sample Problems; Positional Notation; Changing Bases; Addition and Multiplication in Other Bases; Cryptarithmetic; The Chapter in Retrospect; Exercises | |||||||

6. | Solve It With Networks: An Introduction to Graph Theory; Sample Problems; Graphs; Eulerian Paths and Circuits; Odd and Even Vertices; More Than Two Odd Vertices; | |||||||

Directed Graphs; Hamiltonian Circuits; The Knight’s Tour; Other Applications; Coloring Graphs and Maps; The Chapter in Retrospect; Exercises | ||||||||

7. | Games of Strategy for Two Players; Sample problems; Chance-Free Decisionmaking; Games of Perfect Information; Finiteness; The Existence of Winning Strategies; Position--State of the Game; | |||||||

The State Diagram of a Game; How Do We Find a Winning Strategy?; Finding a Winning Strategy by Working Backward; Finding Winning Strategies by Simplifying a Game; | ||||||||

Finding Winning Strategies With a Frontal Assault; How Many Possibilities Need Be Considered?; | ||||||||

Symmetry as a Limiting Factor; Déjà Vu—We’ve Seen it Before; The Game of Nim; Pairing Strategies; Variations of a Game; The Chapter in Retrospect; Exercises | ||||||||

8. | Solitaire Games and Puzzles; Sample Problems; The Tower of Brahma; Dissection Problems; Polyominoes; Soma; Peg Solitaire; The Fifteen Puzzle; Even and Odd Permutations; | |||||||

Coloring and the 15 Puzzle--A Second Approach; Colored Cubes; Colored Cubes--A Second Approach; The Chapter in Retrospect; Exercises | ||||||||

9. | Potpourri; Decimation; Coin Weighing; Shunting; Syllogisms; Grab Bag; The Book in Retrospect | |||||||

Appendix A. | Some Basic Algebraic Techniques | |||||||

Appendix B. | Mathematical Induction | |||||||

Appendix C. | Probability | |||||||

Bibliography; Hints and Solutions; Answers to Selected Problems; Index | ||||||||

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