9780486409177

Problem Solving Through Recreational Mathematics

by ;
  • ISBN13:

    9780486409177

  • ISBN10:

    0486409171

  • Format: Paperback
  • Copyright: 1999-05-27
  • Publisher: Dover Publications

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Summary

Many of the most important mathematical concepts were developed from recreational problems. This book uses problems, puzzles, and games to teach students how to think critically. It emphasizes active participation in problem solving, with emphasis on logic, number and graph theory, games of strategy, and much more. Includes answers to selected problems. Index. 1980 edition.

Table of Contents

Preface ix
To the Reader xiii
Acknowledgments xv
Following the Clues
1(36)
Sample Problems
2(8)
Which Chart or Diagram to Choose
10(1)
Presenting a Solution
11(1)
Some Steps in Problem Solving
11(5)
Tree Diagrams
16(3)
The Multiplication Principle
19(3)
Simplification
22(3)
The Chapter in Retrospect
25(1)
Exercises
26(11)
Solve It With Logic
37(33)
Sample Problems
38(1)
Statements
39(2)
Variables and Connectives
41(1)
Negation
41(1)
``And''-- Conjunction
42(1)
``Or''-- Disjunction
43(1)
Conditional and Biconditional Statements
44(3)
Drawing Conclusions
47(2)
Compound Statements
49(4)
Logical Implication and Equivalence
53(2)
Arguments and Validity
55(5)
The Chapter in Retrospect
60(1)
Exercises
61(9)
From Words to Equations, Algebraic Recreations
70(30)
Sample Problems
71(1)
Introducing Variables
72(12)
The Chapter in Retrospect
84(1)
Exercises
84(16)
Solve If With Integers, Some Topics From Number Theory
100(45)
Sample Problems
101(2)
Diophantine Equations
103(1)
Divisibility
104(2)
Prime Numbers
106(1)
The Infinitude of Primes
106(1)
The Sieve of Eratosthenes
107(1)
More About Primes
108(7)
Linear Diophantine Equations
115(4)
Division With Remainders
119(1)
Congruence
120(5)
Casting Out Nines
125(2)
Solving Linear Congruences
127(4)
Solving Linear Diophantine Equations
131(6)
The Chapter in Retrospect
137(1)
Exercises
138(7)
More About Numbers: Bases and Cryptarithmetic
145(28)
Sample Problems
146(1)
Positional Notation
147(1)
Changing Bases
148(5)
Addition and Multiplication in Other Bases
153(3)
Cryptarithmetic
156(6)
The Chapter in Retrospect
162(1)
Exercises
163(10)
Solve It With Networks: An Introduction to Graph Theory
173(40)
Sample Problems
174(1)
Graphs
175(3)
Eulerian Paths and Circuits
178(2)
Odd and Even Vertices
180(7)
More Than Two Odd Vertices
187(3)
Directed Graphs
190(2)
Hamiltonian Circuits
192(2)
The Knight's Tour
194(2)
Other Applications
196(2)
Coloring Graphs and Maps
198(3)
The Chapter in Retrospect
201(1)
Exercises
202(11)
Games of Strategy for Two Players
213(60)
Sample Problems
214(1)
Chance-Free Decisionmaking
215(1)
Games of Perfect Information
216(1)
Finiteness
216(1)
The Existence of Winning Strategies
217(7)
Position---State of the Game
224(4)
The State Diagram of a Game
228(2)
How Do We Find a Winning Strategy?
230(1)
Finding a Winning Strategy by Working Backward
230(2)
Finding Winning Strategies by Simplifying a Game
232(1)
Finding Winning Strategies With a Frontal Assault
233(1)
How Many Possibilities Need Be Considered?
234(1)
Symmetry as a Limiting Factor
234(7)
Deja Vu---We've Seen It Before
241(5)
The Game of Nim
246(4)
Pairing Strategies
250(1)
Variations of a Game
251(1)
The Chapter in Retrospect
252(1)
Exercises
253(20)
Solitaire Games and Puzzles
273(40)
Sample Problems
274(2)
The Tower of Brahma
276(3)
Dissection Problems
279(2)
Polyominoes
281(3)
Soma
284(1)
Peg Solitaire
285(3)
The Fifteen Puzzle
288(3)
Even and Odd Permutations
291(7)
Coloring and the 15 Puzzle---A Second Approach
298(1)
Colored Cubes
299(4)
Colored Cubes---A Second Approach
303(1)
The Chapter in Retrospect
304(1)
Exercises
305(8)
Potpourri
313(8)
Decimation
313(2)
Coin Weighing
315(1)
Shunting
316(1)
Syllogisms
317(1)
Grab Bag
318(2)
The Book in Retrospect
320(1)
Appendix A---Some Basic Algebraic Techniques 321(11)
Appendix B---Mathematical Induction 332(5)
Appendix C---Probability 337(39)
Bibliography 376(4)
Hints and Solutions 380(53)
Answers to Selected Problems 433(22)
Index 455

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