Problem Solving Through Recreational Mathematics

ISBN-10: 0486409171
ISBN-13: 9780486409177
Edition: N/A
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Description: 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  More...

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Book details

List price: $16.95
Publisher: Dover Publications, Incorporated
Publication date: 5/27/1999
Binding: Paperback
Pages: 480
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 1.804
Language: English

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. Answers to Selected Problems. Index. 1980 edition.

Preface
To the Reader
Acknowledgments
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
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
From Words to Equations: Algebraic Recreations
Sample Problems
Introducing Variables
The Chapter in Retrospect
Exercises
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
More About Numbers: Bases and Cryptarithmetic
Sample Problems
Positional Notation
Changing Bases
Addition and Multiplication in Other Bases
Cryptarithmetic
The Chapter in Retrospect
Exercises
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
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
Deja Vu—We've Seen it Before
The Game of Nim
Pairing Strategies
Variations of a Game
The Chapter in Retrospect
Exercises
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
Potpourri
Decimation
Coin Weighing
Shunting
Syllogisms
Grab Bag
The Book in Retrospect
Some Basic Algebraic Techniques
Mathematical Induction
Probability Bibliography
Hints and Solutions
Answers to Selected Problems
Index

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