Problem Solving Through Recreational Mathematics : Dover Books on Mathema 1.4tics - Bonnie Averbach

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Problem Solving Through Recreational Mathematics

Name: Problem Solving Through Recreational Mathematics
Brand: DOVER
Price: 52.99 AUD

By: Bonnie Averbach, Orin Chein

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Paperback | 28 March 2003

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480 Pages

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16.6 x 23.4 x 2.4

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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 selected problems. An extensive appendix on probability is new to this Dover edition. Free solutions manual available for download at the Dover website.

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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
Table of Contents provided by Publisher. All Rights Reserved.

Problem Solving Through Recreational Mathematics

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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