Problem Solving Through Recreational Mathematics [NOOK Book]

Overview



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 ...
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Problem Solving Through Recreational Mathematics

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Overview



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.
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Product Details

  • ISBN-13: 9780486131740
  • Publisher: Dover Publications
  • Publication date: 2/16/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 480
  • Sales rank: 721,155
  • File size: 29 MB
  • Note: This product may take a few minutes to download.

Table of Contents

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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Customer Reviews

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Sort by: Showing all of 3 Customer Reviews
  • Anonymous

    Posted February 26, 2005

    Excellent introduction to a variety of math methods

    This book has opened up so many doors for me. Each section gradually works its way through a topic, giving a variety of problems to explore the ideas. Lots of solved or answered problems to help with the concepts. Excellent introduction to number theory, game theory, logic, and more. All discussed in an easy manner that disarms any math phobia. Thoroughly enjoyable.

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted June 14, 2009

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    Posted May 7, 2009

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