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    Problem Solving Through Recreational Mathematics (Dover Books on Mathematics) (Paperback) By (author) Bonnie Averbach, By (author) Orin Chein

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    DescriptionHistorically, 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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    Title
    Problem Solving Through Recreational Mathematics
    Authors and contributors
    By (author) Bonnie Averbach, By (author) Orin Chein
    Physical properties
    Format: Paperback
    Number of pages: 480
    Width: 165 mm
    Height: 229 mm
    Thickness: 25 mm
    Weight: 703 g
    Language
    English
    ISBN
    ISBN 13: 9780486409177
    ISBN 10: 0486409171
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    DC21: 510
    DC22: 510
    LC subject heading:
    BIC subject category V2: PB
    LC subject heading:
    B&T Merchandise Category: SCI
    B&T General Subject: 710
    LC subject heading:
    Warengruppen-Systematik des deutschen Buchhandels: 26200
    Abridged Dewey: 510
    Ingram Subject Code: MA
    Libri: I-MA
    LC subject heading: ,
    BISAC V2.8: MAT025000
    LC subject heading:
    LC classification: QA39.2 .A896 2000
    Thema V1.0: PB
    Publisher
    Dover Publications Inc.
    Imprint name
    Dover Publications Inc.
    Publication date
    28 March 2003
    Publication City/Country
    New York
    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