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Problem Solving Through Recreational Mathematics

Publisher: 
Dover Publications
Number of Pages: 
480
Price: 
14.95
ISBN: 
0486409171
Date Received: 
Saturday, March 4, 2006
Reviewable: 
Include In BLL Rating: 
Bonnie Averbach and Orin Chein
Publication Date: 
2000
Format: 
Paperback
Audience: 
Category: 
General
BLL
07/20/2009
BLL Rating: 

 

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
Publish Book: 
Modify Date: 
Monday, July 20, 2009

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