## The Art and Craft of Problem SolvingAppealing to everyone from college-level majors to independent learners, introduces a problem-solving approach to mathematics, as opposed to the traditional exercises approach. The goal of The Art and Craft of Problem Solving is to develop strong problem solving skills, which it achieves by encouraging students to do math rather than just study it. Paul Zeitz draws upon his experience as a coach for the international mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.The Art and Craft of Problem Solving, 3rd Edition |

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### Contents

1 | |

2 Strategies for Investigating Problems | 12 |

3 Tactics for Solving Problems | 58 |

4 Three Important Crossover Tactics | 105 |

5 Algebra | 143 |

6 Combinatorics | 189 |

7 Number Theory | 224 |

8 Geometry for Americans | 258 |

9 Calculus | 316 |

References | 355 |

Index | 357 |

EULA | 367 |

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### Common terms and phrases

algebra algorithm AM-GM AM-GM inequality angle argument assume binomial theorem cards Cauchy–Schwarz inequality circle color complex numbers compute Consider contradiction converges count crux move define denote divisor easy elements equal equation exactly example factor Fermat's little theorem Fibonacci Find finite formula function geometric geometric series graph ideas induction inequality infinite intersection inversion lattice points least line segment look Mathematical Olympiad mean value theorem midpoint modulo multiple notation number theory odd number pairs parity partition Pascal's Triangle penultimate step perfect square permutations perpendicular pigeonhole principle polynomial positive integers possible problem solving Problems and Exercises proof Prove Putnam real numbers rectangle roots of unity rotation sequence Show side similar triangles simple Solution strategy subsets symmetry tactic tangent theorem USAMO vector verify vertex vertices words zero