## Invitation to MathematicsBased on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be termed a sampler of the discipline, Konrad Jacobs discusses an unusually wide range of topics, including such items of contemporary interest as knot theory, optimization theory, and dynamical systems. Using Euclidean geometry and algebra to introduce the mathematical mode of thought, the author then turns to recent developments. In the process he offers what he calls a "Smithsonian of mathematical showpieces": the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot Table, the plane ornaments, Alexander's Horned Sphere, and Antoine's Necklace. The treatments of geometry and algebra are followed by a chapter on induction and one on optimization, game theory, and mathematical economics. The chapter on topology includes a discussion of topological spaces and continuous mappings, curves and knots, Euler's polyhedral formula for surfaces, and the fundamental group. The last chapter deals with dynamics and contains material on the Game of Life, circle rotation, Smale's "horseshoe," and stability and instability, among other topics. |

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### Índice

Geometry | 3 |

2 Possible and Impossible Constructions | 11 |

4 Systematizing Geometry | 28 |

5 Some More Views of Geometry | 40 |

2 Square Roots | 52 |

Questions of Principle | 55 |

4 Solution of Equations and Systems of Equations | 61 |

The Principle of Mathematical Induction | 71 |

4 nPerson Games with n 2 | 133 |

5 Equilibrium | 144 |

Topology | 158 |

3 Surfaces | 170 |

4 Curves on Surfaces | 178 |

6 A Survey of Topology | 188 |

2 Game of Life | 194 |

3 Some Further Dynamical Systems | 202 |

2 Discussion of the Principle of Induction | 84 |

4 The Marriage Theorem | 94 |

7 Recursive Definition | 100 |

Optimization Game Theory and Economics | 109 |

2 Optimal Flows in Networks | 115 |

4 The Shift | 208 |

5 General Results in Dynamics | 216 |

Literature Cited | 225 |

233 | |