## A First Course in Geometric Topology and Differential GeometryThe uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level. |

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This is an absolutely atrocious book. The pages stream at length with wordy nonsense without any sense of direction. Word economy never crossed the mind of this author. For that matter, niether did the relative importance of certain subjects, or how to correctly introduce material. Please find any other book, this thing is punishment.

### Contents

Informal Logic | vii |

Strategies for Proofs | 37 |

Sets | 89 |

Functions | 117 |

Relations | 159 |

Infinite and Finite Sets | 185 |

Selected Topics | 233 |

Number Systems | 305 |

Explorations | 345 |

### Other editions - View all

A First Course in Geometric Topology and Differential Geometry Ethan D. Bloch No preview available - 1997 |

### Common terms and phrases

algebra argument assume axioms bijective map binary operation cardinality Chapter codomain complex numbers compute Corollary countably infinite deduce definition denote the set discussion equation equivalence relation example exists F T F fact false Fibonacci numbers finite sets following theorem formula function f given greatest lower bound Hasse diagrams Hence holds homomorphism identity element implies integer intuitively lattices least upper bound left inverse Lemma Let f Let G Let n e logical map f mathematical induction mathematical proofs mathematicians matrix natural numbers negation non-empty set notation number systems order homomorphism order isomorphism Peano Postulates poset positive integer possible precisely prime numbers properties Prove Theorem quantifiers rational numbers reader in Exercise real numbers reflexive result right inverse rigorous Section sequence standard subset Suppose surjective symbols true truth table unique verify write