## A Panorama of Pure Mathematics, As Seen by N. BourbakiA Panorama of Pure Mathematics, As Seen by N. Bourbaki |

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### Contents

1 | |

7 | |

Chapter A II Differential manifolds Differential geometry | 25 |

Chapter A III Ordinary differential equations | 35 |

Chapter A IV Ergodic theory | 43 |

Chapter A V Partial differential equations | 49 |

Chapter A VI Noncommutative harmonic analysis | 73 |

Chapter A VII Automorphic forms and modular forms | 87 |

Chapter B III Abstract groups | 191 |

Chapter B IV Commutative harmonic analysis | 199 |

Chapter B V Von Neumann algebras | 209 |

Chapter B VI Mathematical logic | 215 |

Chapter B VII Probability theory | 223 |

Chapter C I Categories and sheaves | 231 |

Chapter C II Commutative algebra | 249 |

Chapter C III Spectral theory of operators | 261 |

Chapter A VIII Analytic geometry | 97 |

Chapter A IX Algebraic geometry | 113 |

Chapter A X Theory of numbers | 147 |

Chapter B I Homological algebra | 167 |

Chapter B II Lie groups | 183 |

273 | |

283 | |

Pure and Applied Mathematics | 290 |

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### Common terms and phrases

0x-Module A-algebra A-module abelian group abelian varieties algebraic geometry algebraic group algebraic variety algebraically closed field analogous analytic spaces arbitrary automorphic BAMS Banach bijection Borel bundle called canonical Cartan classical coefficients complex connected consider continuous mapping corresponding defined definition denoted diffeomorphism differential manifold dimension divisor elliptic equivalent example exists fiber finite number Fourier function f functor fundamental Galois global group G harmonic analysis Hilbert space holomorphic functions homology homomorphism homotopy invariants isomorphic Lie algebra Lie groups linear representations locally compact mathematical modular forms modules morphism f neighborhood Neumann algebras Noetherian nonsingular notion number field number theory object obtained open set open subset partial differential equations Poincaré polynomial problem projective properties quotient relations representation of G resp S-scheme scheme semisimple sheaf sheaves singular Spec(A spectral structure subalgebra subspace tangent theorem topological space topology unitary representations variables vector space