## Compositions of Quadratic FormsThe aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany" |

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### Contents

Exercises | 5 |

Chapter | 13 |

Appendix Composition algebras | 21 |

Notes | 36 |

Exercises | 46 |

Chapter 3 | 52 |

Exercises | 64 |

Notes | 71 |

Notes | 175 |

Exercises | 196 |

Notes | 202 |

Appendix Hasse principle for divisibility of forms | 218 |

Introduction | 227 |

Appendix More applications of topology to algebra | 252 |

Notes | 264 |

Integer Composition Formulas | 268 |

Appendix A Hermitian forms over C | 81 |

Notes | 89 |

Exercises | 101 |

Chapter 6 | 108 |

Exercises | 116 |

Exercises | 131 |

Exercises | 150 |

Notes | 157 |

Appendix Pfister forms and function fields | 167 |

Appendix A A new proof of Yuzvinskys theorem | 286 |

Chapter 14 | 299 |

Appendix Compositions of quadratic forms a J y | 317 |

Appendix Polynomial maps between spheres | 348 |

Notes | 361 |

Exercises | 375 |

407 | |