quartonews.it » Math and Science » A Course in Arithmetic (Graduate Texts in Mathematics, Vol. 7)

Author: | J-P. Serre |

Subcategory: | Mathematics |

Language: | English |

Publisher: | Springer; 1st Corrected ed. 1973. Corr. 3rd printing 1996 edition (October 10, 1996) |

Pages: | 119 pages |

Category: | Math and Science |

Rating: | 4.2 |

Other formats: | rtf lrf txt docx |

The book is a showcase of how some results in classical number theory (the Arithmetic of the title) can be derived quickly using abstract algebra.

The book is a showcase of how some results in classical number theory (the Arithmetic of the title) can be derived quickly using abstract algebra. There are a reasonable number of worked examples, and they are very well-chosen. this book will expand your horizons, but you should already have a good knowledge of algebra and of classical number theory before you begin.

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The GTM series is easily identified by a white band at the top of the book.

This book is very elegant, a pleasure to read, but not a great textbook - after reading you are likely not to remember anything other than having enjoyed it (this is particularly true of the proof of Dirichlet's theorem). For actually learning to work in the subject (of analytic number theory), Davenport's book Multiplicative Number Theory is VASTLY superior.

Graduate Texts in Mathematics 10. The prerequisites for reading this book are fairly modest.

The prerequisites for reading this book are fairly modest. We assume that the reader has had a rst course in algebraic number theory, and thus is acquainted with number elds, rings of integers, prime ideals, ramication, absolute values, comple-tions, etc. The contents of any basic text on algebraic number theory, such as or, should more than sufce. Chapter VI, which deals with elliptic curves over C, assumes a familiarity with the basic principles of complex analysis. In Chap-ter X, we use a little bit of group cohomology, but just H0 and H1.

248Graduate Texts in Mathematics. A Course in Arithmetic. Graduate Texts in Mathematics. Introduction to Axiomatic Set Theory. Axiomatic Set Theory. Moreover, it approached buildings from only one point of view, sometimes called the old-fashioned approach: A building is a simplicial complex with certain properties.

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This book is divided into two parts. The first one is purely algebraic. A Course in Arithmetic Graduate Texts in Mathematics (Том 7). Автор. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups.

Serre's work could best be summarized in one word - Elegance. The book comprises of two distinct parts. This short book on number theory by one of the giants of 20th century mathematics is delightful to read. The first one is the 'algebraic' part. Serre's goal in this section is to give a complete classification of the quadratic forms over the rationals. As preliminaries to reaching this goal, he introduces the reader to quadratic reciprocity, p-adic fields and the Hilbert Symbol. Its length motivates one to finish the book, and it is packed full of interesting results. Most of the theory discussed in the book has wide-ranging applications, such as cryptography and dynamical systems.

Gehring . Graduate Texts in Mathematics S. Axler Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo 73 . .

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