Algebraic number theory (Chapman and Hall Mathematics Series) - Couverture souple

Stewart, Ian

Couverture souple

ISBN 10 : 0412138409 ISBN 13 : 9780412138409

Editeur : Chapman and Hall, 1979

Synopsis

The title of this book may be read in two ways. One is 'algebraic number-theory', that is, the theory of numbers viewed algebraically; the other, 'algebraic-number theory', the study of algebraic numbers. Both readings are compatible with our aims, and both are perhaps misleading. Misleading, because a proper coverage of either topic would require more space than is available, and demand more of the reader than we wish to; compatible, because our aim is to illustrate how some of the basic notions of the theory of algebraic numbers may be applied to problems in number theory. Algebra is an easy subject to compartmentalize, with topics such as 'groups', 'rings' or 'modules' being taught in comparative isolation. Many students view it this way. While it would be easy to exaggerate this tendency, it is not an especially desirable one. The leading mathematicians of the nineteenth and early twentieth centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, without ever defining an abstract vector space: nor is there anything to suggest that they suf- fered thereby. This historical fact may indicate that abstrac- tion is not always as necessary as one commonly imagines; on the other hand the axiomatization of mathematics has led to enormous organizational and conceptual gains.

A propos du livre

Présentation de l'éditeur

Contents: Preface. Reader's Guide. Index of Notation. The Origins of Algebraic Number Theory. Part I: Numbers. Quadratic and Cyclotomic Fields. Geometric Methods. Lattices. Minkowski's Theorem. Part II: Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. Part III: Number-Theoretic Applications. Computational Methods. Fermat's Last Theorem. Dirichlet's Units Theorem. Appendix. Quadratic Residues. References. Index.

Détails de l'édition

• Éditeur: Chapman and Hall
• Date d'édition: 1979
• Langue: anglais
• ISBN 10: 0412138409
• ISBN 13: 9780412138409
• Reliure: Broché
• Nombre de pages: 257
• Coordonnées du fabricant: non disponible