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Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 47,92 MB
Release : 2001-02-22
Category : Mathematics
ISBN : 9780521004237
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author : Ian Stewart
Publisher : CRC Press
Page : 334 pages
File Size : 25,77 MB
Release : 2001-12-12
Category : Mathematics
ISBN : 143986408X
First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it
Author : Harry Pollard
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 25,89 MB
Release : 1975-12-31
Category : Algebraic number theory
ISBN : 1614440093
This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Author : Edwin Weiss
Publisher : Courier Corporation
Page : 308 pages
File Size : 12,11 MB
Release : 2012-01-27
Category : Mathematics
ISBN : 048615436X
Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
Author : Richard Dedekind
Publisher : Cambridge University Press
Page : 170 pages
File Size : 25,35 MB
Release : 1996-09-28
Category : Mathematics
ISBN : 0521565189
A translation of a classic work by one of the truly great figures of mathematics.
Author : Paul Pollack
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 12,28 MB
Release : 2017-08-01
Category : Mathematics
ISBN : 1470436531
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Author : M. Ram Murty
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 50,6 MB
Release : 2005-09-28
Category : Mathematics
ISBN : 0387269983
The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 38,11 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 0387216901
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
Author : Jürgen Neukirch
Publisher : Springer
Page : 0 pages
File Size : 22,39 MB
Release : 2010-12-15
Category : Mathematics
ISBN : 9783642084737
This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples. It is the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available.
Author : E. T. Hecke
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 27,68 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475740921
. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.