A conversational introduction to algebraic number theory : arithmetic beyond Z
 Responsibility
 Paul Pollack.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Physical description
 ix, 316 pages : illustrations ; 22 cm.
 Series
 Student mathematical library ; volume 84.
Access
Available online
Science Library (Li and Ma)
Stacks
Call number  Status 

QA247 .P5994 2017  Unknown 
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Creators/Contributors
 Author/Creator
 Pollack, Paul, 1980
Contents/Summary
 Bibliography
 Includes an index.
 Contents

 Getting our feet wetCast of charactersQuadratic number fields: First stepsParadise lostand foundEuclidean quadratic fieldsIdeal theory for quadratic fieldsPrime ideals in quadratic number ringsUnits in quadratic number ringsA touch of classMeasuring the failure of unique factorizationEuler's primeproducing polynomial and the criterion of FrobeniusRabinowitschInterlude: Lattice pointsBack to basics: Starting over with arbitrary number fieldsIntegral bases: From theory to practice, and backIdeal theory in general number ringsFiniteness of the class group and the arithmetic of $\overline{\mathbb{Z}}$Prime decomposition in general number ringsDirichlet's units theorem, IA case study: Units in $\mathbb{Z}[\sqrt[3]{2}]$ and the Diophantine equation $X^32Y^3=\pm1$Dirichlet's units theorem, IIMore Minkowski magic, with a cameo appearance by HermiteDedekind's discriminant theoremThe quadratic Gauss sumIdeal density in quadratic number fieldsDirichlet's class number formulaThree miraculous appearances of quadratic class numbersIndex.
 (source: Nielsen Book Data)9781470436537 20170814
 Publisher's Summary
 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.
(source: Nielsen Book Data)9781470436537 20170814
Subjects
Bibliographic information
 Publication date
 2017
 Series
 Student mathematical library ; volume 84
 ISBN
 9781470436537 (alk. paper)
 1470436531 (alk. paper)