Description 
1 online resource (xi, 197 pages) : illustrations 
Series 
Universitext, 01725939 

Universitext, 01725939

Contents 
Examples  A Crash Course in Ring Theory  Lattices  Arithmetic in Q[[sq. root]D]  The Ideal Class Group and the Geometry of Numbers  Continued Fractions  Quadratic Forms 
Summary 
By focusing on quadratic numbers, this advanced undergraduate or master s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader handson computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory 
Bibliography 
Includes bibliographical references and index 
Notes 
Online resource; title from PDF title page (SpringerLink, viewed September 16, 2013) 
In 
Springer eBooks 
Subject 
Algebraic number theory.


Algebraic number theory.

Form 
Electronic book

ISBN 
9781461477174 

1461477174 

1461477166 

9781461477167 
