| Description |
1 online resource (xi, 197 pages) : illustrations |
| Series |
Universitext, 0172-5939 |
|
Universitext, 0172-5939
|
| 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 hands-on 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.
|
|
Teoría algebraica de números
|
|
Algebraic number theory
|
| Form |
Electronic book
|
| ISBN |
9781461477174 |
|
1461477174 |
|
1461477166 |
|
9781461477167 |
|
