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Author Trifković, Mak, author

Title Algebraic theory of quadratic numbers / Mak Trifković
Published New York : Springer, 2013


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.
Algebraic number theory.
Form Electronic book
ISBN 9781461477174