Algebraic Theory of Quadratic Numbers

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 importan...

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Main Author: Trifković, Mak
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2013, 2013
Edition:1st ed. 2013
Series:Universitext
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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
Physical Description:XI, 197 p. 29 illus online resource
ISBN:9781461477174