Algebraic Theory of Quadratic Numbers

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Mak Trifkovi¿ is an assistant professor of mathematics at the University of Victoria.

Zusammenfassung

Offers an accessible introduction to number theory by focusing on quadratic numbers

Includes many exercises that provide students with hands-on computational experience with quadratic number fields

Presents a modern treatment of binary quadratic forms

Includes supplementary material: [...]

Inhaltsverzeichnis

1 Examples.- 2 A Crash Course in Ring Theory.- 3 Lattices.- 4 Arithmetic in Q[¿D].- 5 The Ideal Class Group and Geometry of Numbers.- 6 Continued Fractions.- 7 Quadratic Forms.- Appendix.- Hints to Selected Exercises.- Index.

Details

Erscheinungsjahr:	2013
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xi 197 S. 29 s/w Illustr. 197 p. 29 illus.
ISBN-13:	9781461477167
ISBN-10:	1461477166
Sprache:	Englisch
Herstellernummer:	80043966
Einband:	Kartoniert / Broschiert
Autor:	Trifkovi¿, Mak
Hersteller:	Springer US Springer New York
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 12 mm
Von/Mit:	Mak Trifkovi¿
Erscheinungsdatum:	14.09.2013
Gewicht:	0,33 kg

Artikel-ID: 105969108