Problems in Algebraic Number Theory

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Sprache: Englisch

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Beschreibung

Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an important role in training the mind of a researcher. It would not be an exaggeration to say that the ability to do mathematical research lies essentially asking "well-posed" questions. The approach taken by the authors in Problems in Algebraic Number Theory is based on the principle that questions focus and orient the mind. The book is a collection of about 500 problems in algebraic number theory, systematically arranged to reveal ideas and concepts in the evolution of the subject. While some problems are easy and straightforward, others are more difficult. For this new edition the authors added a chapter and revised several sections. The text is suitable for a first course in algebraic number theory with minimal supervision by the instructor. The exposition facilitates independent study, and students having taken a basic course in calculus, linear algebra, and abstract algebra will find these problems interesting and challenging. For the same reasons, it is ideal for non-specialists in acquiring a quick introduction to the subject.

Zusammenfassung

This book is a collection of about 500 problems in algebraic number
theory. They are systematically arranged to reveal the evolution of
concepts and ideas of the subject. All of the problems are completely
solved. Any student with the usual background of undergraduate algebra
should be able to work through these problems on his/her own. For this
new edition the authors added a new chapter and revised several
sections.

Inhaltsverzeichnis

Problems.- Elementary Number Theory.- Euclidean Rings.- Algebraic Numbers and Integers.- Integral Bases.- Dedekind Domains.- The Ideal Class Group.- Quadratic Reciprocity.- The Structure of Units.- Higher Reciprocity Laws.- Analytic Methods.- Density Theorems.- Solutions.- Elementary Number Theory.- Euclidean Rings.- Algebraic Numbers and Integers.- Integral Bases.- Dedekind Domains.- The Ideal Class Group.- Quadratic Reciprocity.- The Structure of Units.- Higher Reciprocity Laws.- Analytic Methods.- Density Theorems.

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	372
Reihe:	Graduate Texts in Mathematics
Inhalt:	xvi 352 S.
ISBN-13:	9781441919670
ISBN-10:	1441919678
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Esmonde, Jody (Indigo) Murty, M. Ram
Auflage:	Softcover reprint of hardcover 2nd ed. 2005
Hersteller:	Springer US Springer New York Graduate Texts in Mathematics
Maße:	235 x 155 x 21 mm
Von/Mit:	Jody Esmonde (u. a.)
Erscheinungsdatum:	19.11.2010
Gewicht:	0,563 kg

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