M. Ram Murty, Jody Esmonde (Indigo)

Problems in Algebraic Number Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 352
• Erscheinungstermin: 28. September 2005
• Englisch
• ISBN-13: 9780387269986
• Artikelnr.: 43728042

Autorenporträt

M. Ram Murty, Queen's University, Kingston, ON, Canada / Jody Esmonde, University of California at Berkeley, Berkeley, CA, USA

Inhaltsangabe

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.

Rezensionen

From the reviews of the second edition:

"Problems in Algebraic Number Theory is intended to be used by the students for independent study of the subject. It provides the reader with a large collection of problems (about 500) ... . The reviewer thinks that the authors have done a fantastic job choosing the problems, which are perfectly arranged so the students can progressively move from topic to topic ... . the book is an excellent resource for the instructor and the student as a companion to any algebraic number theory course." (Álvaro Lozano-Robledo, MathDL, May, 2005)

"This second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and L-Functions highlighting some of the analytic aspects of algebraic number theory. ... the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory." (Zentralblatt für Didaktik der Mathematik, August, 2005)

"This is the second edition of Problems in algebraic number theory. ... errors have been corrected ... . The decision to expand the book by including a chapter on density theorems is most welcome." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1055)

"This is the second edition of an unusual introduction to algebraic number theory. ... each chapter is written in straightforward textbook style. All chapters contain a very large number of problems. ... it presents a good way of acquiring a working knowledge of basic algebraic number theory by using it for independent study or as supplementary reading." (Ch. Baxa, Monatshefte für Mathematik, Vol. 149 (4), 2006)

Aus den Rezensionen zur 2. Auflage: "'Learning by doing' ist das Motto dieses Lehrbuchs, das eine Einführung in die algebraische Zahlentheorie bietet ... Der gebotene Stoff ... wird durch etwa 500 Übungen ergänzt, die den ... Leser zum selbstständigen Erarbeiten der algebraischen Zahlentheorie anregen sollen. ... Dieses Buch kann sowohl als Begleitbuch für eine entsprechende Lehrveranstaltung als auch zum Selbststudium für 'Einsteiger' in die algebraische Zahlentheorie empfohlen werden." (Günter Lettl, in: IMN - Internationale Mathematische Nachrichten, 2006, Issue 202, S. 42)