Problems in Algebraic Number Theory

Jody (Indigo) Esmonde

ISBN 10: 1441919678 / ISBN 13: 9781441919670

Editore: Springer New York, Springer US Nov 2010, 2010

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 372 pp. Englisch.

Codice articolo 9781441919670

Dati bibliografici

• Titolo: Problems in Algebraic Number Theory
• Editore: Springer New York, Springer US Nov 2010
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441919678
• ISBN 13: 9781441919670
• Rilegatura: Taschenbuch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 21 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 21 millimetri di profondità
• Peso: 563 grammi

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Riassunto

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.

Dalla quarta di copertina

<p>From Reviews of the First Edition:</p><p>This book provides a problem-oriented first course in algebraic number theory. ... The authors have done a fine job in collecting and arranging the problems. Working through them, with or without help from a teacher, will surely be a most efficient way of learning the theory. Many of the problems are fairly standard, but there are also problems of a more original type. This makes the book a useful supplementary text for anyone studying or teaching the subject. ... This book deserves many readers and users.</p><p>- T. Metsänkylä , Mathematical Reviews</p><p>The book covers topics ranging from elementary number theory (such as the unique factorization of integers or Fermat's little theorem) to Dirichlet's theorem about primes in arithmetic progressions and his class number formula for quadratic fields, and it treats standard material such as Dedekind domains, integral bases, the decomposition of primes not dividing the index, the class group, the Minkowski bound and Dirichlet's unit theorem ... the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory.</p><p>- Franz Lemmermeyer, Zentralblatt</p><p>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.</p>