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Synopsis
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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From the Back Cover
From Reviews of the First Edition:
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.
- T. Metsänkylä , Mathematical Reviews
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.
- Franz Lemmermeyer, Zentralblatt
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.
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- PublisherSpringer
- Publication date2010
- ISBN 10 1441919678
- ISBN 13 9781441919670
- BindingPaperback
- LanguageEnglish
- Edition number2
- Number of pages368
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Problems in Algebraic Number Theory (Graduate Texts in Mathematics, 190)
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Problems in Algebraic Number Theory
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved 372 pp. Englisch. Seller Inventory # 9781441919670
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Problems in Algebraic Number Theory
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Problems in Algebraic Number Theory
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9781441919670
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Problems in Algebraic Number Theory
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