Problems in Algebraic Number Theory (Graduate Texts in Mathematics, 190, Band 190) - Hardcover

Murty, M. Ram; Esmonde, Jody (Indigo)

Hardcover

ISBN 10: 0387221824 ISBN 13: 9780387221823

Verlag: Springer, 2004

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

Sebastian M. Cioaba is Professor at the Department of Mathematical Sciences, University of Delaware, Newark, USA. After his undergraduate studies in mathematics and computer science at the University of Bucharest, Romania, he obtained his Ph.D. in Mathematics at Queen's University at Kingston, Canada. Following postdocs at UC San Diego and the University of Toronto, Sebastian started his teaching position at the University of Delaware in 2009. His research interests are in spectral graph theory, algebraic combinatorics, and their connections and applications to other areas of mathematics and science. He is on the editorial board of several journals including Discrete Mathematics, Linear Algebra and its Applications, and Electronic Journal of Linear Algebra. He has organized several conferences in algebraic combinatorics and spectral graph theory. Sebastian has supervised 5 Ph.D. students, 2 M.Sc. students, 3 undergraduate senior theses, and over 20 summer research students. He has published more than 60 papers, and his research has been supported by NSF, NSA, NSERC, Simons Foundation, IDex Bordeaux, and Japan Society for Promotion of Science. M. Ram Murty is Queen's Research Chair and A.V. Douglas Distinguished University Professor at Queen's University, in Kingston, Ontario, Canada. He obtained his Ph.D. from Massachusetts Institute of Technology, USA, in 1980 and subsequently held positions at the Institute for Advanced Study in Princeton, Tata Institute for Fundamental Research in Mumbai, and McGill University in Montreal. He has authored more than 250 research papers and written more than a dozen mathematical textbooks. His monograph, Non-vanishing of L-functions and Applications, written jointly with Prof. V. Kumar Murty, won the 1996 Balaguer Prize. Ram is Fellow of the Royal Society of Canada, Fellow of the American Mathematical Society, and Fellow of the Indian National Science Academy, India. He also teaches Indian philosophy at Queen's University and has authored Indian Philosophy: An Introduction, published by Broadview Press.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2004
• Sprache: Englisch
• ISBN 10: 0387221824
• ISBN 13: 9780387221823
• Einband: Gebundene Ausgabe
• Auflage: 2
• Anzahl der Seiten: 368
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland