Problems in Algebraic Number Theory
Seiten
1998
Springer-Verlag New York Inc.
978-0-387-98617-3 (ISBN)
Springer-Verlag New York Inc.
978-0-387-98617-3 (ISBN)
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A collection of approximately 500 problems in algebraic number theory, systematically arranged to reveal the evolution of concepts and ideas of the subject. They have been arranged with a didactic purpose in mind and are completely solved.
Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. It is clear, however, that problem solving plays an important role in the training of the research mind. In fact, it would not be an exaggeration to say that the ability to do research is essentially the art of asking the 'right'questions. And indeed, the approach taken here is based on the principle that questions focus the mind. This book is a collection of approximately 500 problems in algebraic number theory, systematically arranged to reveal the evolution of concepts and ideas of the subject. Some are easy and straightforward, others difficult. However, they have all been arranged with a didactic purpose in mind and are completely solved. This text is suitable for a first course in algebraic number theory with minimal supervision by the instructor. The exposition also facilitates independent study, however, and any student who has taken a basic course in calculus, linear algebra and abstract algebra should be able to work through these problems on his/her own.
Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. It is clear, however, that problem solving plays an important role in the training of the research mind. In fact, it would not be an exaggeration to say that the ability to do research is essentially the art of asking the 'right'questions. And indeed, the approach taken here is based on the principle that questions focus the mind. This book is a collection of approximately 500 problems in algebraic number theory, systematically arranged to reveal the evolution of concepts and ideas of the subject. Some are easy and straightforward, others difficult. However, they have all been arranged with a didactic purpose in mind and are completely solved. This text is suitable for a first course in algebraic number theory with minimal supervision by the instructor. The exposition also facilitates independent study, however, and any student who has taken a basic course in calculus, linear algebra and abstract algebra should be able to work through these problems on his/her own.
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 * Solutions for Chapters 1 through 10.
| Reihe/Serie | Graduate Texts in Mathematics ; v. 190 |
|---|---|
| Verlagsort | New York, NY |
| Sprache | englisch |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 0-387-98617-0 / 0387986170 |
| ISBN-13 | 978-0-387-98617-3 / 9780387986173 |
| Zustand | Neuware |
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