Problems in Algebraic Number Theory代数数论问题
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作者： 本社 编
出 版 社：
出版时间： 2004-10-1字数：版次： 1页数： 352印刷时间： 2004/10/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387221823包装： 平装内容简介
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.
目录
Preface to the second edition
Preface to the first edition
Acknowledgments
I Problems
1.Elementary number theory
2.Euclidean rings
3.Algebraic numbers and integers
4.Integral bases
5.Dedekind domains
6.The ideal class group
7.Quadratic reciprocity
8.The structure of units
9.Higher reciproctiy laws
10.Analytic methods
11.Density theorems
II Solutions
1.Elementary number theory
2.Euclidean rings
3.Algebraic numbers and Integers
4.Integral bases
5.Dedeking domaing
6.The ideal class group
7.Quadratic reciprocity
8.The structure of units
9.Higher reciproctiy laws
10.Analytic methods
11.Density theorems
Bibliography
Index
