Problems in Algebraic Number Theory (Graduate Texts in Mathematics)

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 tak...

(展开全部)

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.

Front Matter
Pages i-xvi
Problems
Elementary Number Theory
Pages 3-11
Euclidean Rings
· · · · · · (更多)

Front Matter
Pages i-xvi
Problems
Elementary Number Theory
Pages 3-11
Euclidean Rings
Pages 13-26
Algebraic Numbers and Integers
Pages 27-39
Integral Bases
Pages 41-52
Dedekind Domains
Pages 53-68
The Ideal Class Group
Pages 69-79
Quadratic Reciprocity
Pages 81-97
The Structure of Units
Pages 99-116
Higher Reciprocity Laws
Pages 117-125
Analytic Methods
Pages 127-138
Density Theorems
Pages 139-155
Solutions
Elementary Number Theory
Pages 159-178
Euclidean Rings
Pages 179-196
Algebraic Numbers and Integers
Pages 197-206
Integral Bases
Pages 207-225
Dedekind Domains
Pages 227-244
The Ideal Class Group
Pages 245-262
Quadratic Reciprocity
Pages 263-278
The Structure of Units
Pages 279-298
Solutions
Higher Reciprocity Laws
Pages 299-311
Analytic Methods
Pages 313-331
Density Theorems
Pages 333-346
Back Matter
Pages 347-352
· · · · · · (收起)