PROBLEMS IN ALGEBRAIC NUMBER THEORY: v. 190 (Graduate Texts in Mathematics) - Tapa dura

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 musical masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an important role in training the mind of the researcher. It would not be an exaggeration to say that the ability to do mathematical research lies essentially in asking "well-posed" questions. The approach taken by the authors in Problems in Algebraic Number Theory is based on the principle that "good" questions help focus and orient the mind.
This book is a collection of about 500 problems in algebraic number theory, all systematically arranged to reveal ideas and concepts in the evolution of the subject. While some problems are easy and straightforward, others are more difficult.
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.