Problems in Algebraic Number Theory

Asking how one does mathematical research is like asking how a composer createsa masterpiece. No one really knows. However it is a recognized fact thatproblem s... » 

Asking how one does mathematical research is like asking how a composer createsa masterpiece. No one really knows. However it is a recognized fact thatproblem 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 mathematicalresearch lies essentially asking wellposed questions. The approach taken bythe authors in Problems in Algebraic Number Theory is based on the principlethat questions focus and orient the mind. The book is a collection of about 500problems in algebraic number theory systematically arranged to reveal ideasand concepts in the evolution of the subject. While some problems are easy andstraightforward others are more difficult. For this new edition the authorsadded a chapter and revised several sections. The text is suitable for a firstcourse in algebraic number theory with minimal supervision by the instructor.The exposition facilitates independent study and students having taken a basiccourse in calculus linear algebra and abstract algebra will find theseproblems interesting and challenging. For the same reasons it is ideal fornonspecialists in acquiring a quick introduction to the subject. TOCPrefaceto the Second Edition. Preface to the First Edition. Acknowledgments.Elementary Number Theory. Euclidean Rings. Algebraic Numbers and Integers.Integral Bases. Dedekind Domains. The Ideal Class Group. QuadraticReciprocity. The Structure of Units. Higher Reciprocity Laws. AnalyticMethods. Density Theorems. Solutions for Chapters 1 through 11.Bibliography. Index. «