Problems in algebraic number theory
- M. Ram Murty, Jody Esmonde.
- 2nd ed.
- New York : Springer, c2005.
- Physical description
- xvi, 352 p. ; 25 cm.
- Graduate texts in mathematics 190.
- Includes bibliographical references (p. 347-348) and index.
- Preface to 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.- Quadratic Reciprocity.- The Structure of Units.- Higher Reciprocity Laws.- Analytic Methods.- Density Theorems.- Solutions for Chapters 1 through 11.- Bibliography.- Index.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Publication date
- Graduate texts in mathematics ; 190
- Esmonde's name appears first on the earlier edition.
- 0387221824 (alk. paper)
- 9780387221823 (alk. paper)