A Brief Guide to Algebraic Number Theory [Paperback]

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.This is an account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. The book encompasses everything that graduate students and pure mathematicians interested in the subject are likely to need, and assumes only some undergraduate level material and other prerequisites covered in an appendix. The book covers the two basic methods of approaching Algebraic Number Theory and includes a substantial digression on the classical approach to Fermat's Last Theorem. Many exercises and an annotated reading list are also included.This is an account of Algebraic Number Theory, a field which has grown to touch many other areas of pure mathematics. The book encompasses everything that graduate students and pure mathematicians interested in the subject are likely to need, and assumes only some undergraduate level material and other prerequisites covered in an appendix. The book covers the two basic methods of approaching Algebraic Number Theory and includes a substantial digression on the classical approach to Fermat's Last Theorem. Many exercises and an annotated reading list are also included.This account of Algebraic Number Theory is written primarily for beginning graduate students in pure mathematics, and encompasses everything that most such students are likely to need; others who need the material will also find it accessible. It assumes no prior knowledge of the subject, but a firm basis in the theory of field extensions at an undergraduate level is required, and an appendix covers other prerequisites. The book covers the two basic methods of approaching Algebraic Number Theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to Fermat's Last TheorlW