Marcus D.A. Number Fields

2nd ed. — Springer, 2018. — 213 p. — (Universitext). — ISBN: 9783319902326, 3319902326.Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises. There are several hundred exercises, providing a wealth of both computational and theoretical practice, as well as appendices summarizing the necessary background in algebra.
Now in a newly typeset edition including a foreword by Barry Mazur, this highly regarded textbook will continue to provide lecturers and their students with an invaluable resource and a compelling gateway to a beautiful subject.A Special Case of Fermat’s Conjecture
Number Fields and Number Rings
Prime Decomposition in Number Rings
Galois Theory Applied to Prime Decomposition
The Ideal Class Group and the Unit Group
The Distribution of Ideals in a Number Ring
The Dedekind Zeta Function and the Class Number Formula
The Distribution of Primes and an Introduction to Class Field Theory