Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.

chapter Chapter 1|54 pages

Integral Domains, Ideals, and Unique Factorization

chapter Chapter 2|32 pages

Field Extensions

chapter Chapter 3|52 pages

Class Groups

chapter Chapter 4|42 pages

Applications: Equations and Sieves

chapter Chapter 5|80 pages

Ideal Decomposition in Number Fields

chapter Chapter 6|57 pages

Reciprocity Laws