Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and other
Trade Review
"It is the discussion of [Fermat’s Last Theorem], I think, that sets this book apart from others — there are a number of other texts that introduce algebraic number theory, but I don’t know of any others that combine that material with the kind of detailed exposition of FLT that is found here...To summarize and conclude: this is an interesting and attractive book. It would make an attractive text for an early graduate course on algebraic number theory, as well as a nice source of information for people interested in FLT, and especially its connections with algebraic numbers."
—Dr. Mark Hunacek, MAA Reviews, June 2016
Praise for Previous Editions"The book remains, as before, an extremely attractive introduction to algebraic number theory from the ideal-theoretic perspective."
—Andrew Bremner, Mathematical Reviews, February 2003
Table of Contents
Algebraic Methods: Algebraic Background. Algebraic Numbers. Quadratic and Cylclotomic Fields. Factorization into Irreducibles. Ideals. Geometric Methods: Lattices. Minkowski's Theorem. Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. Number-Theoretic Applications: Computational Methods. Kummer's Special Case of Fermat's Last Theorem. The Path to the Final Breakthrough. Elliptic Curves. Elliptic Functions. Wiles's Strategy and Recent Developments. Appendices: Quadratic Residues. Dirichlet's Units Theorems.
