This text introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics-the quest for a proof of Fermat's Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Along with several recent developments, this fourth edition provides up-to-date information on unique prime factorization for real quadratic number fields and presents Mih¿ilescu's proof of the Catalan conjecture.
"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
-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