Algebraic Number Theory and Fermat's Last Theorem
by Ian Stewart
2020-12-29 10:04:51
Algebraic Number Theory and Fermat's Last Theorem
by Ian Stewart
2020-12-29 10:04:51
Updated to reflect current research, Algebraic Number Theory and Fermatâs Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsâthe quest...
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Updated to reflect current research, Algebraic Number Theory and Fermatâs Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsâthe quest for a proof of Fermatâs 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. Students will see how Wilesâs proof of Fermatâs Last Theorem opened many new areas for future work. New to the Fourth Edition Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harperâs proof that Z(â14) is Euclidean Presents an important new result: MihÄilescuâs proof of the Catalan conjecture of 1844 Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermatâs Last Theorem Improves and updates the index, figures, bibliography, further reading list, and historical remarks Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.
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