Algebraic Number Theory and Fermat's Last Theorem

Algebraic Number Theory and Fermats Last Theorem, Fourth Edition, is a textbook that covers fundamental ideas of algebraic numbers and explores the quest for a proof of Fermats Last Theorem. It provides up-to-date information on unique prime factorization for real quadratic number fields, presents an important new result, and improves and updates the index, figures, bibliography, further reading list, and historical remarks. Written by preeminent mathematicians Ian Stewart and David Tall, the text teaches students how to extend properties of natural numbers to more general number structures and how to solve problems in number theory using basic notions from the theory of algebraic numbers.

Format: Paperback / softback
Length: 344 pages
Publication date: 30 September 2020
Publisher: Taylor & Francis Ltd

Algebraic Number Theory and Fermats Last Theorem, Fourth Edition, is a comprehensive guide that delves into the realm of algebraic numbers and explores one of the most captivating tales in the history of mathematics: the relentless pursuit of a proof for Fermats Last Theorem. Written by renowned mathematicians Ian Stewart and David Tall, this edition offers a fresh perspective on the theory, utilizing Fermats Last Theorem as a motivating force to study algebraic numbers from a concrete standpoint.

The authors employ this celebrated theorem to initiate a comprehensive exploration of the theory of algebraic numbers, presenting students with a clear and accessible approach. Through the lens of Wiless proof of Fermats Last Theorem, students gain insight into the vast potential that this theorem holds, unlocking new avenues for future research.

The Fourth Edition introduces several notable updates, including:

• A comprehensive discussion of unique prime factorization for real quadratic number fields, particularly Harpers proof that Z(√14) is Euclidean.
• An important new result: Mihăilescus proof of the Catalan conjecture of 1844, a theorem that has eluded mathematicians for centuries.
• A revised and expanded chapter that delves into classical ideas about modular functions, highlighting the groundbreaking contributions of Frey, Wiles, and others that ultimately led to the long-sought proof of Fermats Last Theorem.
• An improved and updated index, figures, bibliography, further reading list, and historical remarks to enhance the accessibility and usefulness of the text.

At its core, Algebraic Number Theory and Fermats Last Theorem, Fourth Edition serves as a valuable tool for teaching students how to extend properties of natural numbers to more general number structures, encompassing algebraic number fields and their rings of algebraic integers. The text elucidates how fundamental concepts from the theory of algebraic numbers can be applied to solve problems in number theory, making it an essential resource for both undergraduate and graduate students in mathematics.

With its comprehensive coverage, updated information, and engaging narrative, this edition continues to be a staple in the field of algebraic number theory, guiding students on a journey of discovery and mathematical enlightenment.

Weight: 502g
Dimension: 152 x 227 x 29 (mm)
ISBN-13: 9780367658717
Edition number: 4 New edition