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Algebraic Number Theory and Fermat's Last Theorem
Algebraic Number Theory and Fermat's Last Theorem -

Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition 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. Students will see how Wiles’s proof of Fermat’s 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 Harper’s proof that Z(√14) is Euclidean


  • Presents an important new result: Mihăilescu’s 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 Fermat’s 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.

Algebraic Number Theory 1: Introduction This is the beginning of a video series working through J.S. Milne's notes on Algebraic Number Theory. You can find these notes ... [ANT01] Algebraic number theory: an introduction, via Fermat's last theorem The existence of the Euclidean algorithm is what makes multiplication in Z so nice. But some other rings have Euclidean ... A crash course in Algebraic Number Theory A quick proof of the Prime Ideal Theorem (algebraic analog of the Prime Number Theorem) is presented. In algebraic number ... Algebraic number theory and rings I | Math History | NJ Wildberger In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. Algebraic Number Theory 10: Integral Elements Form a Ring Part 1 Algebraic number theory and rings II | Math History | NJ Wildberger In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. Basics And Definitions Of Algebraic Number Theory Part 1 | Mathematise Yourself Basics And Definitions(Rational Integers, Algebraic Integers, Algebraic Number, Gaussian Integers, Unity of Gaussian Integer, ... Algebraic Number Theory 2: Basic Definitions from Commutative Algebra In this video I recall some basic definitions from commutative algebra. This is from Chapter 1 Section 1 of Milne's notes at: ... CTNT 2018 - "Basic Algebraic Number Theory" (Lecture 1) by Liang Xiao This is lecture 1 of a mini-course on "Basic Algebraic Number Theory", taught by Liang Xiao, during CTNT 2018, the Connecticut ... Jean-Pierre Serre: 50 years ago: a great time for Number Theory This is a talk of Jean-Pierre Serre (College de France) given at Harvard on April 28, 2017. The title was "50 years ago: a great time ... Integral Domains | Introduction to Algebraic Number Theory | Lecture 1| Lecture 14 of the course Integral_Domains. Algebraic Number Theory 4: Noetherian Rings and Modules In this lecture we give an introduction to the basics of Noetherian rings and Noetherian modules. This is Chapter 1 Sections 4 and ... CTNT 2018 - "Basic Algebraic Number Theory" (Lecture 2) by Liang Xiao This is lecture 2 of a mini-course on "Basic Algebraic Number Theory", taught by Liang Xiao, during CTNT 2018, the Connecticut ... Algebraic Number Theory Lecture 1 Algebraic Number Theory 23: Finding the Ring of Integers In this lecture we give some basic tools for computing bases of rings of integers. In particular we give several formulas for the ... Algebraic Number Theory 17: Introduction to Trace and Norm In this video we take a look at two important concepts from Galois theory, the trace and the norm. This will eventually give rise to ... Week 12-Lecture 59 : Some basics of algebraic number theory Week 12-Lecture 59 : Some basics of algebraic number theory.

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