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Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart: New

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Specifiche dell'oggetto

Condizione
Nuovo: Libro nuovo, intatto e non letto, in perfette condizioni, senza pagine mancanti o ...
Book Title
Algebraic Number Theory and Fermat's Last Theorem
Publication Date
2024-12-24
Edition Number
5
Pages
486
ISBN
9781032610931

Informazioni su questo prodotto

Product Identifiers

Publisher
CRC Press LLC
ISBN-10
103261093X
ISBN-13
9781032610931
eBay Product ID (ePID)
7070494404

Product Key Features

Number of Pages
486 Pages
Language
English
Publication Name
Algebraic Number Theory and Fermat's Last Theorem
Subject
General, Number Theory, Combinatorics
Publication Year
2024
Type
Textbook
Author
Ian Stewart, David Tall
Subject Area
Mathematics
Format
Trade Paperback

Dimensions

Item Length
9.2 in
Item Width
6.1 in

Additional Product Features

Edition Number
5
Intended Audience
College Audience
LCCN
2024-028878
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
512.74
Table Of Content
I. Algebraic Methods. 1. Algebraic Background. 2. Algebraic Numbers. 3. Quadratic and Cyclotomic Fields. 4. Pell's Equation. 5. Factorisation into Irreducibles. 6. Ideals. II. Geometric Methods. 7. Lattices. 8. Minkowski's Theorem. 9. Geometric Representation of Algebraic Numbers. 10. Dirichlet's Units Theorem. 11. Class-Group and Class-Number. III. Number-Theoretic Applications. 12. Computational Methods. 13. Kummer's Special Case of Fermat's Last Theorem. IV. Elliptic Curves and Elliptic Functions. 14. Elliptic Curves. 15. Elliptic Functions. V. Wiles's Proof of Fermat's Last Theorem. 16. The Path to the Final Breakthrough. 17. Wiles's Strategy and Subsequent Developments. VI. Galois Theory and Other Topics. 18. Extensions and Galois Theory. 19. Cyclotomic and Cubic Fields. 20. Prime Ideals Revisited. 21. Ramification Theory. 22. Quadratic Reciprocity. 23. Valuations and p-adic Numbers.
Synopsis
Updated to reflect current research and extended to cover more advanced topics as well as the basics, this book 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., Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermat's Last Theorem, Fifth 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, initially 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 Fifth Edition Pell's Equation x^2-dy^2=1: all solutions can be obtained from a single 'fundamental' solution, which can be found using continued fractions. Galois theory of number field extensions, relating the field structure to that of the group of automorphisms. More material on cyclotomic fields, and some results on cubic fields. Advanced properties of prime ideals, including the valuation of a fractional ideal relative to a prime ideal, localisation at a prime ideal, and discrete valuation rings. Ramification theory, which discusses how a prime ideal factorises when the number field is extended to a larger one. A short proof of the Quadratic Reciprocity Law based on properties of cyclotomic fields. This Valuations and p -adic numbers. Topology of the p -adic integers. 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.
LC Classification Number
QA247.S76 2025

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