 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
|
|
|
Algebraic Number Theory and Fermat's Last Theorem
◆Taylor & Francis セール開催中！：2025年6月29日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3-5週間でお届けいたします。 Author: Stewart, Ian / Tall, David (University of Warwick, UK) Publisher: Taylor & Francis ISBN: 9781032602257 Cover: HARDCOVER Date: 2024年12月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION 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. TABLE OF CONTENTS 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
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
