Algebraic Number Theory and Fermat''s Last Theorem | Agenda Bookshop
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A01=David Tall
A01=Ian Stewart
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Author_David Tall
Author_Ian Stewart
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Algebraic Number Theory and Fermat''s Last Theorem

English

By (author): David Tall Ian Stewart

Updated to reflect current research and extended to cover more advanced topics as well as the basics, Algebraic Number Theory and Fermats Last Theorem, Fifth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsthe quest for a proof of Fermats 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 Wiless proof of Fermats 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.

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Current price €155.79
Original price €163.99
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A01=David TallA01=Ian StewartAge Group_UncategorizedAuthor_David TallAuthor_Ian Stewartautomatic-updateCategory1=Non-FictionCategory=PBDCategory=PBFCategory=PBHCategory=PBVCOP=United KingdomDelivery_Pre-orderLanguage_EnglishPA=Not yet availablePrice_€100 and abovePS=Forthcomingsoftlaunch

Will deliver when available. Publication date 24 Dec 2024

Product Details
  • Dimensions: 156 x 234mm
  • Publication Date: 24 Dec 2024
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: United Kingdom
  • Language: English
  • ISBN13: 9781032602257

About David TallIan Stewart

Ian Stewart is an emeritus professor of mathematics at the University of Warwick and a fellow of the Royal Society. Dr. Stewart has been a recipient of many honours including the Royal Societys Faraday Medal the IMA Gold Medal the AAAS Public Understanding of Science and Technology Award the LMS/IMA Zeeman Medal and the University of Warwick Chancellors Medal. He has published more than 220 scientific papers and numerous books including several bestsellers co-authored with Terry Pratchett and Jack Cohen that combine fantasy with nonfiction.David Tall is an emeritus professor of mathematical thinking at the University of Warwick. Dr. Tall has published numerous mathematics textbooks and more than 200 papers on mathematics and mathematics education. His research interests include cognitive theory algebra visualization mathematical thinking and mathematics education.

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