{"product_id":"algebraic-number-theory-and-fermats-last-theorem-paperback","title":"Algebraic Number Theory and Fermat's Last Theorem - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eIan Stewart\u003c\/b\u003e (Author), \u003cb\u003eDavid Tall\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eUpdated to reflect current research and extended to cover more advanced topics as well as the basics, \u003cb\u003eAlgebraic Number Theory and Fermat's Last Theorem, Fifth Edition\u003c\/b\u003e 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cb\u003eNew to the Fifth Edition\u003c\/b\u003e\u003cul\u003e \u003cli\u003ePell's Equation x 2-dy 2=1: all solutions can be obtained from a single  fundamental' solution, which can be found using continued fractions.\u003c\/li\u003e \u003cli\u003eGalois theory of number field extensions, relating the field structure to that of the group of automorphisms.\u003c\/li\u003e \u003cli\u003eMore material on cyclotomic fields, and some results on cubic fields.\u003c\/li\u003e \u003cli\u003eAdvanced 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.\u003c\/li\u003e \u003cli\u003eRamification theory, which discusses how a prime ideal factorises when the number field is extended to a larger one.\u003c\/li\u003e \u003cli\u003eA short proof of the Quadratic Reciprocity Law based on properties of cyclotomic fields. This\u003c\/li\u003e \u003cli\u003eValuations and \u003ci\u003ep\u003c\/i\u003e-adic numbers. Topology of the \u003ci\u003ep\u003c\/i\u003e-adic integers.\u003c\/li\u003e \u003c\/ul\u003e\u003cp\u003eWritten 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.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eIan Stewart \u003c\/b\u003eis 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 Society's 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 Chancellor's 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.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eDavid Tall \u003c\/b\u003eis 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.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 486\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.02 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 24, 2024\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":66038425747847,"sku":"9781032610931","price":129.45,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1025\/5558\/2813\/files\/aK0drc7Oi79781032610931.webp?v=1790405711","url":"https:\/\/novellybooks.com\/products\/algebraic-number-theory-and-fermats-last-theorem-paperback","provider":"Novelly Books","version":"1.0","type":"link"}