{"product_id":"algebraic-number-theory-and-fermats-last-theorem-9781498738392","title":"Algebraic Number Theory and Fermats Last Theorem","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eUpdated to reflect current research, \u003cstrong\u003eAlgebraic Number Theory and Fermat's Last Theorem, Fourth Edition\u003c\/strong\u003e introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsthe 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eNew to the Fourth Edition\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eProvides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper's proof that Z(v14) is Euclidean\u003c\/li\u003e\n\u003cli\u003ePresents an important new result: Mihailescu's proof of the Catalan conjecture of 1844\u003c\/li\u003e\n\u003cli\u003eRevises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and other\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"It is the discussion of [Fermat’s Last Theorem], I think, that sets this book apart from others — there are a number of other texts that introduce algebraic number theory, but I don’t know of any others that combine that material with the kind of detailed exposition of FLT that is found here...To summarize and conclude: this is an interesting and attractive book. It would make an attractive text for an early graduate course on algebraic number theory, as well as a nice source of information for people interested in FLT, and especially its connections with algebraic numbers.\"\u003cbr\u003e\u003cstrong\u003e—\u003c\/strong\u003eDr. Mark Hunacek, \u003cem\u003eMAA Reviews\u003c\/em\u003e, June 2016\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003ePraise for Previous Editions\u003c\/strong\u003e\"The book remains, as before, an extremely attractive introduction to algebraic number theory from the ideal-theoretic perspective.\"\u003cbr\u003e—Andrew Bremner, \u003cem\u003eMathematical Reviews\u003c\/em\u003e, February 2003\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eAlgebraic Methods:\u003c\/strong\u003e Algebraic Background. Algebraic Numbers. Quadratic and Cylclotomic Fields. Factorization into Irreducibles. Ideals. \u003cstrong\u003eGeometric Methods:\u003c\/strong\u003e Lattices. Minkowski's Theorem. Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. \u003cstrong\u003eNumber-Theoretic Applications:\u003c\/strong\u003e Computational Methods. Kummer's Special Case of Fermat's Last Theorem. The Path to the Final Breakthrough. Elliptic Curves. Elliptic Functions. Wiles's Strategy and Recent Developments. \u003cstrong\u003eAppendices:\u003c\/strong\u003e Quadratic Residues. Dirichlet's Units Theorems.\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":51019954717015,"sku":"9781498738392","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498738392.jpg?v=1750781867","url":"https:\/\/bookcurl.com\/products\/algebraic-number-theory-and-fermats-last-theorem-9781498738392","provider":"Book Curl","version":"1.0","type":"link"}