Updated to reflect current research, Algebraic Number Theory and Fermat's Last Theorem, Fourth 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 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 Fourth Edition
Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper's proof that Z(√14) is Euclidean
Presents an important new result: Mihăilescu's proof of the Catalan conjecture of 1844
Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat's Last Theorem
Improves and updates the index, figures, bibliography, further reading list, and historical remarks
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.
Автор: Ceccherini-Silberstein Название: Groups, Graphs and Random Walks ISBN: 1316604403 ISBN-13(EAN): 9781316604403 Издательство: Cambridge Academ Рейтинг: Цена: 11880.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the connections with other branches of mathematics. Covering topics from growth and amenability of groups, Schroedinger operators, and Poisson boundaries, this book provides a valuable and up-to-date reference for both researchers and graduates.
Автор: Mikhail Klin; Gareth A. Jones; Aleksandar Jurisic; Название: Algorithmic Algebraic Combinatorics and Gr?bner Bases ISBN: 3642424384 ISBN-13(EAN): 9783642424380 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries. There is special emphasis on algorithmic aspects and the use of the theory of Grobner bases.
Автор: Godsil Название: Erd?s–Ko–Rado Theorems: Algebraic Approaches ISBN: 1107128447 ISBN-13(EAN): 9781107128446 Издательство: Cambridge Academ Рейтинг: Цена: 11246.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Erdos-Ko-Rado Theorem is a fundamental result in combinatorics. Aimed at graduate students and researchers, this comprehensive text shows how tools from algebraic graph theory can be applied to prove the EKR Theorem and its generalizations. Readers can test their understanding at every step with the end-of-chapter exercises.
Автор: Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf Название: Discrete Algebraic Methods: Arithmetic, Cryptography, Automata and Groups ISBN: 3110413329 ISBN-13(EAN): 9783110413328 Издательство: Walter de Gruyter Цена: 6499.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents:Algebraic structuresCryptographyNumber theoretic algorithmsPolynomial time primality testElliptic curvesCombinatorics on wordsAutomataDiscrete infinite groups
Автор: Barlow Название: Random Walks and Heat Kernels on Graphs ISBN: 1107674425 ISBN-13(EAN): 9781107674424 Издательство: Cambridge Academ Рейтинг: Цена: 9186.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introduction to random walks on infinite graphs, in both discrete and continuous time, gives a systematic account of transition densities, including useful but hard-to-find results. The book is aimed at researchers and graduate students in mathematics who have a basic familiarity with analysis and some familiarity with probability.
Автор: Mahir Can; Zhenheng Li; Benjamin Steinberg; Qiang Название: Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics ISBN: 1493909371 ISBN-13(EAN): 9781493909377 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: "The Fields Institute for Research in the Mathematical Sciences."
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