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Algebraic Number Theory And Fermat S Last Theorem

Author: Ian Stewart
Publisher: CRC Press
ISBN: 1498738400
Size: 67.23 MB
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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.

Klassenk Rpertheorie

Author: Jürgen Neukirch
Publisher: Springer-Verlag
ISBN: 364217325X
Size: 79.93 MB
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Der Klassiker zum Thema bietet Lesern, die mit den Grundlagen der algebraischen Zahlentheorie vertraut sind, einen raschen Zugang zur Klassenkörpertheorie. Die Neuauflage ist eine verbesserte Version des 1969 in der Reihe B. I.-Hochschulskripten (Bibliographisches Institut Mannheim) erschienenen gleichnamigen Bandes. Das Werk besteht aus drei Teilen: Im ersten wird die Kohomologie der endlichen Gruppen behandelt, im zweiten die lokale Klassenkörpertheorie, der dritte Teil widmet sich der Klassenkörpertheorie der endlichen algebraischen Zahlkörper.

A Pythagorean Introduction To Number Theory

Author: Ramin Takloo-Bighash
Publisher: Springer
ISBN: 3030026043
Size: 70.29 MB
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Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.

Fermat S Last Theorem

Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 9780387950020
Size: 32.99 MB
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This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummers theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.

B Renschwur

Author: Ryan Gebhart
Publisher: Aladin
ISBN: 3848960249
Size: 12.61 MB
Format: PDF, Mobi
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Tyson ist dreizehn. Über seine Eltern kann er sich nicht beklagen. Nur dass ihn sein bester Freund gegen ein Footballteam und kichernde Mädchen eingetauscht hat, wurmt ihn. Wirklich versteht ihn aber nur Gramps, sein Großvater, zugleich sein bester Kumpel. Doch dann kommt Gramps in ein Seniorenheim und die Pläne der beiden, noch vor dem Ende der Sommerferien auf die Jagd zu gehen, scheinen zu platzen. Zudem melden die Zeitungen jede Woche neue Opfer von Bärenangriffen in den Wäldern des Grand Teton Nationalpark. Für Tysons Eltern ist klar, dass der Ausflug nicht stattfinden wird. Doch Tyson und Gramps wären nicht das beste Team der Welt, wenn sie keinen Weg fänden, das Verbot zu umgehen. Nur als E-Book erhältlich!

Number Theory

Author: John J. Watkins
Publisher: Princeton University Press
ISBN: 1400848741
Size: 61.38 MB
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The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)

Number Theory

Author: Canadian Number Theory Association. Conference
Publisher: American Mathematical Soc.
ISBN: 9780821803127
Size: 28.87 MB
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This book contains proceedings presented at the fourth Canadian Number Theory Association (CNTA) conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory. Paulo Ribenboim gave an hour-long talk on Fermat's last theorem--which was wide open at the time of the conference. His lecture was entitled Fermat's Last Theorem, Before June 23, 1993. This lecture was open to the public and attracted a large audience from outside the conference. This book contains 34 written versions of the presentations. All papers were refereed.

Das Buch Der Beweise

Author: Martin Aigner
Publisher: Springer-Verlag
ISBN: 3662064545
Size: 14.75 MB
Format: PDF, Kindle
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Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit