Lectures on the Mordell-Weil Theorem, Martin L. Brown; Jean-P. Serre; Michel Waldschmidt
Автор: Matousek Jiri, BjГ¶rner A., Ziegler G.M. Название: Using the Borsuk-Ulam Theorem / Lectures on Topological Methods in Combinatorics and Geometry ISBN: 3540003622 ISBN-13(EAN): 9783540003625 Издательство: Springer Рейтинг: Цена: 55890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists.This book is the first textbook treatment of a significant part of such results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level (for example, homology theory and homotopy groups are completely avoided). No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained. This text started with a one-semester graduate course the author taught in fall 1993 in Prague. The transcripts of the lectures by the participants served as a basis of the first version. Some years later, a course partially based on that text was taught by GГјnter M. Ziegler in Berlin. The book is based on a thoroughly rewritten version prepared during a pre-doctoral course the author taught at the ETH Zurich in fall 2001.Most of the material was covered in the course: Chapter 1 was assigned as an introductory reading text, and the other chapters were presented in approximately 30 hours of teaching (by 45 minutes), with some omissions throughout and with only a sketchy presentation of the last chapter.
Автор: Milnor John Название: Lectures on the H-Cobordism Theorem ISBN: 0691624550 ISBN-13(EAN): 9780691624556 Издательство: Wiley Рейтинг: Цена: 31680.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: These lectures provide students and specialists with preliminary and valuable information from university courses and seminars in mathematics. This set gives new proof of the h-cobordism theorem that is different from the original proof presented by S. Smale. Originally published in 1965. The Princeton Legacy Library uses the latest print-on-dema
Автор: Klaus Schneider; Jens Brandt Название: Theorem Proving in Higher Order Logics ISBN: 3540745904 ISBN-13(EAN): 9783540745907 Издательство: Springer Рейтинг: Цена: 81050.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Constitutes the refereed proceedings of the 20th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2007, held in Kaiserslautern, Germany, in September 2007. This book presents 21 revised full papers together with 5 proof pearls and the abstracts of 3 invited papers that were reviewed and selected from 52 submissions.
Автор: Berto Название: There`s Something About Godel - The Complete Guide to the Incompleteness Theorem ISBN: 1405197668 ISBN-13(EAN): 9781405197663 Издательство: Wiley Рейтинг: Цена: 89710.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: There`s Something About Godel is a lucid and accessible guide to Godel`s revolutionary Incompleteness Theorem , considered one of the most astounding argumentative sequences in the history of human thought. It is also an exploration of the most controversial alleged philosophical outcomes of the Theorem.
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.
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