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: Gallier Jean Название: Guide to the Classification Theorem for Compact Surfaces ISBN: 3642343635 ISBN-13(EAN): 9783642343636 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book offers a detailed proof of the classification theorem for compact surfaces. It presents the technical tools needed to deploy the method effectively as well as demonstrates their use in a clearly structured, worked example.
Автор: Rudolf Fritsch; J.lie Peschke; Gerda Fritsch Название: The Four-Color Theorem ISBN: 1461272548 ISBN-13(EAN): 9781461272540 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color?
Описание: THE main purpose of writing this monograph is to give a picture of the progress made in recent years in understanding three of the deepest results of Functional Analysis-namely, the open-mapping and closed- graph theorems, and the so-called Krein-~mulian theorem.
Автор: Gary Cornell; Joseph H. Silverman; Glenn Stevens Название: Modular Forms and Fermat`s Last Theorem ISBN: 0387989986 ISBN-13(EAN): 9780387989983 Издательство: Springer Рейтинг: Цена: 10480.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Focuses on Andrew Wiles` proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves and the works of Frey, Serre, Ribet showing that Wiles` Theorem would complete the proof of Fermat`s Last Theorem. This book reflects on the history of the problem. It describes the connections of Wiles` work with other parts of mathematics.
Автор: Patrascu Название: The Universal Coefficient Theorem and Quantum Field Theory ISBN: 3319461427 ISBN-13(EAN): 9783319461427 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.
Автор: Eichelsbacher Peter Название: Limit Theorems in Probability, Statistics and Number Theory ISBN: 364236067X ISBN-13(EAN): 9783642360671 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory.
The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich G tze, a noted expert in this field.
Автор: Jean Gallier; Dianna Xu Название: A Guide to the Classification Theorem for Compact Surfaces ISBN: 3642437109 ISBN-13(EAN): 9783642437106 Издательство: Springer Рейтинг: Цена: 5583.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book offers a detailed proof of the classification theorem for compact surfaces. It presents the technical tools needed to deploy the method effectively as well as demonstrates their use in a clearly structured, worked example.
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