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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk ...
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk ...
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
This book contains articles on the notion of a continuous lattice, which has its roots in Dana Scott's work on a mathematical theory of computation, presented at a conference on categorical and topological aspects of continuous lattices held in 1982.
In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed.
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This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples. Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin’s pioneering work gen...
This volume is based on the 2008 Clifford Lectures on Information Flow in Physics, Geometry and Logic and Computation, held March 12-15, 2008, at Tulane University in New Orleans, Louisiana. The varying perspectives of the researchers are evident in the topics represented in the volume, including mathematics, computer science, quantum physics and classical and quantum information. A number of the articles address fundamental questions in quantum information and related topics in quantum physics, using abstract categorical and domain-theoretic models for quantum physics to reason about such systems and to model spacetime. Readers can expect to gain added insight into the notion of information flow and how it can be understood in many settings. They also can learn about new approaches to modeling quantum mechanics that provide simpler and more accessible explanations of quantum phenomena, which don't require the arcane aspects of Hilbert spaces and the cumbersome notation of bras and kets.
Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonne quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, local...