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A New Spin On Mathematics
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Book Synopsis Spin Glasses: A Challenge for Mathematicians by : Michel Talagrand
Download or read book Spin Glasses: A Challenge for Mathematicians written by Michel Talagrand and published by Springer Science & Business Media. This book was released on 2003-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science). This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.
Download or read book Spin Geometry written by H. Blaine Lawson and published by Princeton University Press. This book was released on 2016-06-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Download or read book Spin Glasses written by Erwin Bolthausen and published by Springer. This book was released on 2007-01-11 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a concise introduction to the state-of-the-art of spin glass theory. The collection of review papers are written by leading experts in the field and cover the topic from a wide variety of angles. The book will be useful to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics.
Book Synopsis Putting A New Spin on Groups by : Bud A. McClure
Download or read book Putting A New Spin on Groups written by Bud A. McClure and published by Psychology Press. This book was released on 2005-01-15 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Putting a New Spin on Groups: The Science of Chaos, Second Edition continues to challenge orthodoxy and static ideas about small group dynamics. A primary goal is to offer an alternative model of group development that addresses three factors: *The model integrates old ideas from previous models of group development with new concepts from chaos theory and the work of Arthur Young. *The book emphasizes the importance of conflict in group development and recognizes that group growth--while progressive--is neither linear or unidimensional. *Particular attention is focused on how groups change, evolve, and mature. In addition, this book highlights certain group phenomena that have been given only cursory attention in many group textbooks, including women in authority, group metaphors, regressive groups, and the transpersonal potential of small groups. This book has been revised in response to feedback from reviewers and colleagues and includes new ideas, applications of chaos theory in social sciences, and thinking about group behavior. It is an intellectually challenging read with just the right amount of world application.
Book Synopsis A New Spin on Mathematics by : Linda Emery
Download or read book A New Spin on Mathematics written by Linda Emery and published by . This book was released on 2009 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mean Field Models for Spin Glasses by : Michel Talagrand
Download or read book Mean Field Models for Spin Glasses written by Michel Talagrand and published by . This book was released on 2011 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Conformal Groups in Geometry and Spin Structures by : Pierre Anglès
Download or read book Conformal Groups in Geometry and Spin Structures written by Pierre Anglès and published by Springer Science & Business Media. This book was released on 2007-10-16 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.
Book Synopsis Spin Glasses and Complexity by : Daniel L. Stein
Download or read book Spin Glasses and Complexity written by Daniel L. Stein and published by Princeton University Press. This book was released on 2013-01-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. Spin Glasses and Complexity offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into--and modify--this framework. It then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, Spin Glasses and Complexity also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a must-have book for students and practitioners in the natural and social sciences, with new material even for the experts.
Book Synopsis A New Spin on Mathematical Literacy by : S. Philemon Ntenza
Download or read book A New Spin on Mathematical Literacy written by S. Philemon Ntenza and published by . This book was released on 2009 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mean Field Models for Spin Glasses by : Michel Talagrand
Download or read book Mean Field Models for Spin Glasses written by Michel Talagrand and published by Springer Science & Business Media. This book was released on 2011-08-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition.
Book Synopsis Rotations, Quaternions, and Double Groups by : Simon L. Altmann
Download or read book Rotations, Quaternions, and Double Groups written by Simon L. Altmann and published by Courier Corporation. This book was released on 2013-04-09 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.
Book Synopsis The Theory of Spinors by : Élie Cartan
Download or read book The Theory of Spinors written by Élie Cartan and published by Courier Corporation. This book was released on 2012-04-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
Download or read book Turn to Learn written by Jacquelyn Howes and published by Scholastic. This book was released on 1998-04-01 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: 29 ready-to- reproduce patterns that put a new spin on math skill-building! Covers addition, subtraction, time, money, patterns, and more!
Book Synopsis Our Mathematical Universe by : Max Tegmark
Download or read book Our Mathematical Universe written by Max Tegmark and published by Vintage. This book was released on 2015-02-03 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Book Synopsis An Introduction to the Theory of Spin Glasses and Neural Networks by : Viktor Dotsenko
Download or read book An Introduction to the Theory of Spin Glasses and Neural Networks written by Viktor Dotsenko and published by World Scientific. This book was released on 1994 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to describe in simple terms the new area of statistical mechanics known as spin-glasses, encompassing systems in which quenched disorder is the dominant factor. The book begins with a non-mathematical explanation of the problem, and the modern understanding of the physics of the spin-glass state is formulated in general terms. Next, the 'magic' of the replica symmetry breaking scheme is demonstrated and the physics behind it discussed. Recent experiments on real spin-glass materials are briefly described to demonstrate how this somewhat abstract physics can be studied in the laboratory. The final chapters of the book are devoted to statistical models of neural networks.The material here is self-contained and should be accessible to students with a basic knowledge of theoretical physics and statistical mechanics. It has been used for a one-term graduate lecture course at the Landau Institute for Theoretical Physics.
Book Synopsis Clifford Algebras and their Applications in Mathematical Physics by : Rafal Ablamowicz
Download or read book Clifford Algebras and their Applications in Mathematical Physics written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
Book Synopsis The Sherrington-Kirkpatrick Model by : Dmitry Panchenko
Download or read book The Sherrington-Kirkpatrick Model written by Dmitry Panchenko and published by Springer Science & Business Media. This book was released on 2013-02-26 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The celebrated Parisi solution of the Sherrington-Kirkpatrick model for spin glasses is one of the most important achievements in the field of disordered systems. Over the last three decades, through the efforts of theoretical physicists and mathematicians, the essential aspects of the Parisi solution were clarified and proved mathematically. The core ideas of the theory that emerged are the subject of this book, including the recent solution of the Parisi ultrametricity conjecture and a conceptually simple proof of the Parisi formula for the free energy. The treatment is self-contained and should be accessible to graduate students with a background in probability theory, with no prior knowledge of spin glasses. The methods involved in the analysis of the Sherrington-Kirkpatrick model also serve as a good illustration of such classical topics in probability as the Gaussian interpolation and concentration of measure, Poisson processes, and representation results for exchangeable arrays.
