Monoidal Categories and Topological Field Theory PDF Download

Author: Vladimir Turaev
Publisher: Birkhäuser
ISBN: 3319498347
Category : Mathematics
Languages : ru
Pages : 513

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Book Description
This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.

Author: Rachel Levy
Publisher: SIAM
ISBN: 161197528X
Category : Mathematics
Languages : en
Pages : 154

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Book Description
Jobs using mathematics, statistics, and operations research are projected to grow by almost 30% over the next decade. BIG Jobs Guide helps job seekers at every stage of their careers in these fields explore opportunities in business, industry, and government (BIG). Written in a conversational and practical tone, BIG Jobs Guide offers insight on topics such as: - What skills can I offer employers? - How do I write a high-impact r?esume? - Where can I find a rewarding internship? - What kinds of jobs are out there for me? The Guide also offers insights to advisors and mentors on topics such as how departments can help students get BIG jobs and how faculty members and internship mentors can build institutional relationships. Whether you're an undergraduate or graduate student or a job seeker in mathematics, statistics, or operations research, this hands-on book will help you reach your goal?landing an internship, getting your first job or transitioning to a new one.

Author: Dana Vrajitoru
Publisher: Springer
ISBN: 3319098888
Category : Computers
Languages : en
Pages : 475

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Book Description
This book introduces the essential concepts of algorithm analysis required by core undergraduate and graduate computer science courses, in addition to providing a review of the fundamental mathematical notions necessary to understand these concepts. Features: includes numerous fully-worked examples and step-by-step proofs, assuming no strong mathematical background; describes the foundation of the analysis of algorithms theory in terms of the big-Oh, Omega, and Theta notations; examines recurrence relations; discusses the concepts of basic operation, traditional loop counting, and best case and worst case complexities; reviews various algorithms of a probabilistic nature, and uses elements of probability theory to compute the average complexity of algorithms such as Quicksort; introduces a variety of classical finite graph algorithms, together with an analysis of their complexity; provides an appendix on probability theory, reviewing the major definitions and theorems used in the book.

Author: Hidetoshi Nishimori
Publisher: Oxford University Press
ISBN: 0199577226
Category : Science
Languages : en
Pages : 373

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Book Description
As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.

Author: Das
Publisher: Scarecrow Press
ISBN: 0585479941
Category : Political Science
Languages : en
Pages : 262

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Book Description
What is the best management style for the police? Police Mission discusses the values and norms inherent in the American police mission, and examines how police respond to challenges that arise while attempting to uphold this mission. It reveals that the way officers are being trained in ethics and human relations are not effective as they could be, and argues that policing has to move towards a greater emphasis on human values, moral sensitivity, and discerning judgment. A large number of themes ranging from personnel management, occupational culture, and innovative experiments in US policing techniques are examined. Several organizational theories as well as examples of international policing efforts from England to Japan are also analyzed. An important contribution to police literature, this book will be a valuable aid to students of criminology as well as practitioners and researchers of police science.

Author: Carl R. Weinberg
Publisher: Cornell University Press
ISBN: 1501759310
Category : Religion
Languages : en
Pages : 444

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Book Description
In Red Dynamite, Carl R. Weinberg argues that creationism's tenacious hold on American public life depended on culture-war politics inextricably embedded in religion. Many Christian conservatives were convinced that evolutionary thought promoted immoral and even bestial social, sexual, and political behavior. The "fruits" of subscribing to Darwinism were, in their minds, a dangerous rearrangement of God-given standards and the unsettling of traditional hierarchies of power. Despite claiming to focus exclusively on science and religion, creationists were practicing politics. Their anticommunist campaign, often infused with conspiracy theory, gained power from the fact that the Marxist founders, the early Bolshevik leaders, and their American allies were staunch evolutionists. Using the Scopes "Monkey" Trial as a starting point, Red Dynamite traces the politically explosive union of Darwinism and communism over the next century. Across those years, social evolution was the primary target of creationists, and their "ideas have consequences" strategy instilled fear that shaped the contours of America's culture wars. By taking the anticommunist arguments of creationists seriously, Weinberg reveals a neglected dimension of antievolutionism and illuminates a source of the creationist movement's continuing strength. Thanks to generous funding from Indiana University and its participation in TOME (Toward an Open Monograph Ecosystem), the ebook editions of this book are available as Open Access volumes from Cornell Open (cornellpress.cornell.edu/cornell-open) and other repositories.

Author: Julian Hook
Publisher: Oxford University Press
ISBN: 0190246014
Category :
Languages : en
Pages : 681

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Book Description
Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric models--the first examples of the musical spaces of the book's title--depicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.

Author: Christian Kassel
Publisher: Springer Science & Business Media
ISBN: 0387685480
Category : Mathematics
Languages : en
Pages : 349

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Book Description
In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.

Author: Rebekah Sheldon
Publisher: U of Minnesota Press
ISBN: 1452953082
Category : Literary Criticism
Languages : en
Pages : 268

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Book Description
Generation Anthropocene. Storms of My Grandchildren. Our Children’s Trust. Why do these and other attempts to imagine the planet’s uncertain future return us—again and again—to the image of the child? In The Child to Come, Rebekah Sheldon demonstrates the pervasive conjunction of the imperiled child and the threatened Earth and blisteringly critiques the logic of catastrophe that serves as its motive and its method. Sheldon explores representations of this perilous future and the new figurations of the child that have arisen in response to it. Analyzing catastrophe discourse from the 1960s to the present—books by Joanna Russ, Margaret Atwood, and Cormac McCarthy; films and television series including Southland Tales, Battlestar Galactica, and Children of Men; and popular environmentalism—Sheldon finds the child standing in the place of the human species, coordinating its safe passage into the future through the promise of one more generation. Yet, she contends, the child figure emerges bound to the very forces of nonhuman vitality he was forged to contain. Bringing together queer theory, ecocriticism, and science studies, The Child to Come draws on and extends arguments in childhood studies about the interweaving of the child with the life sciences. Sheldon reveals that neither life nor the child are what they used to be. Under pressure from ecological change, artificial reproductive technology, genetic engineering, and the neoliberalization of the economy, the queerly human child signals something new: the biopolitics of reproduction. By promising the pliability of the body’s vitality, the pregnant woman and the sacred child have become the paradigmatic figures for twenty-first century biopolitics.

Author: Carl C. Cowen Jr.
Publisher: Routledge
ISBN: 1351459139
Category : Mathematics
Languages : en
Pages : 404

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Book Description
The study of composition operators lies at the interface of analytic function theory and operator theory. Composition Operators on Spaces of Analytic Functions synthesizes the achievements of the past 25 years and brings into focus the broad outlines of the developing theory. It provides a comprehensive introduction to the linear operators of composition with a fixed function acting on a space of analytic functions. This new book both highlights the unifying ideas behind the major theorems and contrasts the differences between results for related spaces. Nine chapters introduce the main analytic techniques needed, Carleson measure and other integral estimates, linear fractional models, and kernel function techniques, and demonstrate their application to problems of boundedness, compactness, spectra, normality, and so on, of composition operators. Intended as a graduate-level textbook, the prerequisites are minimal. Numerous exercises illustrate and extend the theory. For students and non-students alike, the exercises are an integral part of the book. By including the theory for both one and several variables, historical notes, and a comprehensive bibliography, the book leaves the reader well grounded for future research on composition operators and related areas in operator or function theory.