Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals.
 The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Ub-3.0 qb0(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.

The Classical and Quantum 6j-symbols. (MN-43)

Science & Math

Flath, Daniel E.

Saito, Masahico

Carter, J. Scott

Mathematics

Princeton University Press

Sociology

This best-selling textbook returns for an eighth edition with material on the most fundamental issues in sociology today. The authors continue their tradition of focusing on the big picture, with an emphasis on race, class, and gender in every chapter--building on the seventh edition's discussion of reproductive justice after the revocation of Roe v. Wade, social movements such as Black Lives Matter and #MeToo, a discussion of the Covid-19 pandemic and Donald Trump and Joe Biden.The text frames sociological debates around the major theoretical perspectives of sociology and focuses on capturing students' imaginations with cutting-edge research and real-world events. The hallmark of the book continues to be clear writing that helps students understand the intricacies of the discipline like no other textbook on the market.New to the eighth editionThinking outside the box (or inside it...)Selected chapters contain thematically linked boxed inserts aimed at bringing analytical and expositional focus to certain issues, as follows: <ul> <li> Sociological Insights: These boxes focus on how sociology can help us better understand a variety of issues and how examples from everyday life can help us to understand sociological principles, illustrating how topics are carefully linked to that material.</li> <li> Global Sociology: One of the most pronounced social changes of the past century has been globalization--a transition from the dominance of nation-states and national economies to global interactions. These boxes examine how social change moves around the world.</li> <li> Sociological Surprises: One common criticism of sociologists is that we sometimes expend a great deal of effort to prove things that are obvious. On the contrary, the reality is that what we find often goes against what people commonly believe and even against what sociological researchers expect to find. These boxes focus on such unexpected findings, analyzing why the social reality turns out to be something different from what is expected.</li> <li> Understanding Race, Class, and Gender: These boxes give added emphasis to the book's focus on race, class, and gender inequality. In every issue that sociologists study, race, class, and gender play a key role--and these boxes provide students with clear and concrete examples of how this occurs.</li> <li> Student Life: These boxes, which discuss student life from a sociological viewpoint, show how sociology is relevant to students in their everyday lives, covering race relations to dating to paying for college, and draws out their sociological implications.</li> <li> Putting Sociology to Work: These boxes focus on application: How can sociology be used to solve a social problem or to make an important decision?</li> </ul>

Politics & Social Sciences

Farley, John E.

Flota, Michael W.

Routledge

This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.

Diagrammatic Algebra (Mathematical Surveys and Monographs, 264)

Kamada, Seiichi

American Mathematical Society

The Death of Affirmative Action?: Racialized Framing and the Fight Against Racial Preference in College Admissions (Sociology of Diversity)

Lippard, Cameron D.

Policy Press

Affirmative action in US college admissions has inspired fierce debate as well as several US Supreme Court cases. In this significant study, leading US professors J. Scott Carter and Cameron D. Lippard provide an in-depth examination of the issue using sociological, policy and legal perspectives to frame both pro- and anti-affirmative action arguments, within past and present Supreme Court cases. With affirmative action policy under constant attack, this is a crucial book that not only explains the state of this policy but also further deconstructs the state of race and racism in American society today.

Bristol University Press

This is a book of pictures that illustrates standard examples in low dimensional topology. The text starts at the most basic level (the intersection of coordinate planes) and gives hands on constructions of beautiful examples in topology: the projective plane, Poincare's example of a homology sphere, lens spaces, knotted surfaces, 2-sphere eversions, and higher dimensional manifolds. The text carefully explains the importance of the examples and the techniques without being bogged down in a morass of technicalities. The book seeks to be an entertaining introduction to topology for the lay-person, and can be used as a tool book for the expert. The book opens with the classification theorem of surfaces and then discusses the building blocks of surfaces mapped into space. These are branch points, double points, and triple points. The second chapter gives various constructions of the projective plane as it intersects itself in ordinary 3-space. The third chapter includes further examples and methods for constructing surfaces in 3-space. In chapter 4, other 3-dimensional spaces that are constructed by gluing standard pieces of ordinary 3-space together are discussed. In chapter 5, knots and surfaces bounded by these 3-spaces are discussed. Chapter 6 contains come current research on embedded surfaces in 4-dimensions. Chapter 7 gives a movie move decomposition of the famous 2-sphere eversion. Chapter 8 contains explorations into higher dimensions.

How Surfaces Intersect in Space: An Introduction to Topology (Series on Knots and Everything)

World Scientific Pub Co Inc

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Möbius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced. In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space. Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface. Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book! In the last chapter higher dimensional spaces are examined from an elementary point of view. This is a guide book to a wide variety of topics. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

HOW SURFACES INTERSECT IN SPACE: AN INTRODUCTION TO TOPOLOGY (2ND EDITION) (Knots and Everything)

World Scientific Publishing Company

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Möbius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced. In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space.Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface.Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view.This is a guide book to a wide variety of topics. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

How Surfaces Intersect In Space: An Introduction To Topology (2Nd Edition) (Knots and Everything)

WSPC

The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations.The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.

An Excursion in Diagrammatic Algebra: Turning a Sphere from Red to Blue (Series on Knots and Everything)

See the best price to sell, buy, or rent books by Carter, J. Scott. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Carter, J. Scott

See the best price to sell, buy, or rent books by Carter, J. Scott. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The Classical and Quantum 6j-symbols. (MN-43)

Sociology

Sociology

Diagrammatic Algebra (Mathematical Surveys and Monographs, 264)

The Death of Affirmative Action?: Racialized Framing and the Fight Against Racial Preference in College Admissions (Sociology of Diversity)

The Death of Affirmative Action?: Racialized Framing and the Fight Against Racial Preference in College Admissions (Sociology of Diversity)

How Surfaces Intersect in Space: An Introduction to Topology (Series on Knots and Everything)

HOW SURFACES INTERSECT IN SPACE: AN INTRODUCTION TO TOPOLOGY (2ND EDITION) (Knots and Everything)

How Surfaces Intersect In Space: An Introduction To Topology (2Nd Edition) (Knots and Everything)

An Excursion in Diagrammatic Algebra: Turning a Sphere from Red to Blue (Series on Knots and Everything)