J. Scott Carter - Böcker

Insights into the racialized fear of change in US societyThe standoff at Cliven Bundy’s ranch, the rise of white identity activists on college campuses, and the viral growth of white nationalist videos on YouTube vividly illustrate the resurgence of white supremacy and overt racism in the United States. White resistance to racial equality can be subtle as well—like art museums that enforce their boundaries as elite white spaces, “right on crime” policies that impose new modes of surveillance and punishment for people of color, and environmental groups whose work reinforces settler colonial norms. In this incisive volume, twenty-four leading sociologists assess contemporary shifts in white attitudes about racial justice in the US. Using case studies, they investigate the entrenchment of white privilege in institutions, new twists in anti-equality ideologies, and “whitelash” in the actions of social movements. Their examinations of new manifestations of racist aggression help make sense of the larger forces that underpin enduring racial inequalities and how they reinvent themselves for each new generation.

Insights into the racialized fear of change in US societyThe standoff at Cliven Bundy’s ranch, the rise of white identity activists on college campuses, and the viral growth of white nationalist videos on YouTube vividly illustrate the resurgence of white supremacy and overt racism in the United States. White resistance to racial equality can be subtle as well—like art museums that enforce their boundaries as elite white spaces, “right on crime” policies that impose new modes of surveillance and punishment for people of color, and environmental groups whose work reinforces settler colonial norms. In this incisive volume, twenty-four leading sociologists assess contemporary shifts in white attitudes about racial justice in the US. Using case studies, they investigate the entrenchment of white privilege in institutions, new twists in anti-equality ideologies, and “whitelash” in the actions of social movements. Their examinations of new manifestations of racist aggression help make sense of the larger forces that underpin enduring racial inequalities and how they reinvent themselves for each new generation.

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.

Original Sin? explores the ways that a multiracial church struggles with race, racism, and social activism during a turbulent time in U.S. history. In the shadow of the murder of George Floyd, the authors show how members and leaders of Without Walls Church, a multiracial church claiming over thirty-six thousand members, perpetuate a racial ideology based in color-blind theological teachings that minimizes teachings on racism in the church and social activism outside the church. Barnes and Carter also shed light on church practices and policies that reproduce racial inequality and shaped the church’s early response to the murder of George Floyd. Original Sin? shows us that despite being diverse places of worship and despite shifting demographics, churches like this one face challenges that lead to the reproduction of the racial status quo.

Original Sin? explores the ways that a multiracial church struggles with race, racism, and social activism during a turbulent time in U.S. history. In the shadow of the murder of George Floyd, the authors show how members and leaders of Without Walls Church, a multiracial church claiming over thirty-six thousand members, perpetuate a racial ideology based in color-blind theological teachings that minimizes teachings on racism in the church and social activism outside the church. Barnes and Carter also shed light on church practices and policies that reproduce racial inequality and shaped the church’s early response to the murder of George Floyd. Original Sin? shows us that despite being diverse places of worship and despite shifting demographics, churches like this one face challenges that lead to the reproduction of the racial status quo.

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: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.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.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.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.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.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?

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: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.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.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.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.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.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?

Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law $x(yz)=(xy)z$. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications.This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29-August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables.An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.

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.

This volume contains the proceedings of the AMS Western Sectional Meeting on Algebraic Structures in Knot Theory held on May 6-7, 2023, at California State University, Fresno, California. Modern knot theory includes the study of a diversity of different knotted objects-classical knots, surface-links, knotoids, spatial graphs, and more. Knot invariants are tools for probing the structure of these generalized knots. Many of the most effective knot invariants take the form of algebraic structures. In this volume we collect some recent work on algebraic structures in knot theory, including topics such as braid groups, skein algebras, Gram determinants, and categorifications such as Khovanov homology.

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.

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.

This is a book of marvelous 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 the most 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.Chapter 1 opens with the classification of orientable surfaces, and the meaning of space. Chapter 2 discusses examples of non-orientable surfaces including models of the projective plane and the Klein bottle. Chapter 3 discusses how curves fit on surfaces and gives a general discussion of knotted strings in space. In Chapter 4, some examples of other 3-dimensional spaces are described. These include the 3-dimensional sphere, lens spaces, and the quaternionic projective space. In Chapter 5, the author reviews the movie techniques of studying surfaces in 4-dimensions. He shows how to move among the standard examples of Klein bottles, and he gives a “movie move” decomposition of turning the 2-sphere inside out. In the final Chapter, higher dimensional spaces are examined from the same elementary point of view.The book is a guide book to a wide variety of topics. It will be of value to undergraduates who want to learn geometric topology and to graduate students who want examples with which they can make computations and who need an elementary description of topological spaces. Finally, the book should be interesting to other scientists and mathematicians who want to learn some examples of topological spaces.

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.

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.

This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.

This volume gathers the contributions from the international conference “Intelligence of Low Dimensional Topology 2006,” which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.