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This book is an introduction to basic topics in inequalities and their applications. These include the arithmetic mean-geometric mean inequality, Cauchy-Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. More than 400 problems are included in the book and their solutions are explained. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students in consolidating their knowledge of inequalities and their applications. The author has been involved in training Indian students for mathematical olympiads for more than 25 years.

This textbook reflects a hybrid approach to studying stratification. It addresses the knowledge accumulated by stratification scholars and challenges students to apply this information to their social world. Features include: · The text is divided into basic concepts (theoretical and methodological) and applications (e.g., to class, poverty, mobility, education, gender, race). · Each chapter includes a list of key concepts, questions for thought, suggested exercises, and multimedia resources (print, internet, and films). · A unique methodological chapter provides students the skills they will need to be able to read contemporary sociological literature. · The selection of chapters and chapter content provide students a sense of the topics, questions, and research that dominate contemporary research on social stratification and inequality. · Research-oriented approach reflecting the field of stratification studies. Additional ancillary material may be found at www.stratificationandinequality.com

In this deft analysis, Amartya Sen argues that the dictum "all men are created equal" serves largely to deflect attention from the fact that we differ in age, gender, talents, physical abilities as well as in material advantages and social background. He argues for concentrating on higher and more basic values: individual capabilities and freedom to achieve objectives.

Contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.

This book undertakes the first systematic, multi-country investigation into how regimes of place equality, consisting of multilevel policies, institutions and governance at multiple scales, influence spatial inequality in metropolitan regions. Extended, diversified metropolitan regions have become the dominant form of human settlement, and disparities among metropolitan places figure increasingly in wider trends toward growing inequality. Regimes of place equality are increasingly critical components of welfare states and territorial administration. They can aggravate disparities in services and taxes, or mitigate and compensate for local differences. The volume examines these regimes in a global sample of eleven democracies, including developed and developing countries on five continents. The analyses reveal new dimensions of efforts to grapple with growing inequality around the world, and a variety of institutional blueprints to address one of the most daunting challenges of twenty-first century governance. 

Since the great recession hit in 2008, the 1% has only grown richer while the rest find life increasingly tough. The gap between the haves and the have-nots has turned into a chasm. While the rich have found new ways of protecting their wealth, everyone else has suffered the penalties of austerity.But inequality is more than just economics. Being born outside the 1% has a dramatic impact on a person's potential: reducing life expectancy, limiting education and work prospects, and even affecting mental health.What is to be done? In Inequality and the 1% leading social thinker Danny Dorling lays bare the extent and true cost of the division in our society and asks what have the superrich ever done for us. He shows that inquality is the greatest threat we face and why we must urgently redress the balance.

In Inequality in US Social Policy: An Historic Analysis, Bryan Warde illuminates the pervasive and powerful role that social inequality based on race and ethnicity, gender, immigration status, sexual orientation, class, and disability plays and has historically played in informing social policy. Using critical race theory and other structural oppression theoretical frameworks, this book examines social inequalities as they relate to social welfare, education, housing, employment, health care, and child welfare, immigration, and criminal justice. This book will help social work students better understand the origins of inequalities that their clients face.

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This book argues that political and economic inequalities following group lines generate grievances that in turn can motivate civil war. Lars-Erik Cederman, Kristian Skrede Gleditsch, and Halvard Buhaug offer a theoretical approach that highlights ethnonationalism and how the relationship between group identities and inequalities are fundamental for successful mobilization to resort to violence. Although previous research highlighted grievances as a key motivation for political violence, contemporary research on civil war has largely dismissed grievances as irrelevant, emphasizing instead the role of opportunities. This book shows that the alleged non-results for grievances in previous research stemmed primarily from atheoretical measures, typically based on individual data. The authors develop new indicators of political and economic exclusion at the group level, and show that these exert strong effects on the risk of civil war. They provide new analyses of the effects of transnational ethnic links and the duration of civil wars, and extended case discussions illustrating causal mechanisms.

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In Inequality in US Social Policy: An Historic Analysis, Bryan Warde illuminates the pervasive and powerful role that social inequality based on race and ethnicity, gender, immigration status, sexual orientation, class, and disability plays and has historically played in informing social policy. Using critical race theory and other structural oppression theoretical frameworks, this book examines social inequalities as they relate to social welfare, education, housing, employment, health care, and child welfare, immigration, and criminal justice. This book will help social work students better understand the origins of inequalities that their clients face.

1. We begin by giving a simple example of a partial differential inequality that occurs in an elementary physics problem. We consider a fluid with pressure u(x, t) at the point x at the instant t that 3 occupies a region Q oflR bounded by a membrane r of negligible thickness that, however, is semi-permeable, i. e., a membrane that permits the fluid to enter Q freely but that prevents all outflow of fluid. One can prove then (cf. the details in Chapter 1, Section 2.2.1) that au (aZu azu aZu) (1) in Q, t>o, -a - du = g du = -a z + -a z + -a z t Xl X X3 z l g a given function, with boundary conditions in the form of inequalities u(X,t»o => au(x,t)/an=O, XEr, (2) u(x,t)=o => au(x,t)/an?:O, XEr, to which is added the initial condition (3) u(x,O)=uo(x). We note that conditions (2) are non linear; they imply that, at each fixed instant t, there exist on r two regions r~ and n where u(x, t) =0 and au (x, t)/an = 0, respectively. These regions are not prescribed; thus we deal with a "free boundary" problem.

In this deft analysis, Amartya Sen argues that the dictum ”all people are created equal” serves largely to deflect attention from the fact that we differ in age, gender, talents, and physical abilities as well as in material advantages and social background. He argues for concentrating on higher and more basic values: individual capabilities and freedom to achieve objectives. By concentrating on the equity and efficiency of social arrangements in promoting freedoms and capabilities of individuals, Sen adds an important new angle to arguments about such vital issues as gender inequalities, welfare policies, affirmative action, and public provision of health care and education.

This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

Nestled in neighborhoods of varying degrees of affluence, suburban public schools are typically better resourced than their inner-city peers and known for their extracurricular offerings and college preparatory programs. Despite the glowing opportunities that many families associate with suburban schooling, accessing a district's resources is not always straightforward, particularly for black and poorer families. Moving beyond class- and race-based explanations, Inequality in the Promised Land focuses on the everyday interactions between parents, students, teachers, and school administrators in order to understand why resources seldom trickle down to a district's racial and economic minorities. Rolling Acres Public Schools (RAPS) is one of the many well-appointed suburban school districts across the United States that has become increasingly racially and economically diverse over the last forty years. Expanding on Charles Tilly's model of relational analysis and drawing on 100 in-depth interviews as well participant observation and archival research, R. L'Heureux Lewis-McCoy examines the pathways of resources in RAPS. He discovers that―due to structural factors, social and class positions, and past experiences―resources are not valued equally among families and, even when deemed valuable, financial factors and issues of opportunity hoarding often prevent certain RAPS families from accessing that resource. In addition to its fresh and incisive insights into educational inequality, this groundbreaking book also presents valuable policy-orientated solutions for administrators, teachers, activists, and politicians.

This book provides selections from the seminal works of Karl Marx, Max Weber, W.E.B. Du Bois, and Charlotte Perkins Gilman that reveal some of the reasons why class, race, and gender inequalities have proven very adaptive and can flourish even today in the 21st century.

Oriented toward the introductory student, The Inequality Reader is the essential textbook for today's undergraduate courses. The editors, David B. Grusky and Szonja Szelenyi, have assembled the most important classic and contemporary readings about how poverty and inequality are generated and how they might be reduced. With thirty new readings, the second edition provides new materials on anti-poverty policies as well as new qualitative readings that make the scholarship more alive, more accessible, and more relevant. Now more than ever, The Inequality Reader is the one-stop compendium of all the must-read pieces, simply the best available introduction to the stratifi cation canon.

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