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This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "e;corresponding"e; situations, which provide a systematic explanation of the remarkable "e;coincidences"e; found "e;by hand"e; in the hypergeometric case.

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

The 1950s religious boom was organized around the male-breadwinner lifestyle in the burgeoning postwar suburbs. But since the 1950s, family life has been fundamentally reconfigured in the United States. How do religion and family fit together today? This book examines how religious congregations in America have responded to changes in family structure, and how families participate in local religious life. Based on a study of congregations and community residents in upstate New York, sociologist Penny Edgell argues that while some religious groups may be nostalgic for the Ozzie and Harriet days, others are changing, knowing that fewer and fewer families fit this traditional pattern. In order to keep members with nontraditional family arrangements within the congregation, these innovators have sought to emphasize individual freedom and personal spirituality and actively to welcome single adults and those from nontraditional families. Edgell shows that mothers and fathers seek involvement in congregations for different reasons. Men tend to think of congregations as social support structures, and to get involved as a means of participating in the lives of their children. Women, by contrast, are more often motivated by the quest for religious experience, and can adapt more readily to pluralist ideas about family structure. This, Edgell concludes, may explain the attraction of men to more conservative congregations, and women to nontraditional religious groups.

The past decade has seen a profound change in the scientific understanding of reproduction. The traditional view of reproduction as a joint venture undertaken by two individuals, aimed at replicating their common genome, is being challenged by a growing body of evidence showing that the evolutionary interests of interacting males and females diverge. This book demonstrates that, despite a shared genome, conflicts between interacting males and females are ubiquitous, and that selection in the two sexes is continuously pulling this genome in opposite directions. These conflicts drive the evolution of a great variety of those traits that distinguish the sexes and also contribute to the diversification of lineages. Goran Arnqvist and Locke Rowe present an array of evidence for sexual conflict throughout nature, and they set these conflicts into the well-established theoretical framework of sexual selection. The recognition of conflict between the sexes is transforming our theories for the evolution of mating systems and the sexes themselves. Written by two top researchers in the field, Sexual Conflict is the first book to describe this transformation. It is a must read for all scholars and students interested in the evolutionary biology of reproduction.

The description for this book, Order-Preserving Maps and Integration Processes. (AM-31), Volume 31, will be forthcoming.

How do we know that Emily Dickinson wrote poems? How do we recognize a poem when we see one? In Dickinson's Misery, Virginia Jackson poses fundamental questions about reading habits we have come to take for granted. Because Dickinson's writing remained largely unpublished when she died in 1886, decisions about what it was that Dickinson wrote have been left to the editors, publishers, and critics who have brought Dickinson's work into public view. The familiar letters, notes on advertising fliers, verses on split-open envelopes, and collections of verses on personal stationery tied together with string have become the Dickinson poems celebrated since her death as exemplary lyrics. Jackson makes the larger argument that the century and a half spanning the circulation of Dickinson's work tells the story of a shift in the publication, consumption, and interpretation of lyric poetry. This shift took the form of what this book calls the "e;lyricization of poetry,"e; a set of print and pedagogical practices that collapsed the variety of poetic genres into lyric as a synonym for poetry. Featuring many new illustrations from Dickinson's manuscripts, this book makes a major contribution to the study of Dickinson and of nineteenth-century American poetry. It maps out the future for new work in historical poetics and lyric theory.

The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.

The description for this book, An Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4, will be forthcoming.

Measures and integrals

The description for this book, Introduction to Non-Linear Mechanics. (AM-11), Volume 11, will be forthcoming.

The description for this book, Meromorphic Functions and Analytic Curves. (AM-12), will be forthcoming.

The description for this book, Fourier Transforms. (AM-19), Volume 19, will be forthcoming.

The description for this book, Existence Theorems in Partial Differential Equations. (AM-23), Volume 23, will be forthcoming.

The description for this book, Curvature and Betti Numbers. (AM-32), Volume 32, will be forthcoming.

The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9, will be forthcoming.

As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "e;his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."e;

In May of 1919, women from around the world gathered in Zurich, Switzerland, and proclaimed, "e;We dedicate ourselves to peace!"e; Just months after the end of World War I, the Womens International League for Peace and Freedom--a group led by American progressive Jane Addams and comprising veteran campaigners for social reform--knew that a peaceful world was essential to their ongoing quest for social and economic justice. Alan Dawley tells the story of American progressives during the decade spanning World War I and its aftermath. He shows how they laid the foundation for progressive internationalism in their efforts to improve the world both at home and abroad. Unlike other accounts of the progressive movement--and of American politics in general--this book fuses social and international history. Dawley shows how interventions in Latin America and Europe affected domestic plans for social reform and civic engagement, and he depicts internal battles among progressives between unabashed imperialists like Theodore Roosevelt and their implacable opponents like Robert La Follette. He draws a contrast between Woodrow Wilson's use of force in exporting American ideals and Addams's more cosmopolitan pursuit of economic justice and world peace. In discussing the debate over the League of Nations within the context of turbulent domestic affairs, Dawley brings keen insight into that complicated moment in American history. In striking and original ways, Dawley brings together domestic and world affairs to argue that American progressivism cannot be understood apart from its international context. Focusing on world-historical events of empire, revolution, war, and peace, he shows how American reformers invented a new politics built around progressive internationalism. Changing the World retrieves the progressive tradition in American politics and makes it available to contemporary debates. The book speaks to anyone seeking to be both a good citizen within the nation and a good citizen of today's troubled world.

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III, will be forthcoming.

The description for this book, Contributions to the Theory of Partial Differential Equations. (AM-33), Volume 33, will be forthcoming.

A sophisticated introduction to how astronomers identify, observe, and understand black holesEmitting no radiation or any other kind of information, black holes mark the edge of the universe-both physically and in our scientific understanding. Yet astronomers have found clear evidence for the existence of black holes, employing the same tools and techniques used to explore other celestial objects. In this sophisticated introduction, leading astronomer Charles Bailyn goes behind the theory and physics of black holes to describe how astronomers are observing these enigmatic objects and developing a remarkably detailed picture of what they look like and how they interact with their surroundings.Accessible to undergraduates and others with some knowledge of introductory college-level physics, this book presents the techniques used to identify and measure the mass and spin of celestial black holes. These key measurements demonstrate the existence of two kinds of black holes, those with masses a few times that of a typical star, and those with masses comparable to whole galaxies-supermassive black holes. The book provides a detailed account of the nature, formation, and growth of both kinds of black holes. The book also describes the possibility of observing theoretically predicted phenomena such as gravitational waves, wormholes, and Hawking radiation.A cutting-edge introduction to a subject that was once on the border between physics and science fiction, this book shows how black holes are becoming routine objects of empirical scientific study.

The essential introduction to computational science-now fully updated and expandedComputational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. This textbook provides students with a versatile and accessible introduction to the subject. It assumes only a background in high school algebra, enables instructors to follow tailored pathways through the material, and is the only textbook of its kind designed specifically for an introductory course in the computational science and engineering curriculum. While the text itself is generic, an accompanying website offers tutorials and files in a variety of software packages.This fully updated and expanded edition features two new chapters on agent-based simulations and modeling with matrices, ten new project modules, and an additional module on diffusion. Besides increased treatment of high-performance computing and its applications, the book also includes additional quick review questions with answers, exercises, and individual and team projects.The only introductory textbook of its kind-now fully updated and expandedFeatures two new chapters on agent-based simulations and modeling with matricesIncreased coverage of high-performance computing and its applicationsIncludes additional modules, review questions, exercises, and projectsAn online instructor's manual with exercise answers, selected project solutions, and a test bank and solutions (available only to professors)An online illustration package is available to professors

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic.Sogge begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. He avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. The author also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, Sogge demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity.

The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is applied to the recent developments in the classical problem of isometric embeddings of Riemannian manifolds.

This is a study of the theory of models with truth values in a compact Hausdorff topological space.

The description for this book, Flows on Homogeneous Spaces. (AM-53), Volume 53, will be forthcoming.

In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The volume is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by Voisin. The book focuses on two central objects: the diagonal of a variety-and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups-as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by Voisin looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kahler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.

In politics, ideas matter. They provide the foundation for economic policymaking, which in turn shapes what is possible in domestic and international politics. Yet until now, little attention has been paid to how these ideas are produced and disseminated, and how this process varies between countries. The National Origins of Policy Ideas provides the first comparative analysis of how "e;knowledge regimes"e;-communities of policy research organizations like think tanks, political party foundations, ad hoc commissions, and state research offices, and the institutions that govern them-generate ideas and communicate them to policymakers.John Campbell and Ove Pedersen examine how knowledge regimes are organized, operate, and have changed over the last thirty years in the United States, France, Germany, and Denmark. They show how there are persistent national differences in how policy ideas are produced. Some countries do so in contentious, politically partisan ways, while others are cooperative and consensus oriented. They find that while knowledge regimes have adopted some common practices since the 1970s, tendencies toward convergence have been limited and outcomes have been heavily shaped by national contexts.Drawing on extensive interviews with top officials at leading policy research organizations, this book demonstrates why knowledge regimes are as important to capitalism as the state and the firm, and sheds new light on debates about the effects of globalization, the rise of neoliberalism, and the orientation of comparative political economy in political science and sociology.

What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century.Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era.Taming the Unknown follows algebra's remarkable growth through different epochs around the globe.

Health care costs make up nearly a fifth of U.S. gross domestic product, but health care is a peculiar thing to buy and sell. Both a scarce resource and a basic need, it involves physical and emotional vulnerability and at the same time it operates as big business. Patients have little choice but to trust those who provide them care, but even those providers confront a great deal of medical uncertainty about the services they offer. Selling Our Souls looks at the contradictions inherent in one particular health care market-hospital care. Based on extensive interviews and observations across the three hospitals of one California city, the book explores the tensions embedded in the market for hospital care, how different hospitals manage these tensions, the historical trajectories driving disparities in contemporary hospital practice, and the perils and possibilities of various models of care.As Adam Reich shows, the book's three featured hospitals could not be more different in background or contemporary practice. PubliCare was founded in the late nineteenth century as an almshouse in order to address the needs of the destitute. HolyCare was founded by an order of nuns in the mid-twentieth century, offering spiritual comfort to the paying patient. And GroupCare was founded in the late twentieth century to rationalize and economize care for middle-class patients and their employers. Reich explains how these legacies play out today in terms of the hospitals' different responses to similar market pressures, and the varieties of care that result.Selling Our Souls is an in-depth investigation into how hospital organizations and the people who work in them make sense of and respond to the modern health care market.