Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an "inequality" version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erdős-Ginzberg-Ziv theorem, and the number of arithmetic progressions under arbitrary colorings. Many new results and proofs have been added, most of which were not known when the first edition was published. Furthermore, the book's tables, exercises, lists of open research problems, and bibliography have all been significantly updated. This innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subject. This breakthrough book will engage students, teachers, and researchers alike.
A Washington Post most anticipated fall book | One of Literary Hub's most anticipated books of 2024 A lyrical meditation on how Black Americans have envisioned utopia—and sought to transform their lives. How do the disillusioned, the forgotten, and the persecuted not merely hold on to life but expand its possibilities and preserve its beauty? What, in other words, does utopia look like in black? These questions animate Aaron Robertson’s exploration of Black Americans' efforts to remake the conditions of their lives. Writing in the tradition of Saidiya Hartman and Ta-Nehisi Coates, Robertson makes his way from his ancestral hometown of Promise Land, Tennessee, to Detroit—the city where he was born, and where one of the country’s most remarkable Black utopian experiments got its start. Founded by the brilliant preacher Albert Cleage Jr., the Shrine of the Black Madonna combined Afrocentric Christian practice with radical social projects to transform the self-conception of its members. Central to this endeavor was the Shrine’s chancel mural of a Black Virgin and child, the icon of a nationwide liberation movement that would come to be known as Black Christian Nationalism. The Shrine’s members opened bookstores and co-ops, created a self-defense force, and raised their children communally, eventually working to establish the country’s largest Black-owned farm, where attempts to create an earthly paradise for Black people continues today. Alongside the Shrine’s story, Robertson reflects on a diverse array of Black utopian visions, from the Reconstruction era through the countercultural fervor of the 1960s and 1970s and into the present day. By doing so, Robertson showcases the enduring quest of collectives and individuals for a world beyond the constraints of systemic racism. The Black Utopians offers a nuanced portrait of the struggle for spaces—both ideological and physical—where Black dignity, protection, and nourishment are paramount. This book is the story of a movement and of a world still in the making—one that points the way toward radical alternatives for the future.
Central America was the only part of the far-reaching Spanish Empire in continental America not to experience destructive independence wars in the period between 1810 and 1824. The essays in this volume draw on new historical research to explain why, and to delve into what did happen during the independence period in Central America and Chiapas. The contributors, distinguished scholars from Central America, North America, and Europe, consider themes of power, rebellion, sovereignty, and resistance throughout the Kingdom of Guatemala beginning in the late eighteenth century and ending with independence from Spain and the debate surrounding the decision to join the Mexican Empire. Their work reveals that a “conflict-free” separation from Spain was more complex than is usually understood, and shows how such a separation was crucial to late-nineteenth-century developments. These essays tell us how different groups seized on the political instabilities of Spain to maximize their interests; how Latin American elites prepared elaborate rituals to legitimize power dynamics; why the Spanish military governor Bustamante’s role in Central America should be reconsidered; how Indian and popular uprisings had more to do with tax burdens than with independence rhetoric; how the scholastic thought of Thomas Aquinas played a role in political thinking during the independence period; and why Mexico’s Plan de Iguala, the independence program promoted by Agustín de Iturbide, finally broke Central American elites’ ties to Spain. Focusing on regional and small-town dynamics as well as urban elites, these essays combine to offer an unusually broad and varied perspective on and a new understanding of Central America in the period of independence.
Short-listed for the Art and Christian Enquiry/Mercers' International Book Award 2009: 'a book which makes an outstanding contribution to the dialogue between religious faith and the visual arts'. What does modern Jewish art look like? Where many scholars, critics, and curators have gone searching for the essence of Jewish art in Biblical illustrations and other traditional subjects, Rosen sets out to discover Jewishness in unlikely places. How, he asks, have modern Jewish painters explored their Jewish identity using an artistic past which is- by and large - non-Jewish? In this new book we encounter some of the great works of Western art history through Jewish eyes. We see Matthias Grunewald's Isenheim Altarpiece re-imagined by Marc Chagall (1887-1985), traces of Paolo Uccello and Piero della Francesca in Philip Guston (1913-1980), and images by Diego Velazquez and Paul Cezanne studiously reworked by R.B. Kitaj (1932-2007). This highly comparative study draws on theological, philosophical and literary sources from Franz Rosenzweig to Franz Kafka and Philip Roth. Rosen deepens our understanding not only of Chagall, Guston, and Kitaj but also of how art might serve as a key resource for rethinking such fundamental Jewish concepts as family, tradition, and homeland.
At its root, modernism is that fundamental. It is a question of having something to represent that is of the moment. In the most radical interpretation, modernism always comes too late. The modern is that which is always new, which is to say, always changing and already old by the time it has appeared. Modernism is always a retrospective act, one of documenting or trying to catch what has already appeared - an attempt to fix life as it is being lived. Modernity is just the very fact that we as human beings are continually remaking the world around us through our actions, and are doing so consciously. Modernism is a monument to or memory of that act, which in its own making tries to remake the world it is pretending to represent.
What if the Renaissance had the right idea about character? Most readers today think that characters are individuals. Poets of the Renaissance understood characters as types. They thought the job of a character was to collect every example of a kind, in the same way that an entry in a dictionary collects definitions of a word. Character as Form celebrates the old meaning of character. The advantage of the old meaning is that it allows for generalization. Characters funnel whole societies of beings into shapes that are compact, elegant, and portable. This book tests the old meaning of character against modern examples from poems, novels, comics, and performances in theater and film by Shakespeare, Molière, Austen, the Marx Brothers, Raul Ruiz, Denton Welch, and Lynda Barry. The heart of the book is the character of the misanthrope, who, in Shakespeare's phrase, “banishes the world.”
The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.
This volume deals with medieval comparative Semitic philology (Hebrew/Aramaic/Arabic) as practised by Hebrew philologists in the Arabic speaking lands, from Iraq to Spain, discussing its development through the generations, its technics and its theoretical basis. This research is based upon an analysis of over ten thousand occurrences of comparisons in linguistic works, biblical commentaries and the like, made by fourteen Hebrew scholars from the 10th-12th centuries CE, among them Sa adiah Gaon, Judah b. Quraysh, David b. Abraham Alfasi, Jonah b. Janah and Isaac b. Bar n. Several aspects of this comparisons are presented and studied here for the first time.
The Solitary Sphere in the Age of Virgil uses an enriched tripartite model of Roman culture-touching not only the public and the private, but also the solitary-in order to present a radical re-interpretation of Latin literature and of the historical causes of this third sphere's relative invisibility in scholarship. By connecting Cosmos and Imperium to the Individual, the solitary sphere was not so much a way of avoiding politics, as a political education in itself. As re-imagined by literature in this age literature, this sphere was an essential space for the formation of the new Roman citizen of the Augustan revolution, and was behind many of the notable features of the literary revolution of Virgil's age: the expansion of the possibilities of the book of poetry, the birth of the literary cursus, new coordinations of cosmology and politics within strictly organized schemes, the attraction of first-person genres, and the subjective style. Through close readings of Cicero's late works and the oeuvres of Virgil, Horace, and Propertius and the works of other authors in the age of Virgil, The Solitary Sphere thus presents a revelatory reassessment of the classicism of classical Roman literature, and contributes to the study of pre-modern culture more generally, especially for traditions that have taken antiquity as too fixed a point in their own literary, religious, and cultural histories.
Over the course of the Middle Ages, the economies of Europe, Asia, and northern Africa became more closely integrated, fostering the international and intercontinental journeys of merchants, pilgrims, diplomats, missionaries, and adventurers. During a time in history when travel was often difficult, expensive, and fraught with danger, these wayfarers composed accounts of their experiences in unprecedented numbers and transformed traditional conceptions of human mobility. Exploring this phenomenon, The Medieval Invention of Travel draws on an impressive array of sources to develop original readings of canonical figures such as Marco Polo, John Mandeville, and Petrarch, as well as a host of lesser-known travel writers. As Shayne Aaron Legassie demonstrates, the Middle Ages inherited a Greco-Roman model of heroic travel, which viewed the ideal journey as a triumph over temptation and bodily travail. Medieval travel writers revolutionized this ancient paradigm by incorporating practices of reading and writing into the ascetic regime of the heroic voyager, fashioning a bold new conception of travel that would endure into modern times. Engaging methods and insights from a range of disciplines, The Medieval Invention of Travel offers a comprehensive account of how medieval travel writers and their audiences reshaped the intellectual and material culture of Europe for centuries to come.
Baal and the Politics of Poetry provides a thoroughly new interpretation of the Ugaritic Baal Cycle that simultaneously inaugurates an innovative approach to studying ancient Near Eastern literature within the political context of its production. The book argues that the poem, written in the last decades of the Bronze Age, takes aim at the reigning political-theological norms of its day and uses the depiction of a divine world to educate its audience about the nature of human politics. By attuning ourselves to the specific historical context of this one poem, we can develop more nuanced appreciation of how poetry, politics, and religion have interacted—in antiquity, and beyond.
Aaron Gurevich has long been considered one of the world's leading medievalists and a pioneer in the field of historical anthropology. This book brings together eleven of his most important essays—many difficult to find and some never before available in English. Gurevich's writing, while informed by the history of mentalities as practiced by the French school of Le Goff and Duby, reflects a broader view of European culture outside France. He rejects reductionist concepts and operates with a total view of culture, using a wide range of sources—legal as well as ecclesiastical, popular as well as learned, oral and visual as well as literary. This collection amply demonstrates this breadth of Gurevich's work and highlights his ability to synthesize historical, anthropological, and semiotic approaches to culture. Especially valuable are pieces such as Gurevich's essay Wealth and Gift-Bestowal Among the Ancient Scandinavians, about the importance of gift exchange in the medieval world. One of the first studies for this practice, this classic essay has for years been unavailable. Other pieces range from the deities and heroes of Germanic poetry to the image of the Beyond in the Middle Ages.
The Large Hadron Collider (LHC), located at CERN, Geneva, Switzerland, is the world's largest and highest energy and highest intensity particle accelerator. This book provides an overview on the techniques that will be crucial for finding new physics at the LHC, as well as perspectives on the importance and implications of the discoveries. Among the contributors to this book are leaders and visionaries in the field of particle physics beyond the Standard Model, including two Nobel Laureates (Steven Weinberg and Frank Wilczek), and presumably some future Nobel Laureates, plus top younger theorists and experimenters.
For the past 30 years, the so-called 'Troubles' thriller has been the dominant fictional mode for representing Northern Ireland, leading to the charge that the crudity of this popular genre appropriately reflects the social degradation of the North. Aaron Kelly challenges both these judgments, showing that the historical questions raised by setting a thriller in Northern Ireland disrupt the conventions of the crime novel and allow for a new understanding of both the genre and the country. Two essays on crime fiction by Walter Benjamin and Berthold Brecht appear here for the first time in English translation. By demonstrating the relevance of these theorists as well as other key European thinkers such as Antonio Gramsci, Louis Althusser, and Slavoj Zizek to his interdisciplinary study of Irish culture and the crime novel, Kelly refutes the idea that Northern Ireland is a stagnate anomaly that has been bypassed by European history and remained impervious to cultural transformation. On the contrary, Kelly's examination of authors such as Jack Higgins, Tom Clancy, Gerald Seymour, Colin Bateman, and Eoin McNamee shows that profound historical change and complexity have characterized both Northern Ireland and the thriller form.
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