The theory of sets of multiples, a subject that lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of "Sequences" by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many of them still unsolved or arising from current work. In this book, the author gives a coherent, self-contained account of the existing theory, bringing the reader to the frontiers of research. One of the fascinations of the theory is the variety of methods applicable to it, which include Fourier analysis, group theory, high and ultra-low moments, probability and elementary inequalities, and several branches of number theory.

In the generation that followed Martin Luther's protest the evangelical movement in Europe attracted very different levels of support in different parts of the continent. Whereas in eastern and central Europe the new movement brought a swift transformation of the religious and political landscape, progress elsewhere was more halting: in the Mediterranean lands and western Europe initial enthusiasm for reform failed to bring about the wholesale renovation of society for which evangelicals had hoped. These fascinating contrasts are the main focus of this volume of specially commissioned essays, each of which charts the progress of reform in one country or region of Europe. Written in each case by a leading specialist in the field, they provide a survey based on primary research and a thorough grasp of the vernacular literature. For both scholars and students they will be an invaluable guide to recent debates and literature on the success or failure of the first generation of reform.

Table of contents

A history of political debate and theory in England (later Britain) between the English Reformation and French Revolution.

It is a commonly held belief that medieval Catholics were focussed on the 'bells and whistles' of religious practices, the smoke, images, sights and sounds that dazzled pre-modern churchgoers. Protestantism, in contrast, has been cast as Catholicism's austere, intellective and less sensual rival sibling. With iis white-washed walls, lack of incense (and often music) Protestantism worship emphasised preaching and scripture, making the new religion a drab and disengaged sensual experience. In order to challenge such entrenched assumptions, this book examines Tudor views on the senses to create a new lens through which to explore the English Reformation. Divided into two sections, the book begins with an examination of pre-Reformation beliefs and practices, establishing intellectual views on the senses in fifteenth-century England, and situating them within their contemporary philosophical and cultural tensions. Having established the parameters for the role of sense before the Reformation, the second half of the book mirrors these concerns in the post-1520 world, looking at how, and to what degree, the relationship between religious practices and sensation changed as a result of the Reformation. By taking this long-term, binary approach, the study is able to tackle fundamental questions regarding the role of the senses in late-medieval and early modern English Christianity. By looking at what English men and women thought about sight, hearing, smell, taste and touch, the stereotype that Protestantism was not sensual, and that Catholicism was overly sensualised is wholly undermined. Through this examination of how worship was transformed in its textual and liturgical forms, the book illustrates how English religion sought to reflect changing ideas surrounding the senses and their place in religious life. Worship had to be 'sensible', and following how reformers and their opponents built liturgy around experience of the sacred through the physical allows us to tease out the tensions and pressures which shaped religious reform.

Building on current scholarly interest in the religious dimensions of the play, this study shows how Shakespeare uses Hamlet to comment on the Calvinistic Protestantism predominant around 1600. By considering the play's inner workings against the religious ideas of its time, John Curran explores how Shakespeare portrays in this work a completely deterministic universe in the Calvinist mode, and, Curran argues, exposes the disturbing aspects of Calvinism. By rendering a Catholic Prince Hamlet caught in a Protestant world which consistently denies him his aspirations for a noble life, Shakespeare is able in this play, his most theologically engaged, to delineate the differences between the two belief systems, but also to demonstrate the consequences of replacing the old religion so completely with the new.

The book will be invaluable reading for students of the social, ecclesiastical and political history of early modern England.

The 'problem of authority' was not an invention of the Protestant Reformation, but, as the essays contained in this volume demonstrate, its discussion, in ever greater complexity, was one of the ramifications (if not causes) of the deepening divisions within the Christian church in the sixteenth century. Any optimism that the principle of sola scriptura might provide a vehicle for unity and concord in the post-Reformation church was soon to be dented by a growing uncertainty and division, evident even in early evangelical writing and preaching. Representing a new approach to an important subject this volume of essays widens the understanding and interpretation of authority in the debates of the Reformation. The fruits of original and recent research, each essay builds with careful scholarship on solid historiographical foundations, ensuring that the content and ultimate conclusions do much to challenge long-standing assumptions about perceptions of authority in the aftermath of the Reformation. Rather than dealing with individual sources of authority in isolation, the volume examines the juxtapositions of and negotiations between elements of the authoritative synthesis, and thereby throws new light on the nature of authority in early-modern Europe as a whole. This volume is thus an ideal vehicle with which to bring high quality, new, and significant research into the public domain for the first time, whilst adding substantially to the existing corpus of Reformation scholarship.

In this examination of evangelical reformer Robert Barnes, the author provides a survey of his stormy career, a clear and concise analysis of his often misconstrued theology and a persuasive argument that the influence of Barnes and his polemical programme extended not only throughout England, but throughout Europe.

Superstition and Magic in Early Modern Europe brings together a rich selection of essays which represent the most important historical research on religion, magic and superstition in early modern Europe. Each essay makes a significant contribution to the history of magic and religion in its own right, while together they demonstrate how debates over the topic have evolved over time, providing invaluable intellectual, historical, and socio-political context for readers approaching the subject for the first time. The essays are organised around five key themes and areas of controversy. Part One tackles superstition; Part Two, the tension between miracles and magic; Part Three, ghosts and apparitions; Part Four, witchcraft and witch trials; and Part Five, the gradual disintegration of the 'magical universe' in the face of scientific, religious and practical opposition. Each part is prefaced by an introduction that provides an outline of the historiography and engages with recent scholarship and debate, setting the context for the essays that follow and providing a foundation for further study. This collection is an invaluable toolkit for students of early modern Europe, providing both a focused overview and a springboard for broader thinking about the underlying continuities and discontinuities that make the study of magic and superstition a perennially fascinating topic.