Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

This book examines the organisation of specialised salt production at Zhongba, one of the most important prehistoric sites in the Three Gorges of China's Yangzi River valley. Rowan K. Flad demonstrates that salt production emerged in the second millennium BCE and developed into a large-scale, intense activity. As the intensity of this activity increased during the early Bronze Age, production became more coordinated, perhaps by an emergent elite who appear to have supported their position of authority by means of divination and the control of ritual knowledge. This study explores evidence of these changes in ceramics, the layout of space at the site and animal remains. It synthesises the data retrieved from years of excavation, showing not only the evolution of production methods, but also the emergence of social hierarchy in the Three Gorges region over two millennia. • Relates to the Three Gorges of China, a region of international interest because of the recently constructed dam • Salt is a vital resource for all human societies and this study helps us understand how early populations acquired it • Contains a personal account of a foreign archaeologist working in China

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science. Clarifies both traditional methods and current, popular algorithms (e.g. neural nets, random forests) Written by two world-leading researchers Addressed to all fields that work with data

Class Counts combines theoretical discussions of the concept of class with a wide range of comparative empirical investigations of class and its ramifications in developed capitalist societies. What unites the topics is not a preoccupation with a common object of explanation, but rather a common explanatory factor: class. Four broad themes are explored: class structure and its transformations; the permeability of class boundaries; class and gender; class consciousness. The specific empirical studies include such diverse topics as the sexual division of labour in housework, gender differences in managerial authority, friendship networks in the class structure, the expansion of self-employment in the United States in the past two decades, and the class consciousness of state and private-sector employees. The results of these studies are then evaluated in terms of how they confirm certain expectations within the Marxist tradition of class analysis and how they pose challenging surprises.

What forces lead to democracy's creation? Why does it sometimes consolidate only to collapse at other times? Written by two of the foremost authorities on this subject in the world, this volume develops a framework for analyzing the creation and consolidation of democracy. It revolutionizes scholarship on the factors underlying government and popular movements toward democracy or dictatorship. Daron Acemoglu and James Robinson argue that different social groups prefer different political institutions because of the way they allocate political power and resources. Their book, the subject of a four-day seminar at Harvard's Center for Basic Research in the Social Sciences, was also the basis for the Walras-Bowley lecture at the joint meetings of the European Economic Association and Econometric Society in 2003 and is the winner of the John Bates Clark Medal.

Problems are a central part of human life. The Psychology of Problem Solving organizes in one volume much of what psychologists know about problem solving and the factors that contribute to its success or failure. There are chapters by leading experts in this field, including Miriam Bassok, Randall Engle, Anders Ericsson, Arthur Graesser, Keith Stanovich, Norbert Schwarz, and Barry Zimmerman, among others. The Psychology of Problem Solving is divided into four parts. Following an introduction that reviews the nature of problems and the history and methods of the field, Part II focuses on individual differences in, and the influence of, the abilities and skills that humans bring to problem situations. Part III examines motivational and emotional states and cognitive strategies that influence problem solving performance, while Part IV summarizes and integrates the various views of problem solving proposed in the preceding chapters.

In this major new collection, an international team of scholars examine the relationship between the Chinese women's periodical press and global modernity in the late nineteenth and twentieth centuries. The essays in this richly illustrated volume probe the ramifications for women of two monumental developments in this period: the intensification of China's encounters with foreign powers and a media transformation comparable in its impact to the current internet age. The book offers a distinctive methodology for studying the periodical press, which is supported by the development of a bilingual database of early Chinese periodicals. Throughout the study, essays on China are punctuated by transdisciplinary reflections from scholars working on periodicals outside of the Chinese context, encouraging readers to rethink common stereotypes about lived womanhood in modern China, and to reconsider the nature of Chinese modernity in a global context. Presents the first close reading of the Chinese periodical press in a global, transregional and transdisciplinary context Proposes a distinctive new methodology for studying the periodical press Encourages readers to rethink issues of gender and genre in the digital age

This collection of original essays by leading historians of political thought examines modern European thinkers' writings about conquest, colonization and empire. The creation of vast transcontinental empires and imperial trading networks played a key role in the development of modern European political thought. The rise of modern empires raised fundamental questions about virtually the entire contested set of concepts that lay at the heart of modern political philosophy, such as property, sovereignty, international justice, war, trade, rights, transnational duties, civilization and progress. From Renaissance republican writings about conquest and liberty to sixteenth-century writings about the Spanish conquest of the Americas through Enlightenment perspectives about conquest and global commerce and nineteenth-century writings about imperial activities both within and outside of Europe, these essays survey the central moral and political questions occasioned by the development of overseas empires and European encounters with the non-European world among theologians, historians, philosophers, diplomats and merchants.

A fully updated version of the world's best-selling grammar title. English Grammar in Use Third edition is a fully updated version of the classic grammar title. It retains all the key features of clarity and accessibility that have made the book so popular with students and teachers alike. This edition, with answers, is ideal for self-study and comes with a handy pull-out reference panel which allows students to review key grammar points at a glance.

The meaning that people attribute to things necessarily derives from human transactions and motivations, particularly from how those things are used and circulated. The contributors to this volume examine how things are sold and traded in a variety of social and cultural settings, both present and past. Focusing on culturally defined aspects of exchange and socially regulated processes of circulation, the essays illuminate the ways in which people find value in things and things give value to social relations. By looking at things as if they lead social lives, the authors provide a new way to understand how value is externalized and sought after. They discuss a wide range of goods - from oriental carpets to human relics - to reveal both that the underlying logic of everyday economic life is not so far removed from that which explains the circulation of exotica, and that the distinction between contemporary economies and simpler, more distant ones is less obvious than has been thought. As the editor argues in his introduction, beneath the seeming infinitude of human wants, and the apparent multiplicity of material forms, there in fact lie complex, but specific, social and political mechanisms that regulate taste, trade, and desire. Containing contributions from American and British social anthropologists and historians, the volume bridges the disciplines of social history, cultural anthropology, and economics, and marks a major step in our understanding of the cultural basis of economic life and the sociology of culture. It will appeal to anthropologists, social historians, economists. archaeologists, and historians of art.

G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

In its original edition, Bruce Trigger’s book was the first ever to examine the history of archaeological thought from medieval times to the present in world-wide perspective. Now, in this new edition, he both updates the original work and introduces new archaeological perspectives and concerns. At once stimulating and even-handed, it places the development of archaeological thought and theory throughout within a broad social and intellectual framework. The successive but interacting trends apparent in archaeological thought are defined and the author seeks to determine the extent to which these trends were a reflection of the personal and collective interests of archaeologists as these relate - in the West at least - to the fluctuating fortunes of the middle classes. While subjective influences have been powerful, Professor Trigger argues that the gradual accumulation of archaeological data has exercised a growing constraint on interpretation. In turn, this has increased the objectivity of archaeological research and enhanced its value for understanding the entire span of human history and the human condition in general.

Svat Soucek's book offers a short and accessible introduction to the history of Inner Asia. The narrative, which begins with the arrival of Islam, charts the rise and fall of the different dynasties right up to the Russian conquest. Dynastic tables and maps augment and elucidate the text. The contemporary focus rests on the seven countries which make up the core of present-day Eurasia, that is Uzbekistan, Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, Sinkiang and Mongolia. Since the fall of the Soviet Union in 1991, renewed interest in these countries has prompted considerable political, cultural, economic and religious debate. While a divergent literature has evolved in consequence, no comprehensive survey of the region has been attempted. Soucek's history promises to fill this gap and to become an indispensable source of information for anyone studying or visiting the region.

Statesmen and Gentlemen is an important study of the way in which, during the twelfth- and thirteenth-centuries, China's ruling meritocracy was transformed into a locally rooted elite whose principal aim was the consolidation of their power, wealth and influence on a local as opposed to a national and dynastic basis. Professor Hymes offers a remarkable picture of the institutional and social changes this process entailed, but he also examines in detail the subtle ways in which the elite's perception of itself and its social role changed and it came to offer powerful support to local self-defence, social welfare, religious cults and temple-building.

Outline of a Theory of Practice is recognized as a major theoretical text on the foundations of anthropology and sociology. Pierre Bourdieu, a distinguished French anthropologist, develops a theory of practice which is simultaneously a critique of the methods and postures of social science and a general account of how human action should be understood. With his central concept of the habitus, the principle which negotiates between objective structures and practices, Bourdieu is able to transcend the dichotomies which have shaped theoretical thinking about the social world. The author draws on his fieldwork in Kabylia (Algeria) to illustrate his theoretical propositions. With detailed study of matrimonial strategies and the role of rite and myth, he analyses the dialectical process of the 'incorporation of structures' and the objectification of habitus, whereby social formations tend to reproduce themselves. A rigorous consistent materialist approach lays the foundations for a theory of symbolic capital and, through analysis of the different modes of domination, a theory of symbolic power.

The empire of the Qara Khitai, which was one of the least known and most fascinating dynasties in the history of Central Asia, existed for nearly a century before it was conquered by the Mongols in 1218. Arriving in Central Asia from China, the Qara Khitai ruled over a mostly Muslim population. Their history affords a unique window onto the extensive cross-cultural contacts between China, Inner Asian nomads and the Muslim world in the period preceding the rise of Chinggis Khan. Using an extensive corpus of Muslim and Chinese sources, Michal Biran comprehensively examines the political, institutional and cultural histories of the Qara Khitai. Her book explores a range of topics including the organization of the army, the position of women, the image of China in Muslim Central Asia,the religions of the Qara Khitai and the legacy they left for the Mongols. Crucially she asks why they did not, unlike their predecessors and successors in Central Asia, embrace Islam. The book represents a groundbreaking contribution to the field of Eurasian history for students of the Islamic world, China and Central Asia. • First book in Western language on a crucial period of Central Asia • Major contribution to the emerging field of Eurasian history, examining cross-cultural and long distance political interactions • Written by a highly regarded, established scholar in this field Contents Part I. Political History: 1. From Liao to Western Liao: Yelü Dashi and the establishment of the Qara Khitai Empire; 2. The quiet period: the reign of Yilie and the Empresses; 3. The fall: between the Khwarazm Shah and the Mongols. Epilogue: what became of the Qara Khitai?; Part II. Aspects of Cultural and Institutional History: 4. China; 5. Nomads; 6. Islam.