The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

The lack of effective DC fault protection technology remains a major barrier for the DC paradigm shift. In addressing the key challenges, Direct Current Fault Protection: Basic Concepts and Technology Advances starts with an introduction to the advantages of DC power systems before moving on to an in-depth review of DC fault protection technologies, including mechanical circuit breaker (MCB), solid-state circuit breaker (SSCB), hybrid circuit breaker (HCB), converter based (breakerless) protection, and fault current limiter (FCL). Coverage includes a comprehensive comparison of various DC fault interruption technologies and their suitable applications, state-of-the-art DC fault protection concepts and advances in research, identification of fundamental challenges and future directions in the field, and commercialization aspects. This book will be a valuable reference for practicing engineers, researchers, and graduate students in the field of power electronics and DC power systems.

The Routledge Companion to John Wesley provides an overview of the work and ideas of one of the principal founders of Methodism, John Wesley (1703-91). Wesley remains highly influential, especially within the worldwide Methodist movement of some eighty million people. As a preacher and religious reformer his efforts led to the rise of a global Protestant movement, but the wide-ranging topics addressed in his writings also suggest a mind steeped in the intellectual developments of the North Atlantic, early modern world. His numerous publications cover not only theology but ethics, history, aesthetics, politics, human rights, health and wellbeing, cosmology and ecology. This volume places Wesley within his eighteenth-century context, analyzes his contribution to thought across his multiple interests, and assesses his continuing relevance today. It contains essays by an international team of scholars, drawn from within the Methodist tradition and beyond. This is a valuable reference particularly for scholars of Methodist Studies, theology, church history and religious history.

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student's preparation and the mathematical skills that are required to be successful in such a course. Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers. Features Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis Suitable for junior or senior undergraduates majoring in mathematics.

As computers proliferate and as the field of computer graphics matures, it has become increasingly important for computer scientists to understand how users perceive and interpret computer graphics. Experimental Design: From User Studies to Psychophysics is an accessible introduction to psychological experiments and experimental design, covering the major components in the design, execution, and analysis of perceptual studies. The book begins with an introduction to the concepts central to designing and understanding experiments, including developing a research question, setting conditions and controls, and balancing specificity with generality. The book then explores in detail a number of types of experimental tasks: free description, rating scales, forced-choice, specialized multiple choice, and real-world tasks as well as physiological studies. It discusses the advantages and disadvantages of each type and provides examples of that type of experiment from the authors' own work. The book also covers stimulus-related issues, including popular stimulus resources. It concludes with a thorough examination of statistical techniques for analyzing results, including methods specific to individual tasks.

Perceptible inspiration, a term used by John Wesley to describe the complicated relationship between Holy Spirit, religious knowledge, and the nature of spiritual being, is not unlike the term 'Methodist' which was also coined by critics of Methodism during the eighteenth century in Britain. John Wesley's adversaries, especially the pseudonymous John Smith with whom Wesley exchanged letters for a period of three years, frequently challenged the plausibility of direct spiritual sensation, which Wesley defended. What does Wesley mean by perceptible inspiration? What does the teaching reveal about the nature and existence of God in Wesley's thinking? What does it suggest about the spiritual nature of humankind? In John Wesley's Pneumatology, it is argued that 'perceptible inspiration' more than a sidebar of Methodist thought, offers a useful model for considering the various features of Wesley's views on the work of the Spirit in relation to human existence, participatory religious knowledge, and moral theology.

Perceptible inspiration, a term used by John Wesley to describe the complicated relationship between Holy Spirit, religious knowledge, and the nature of spiritual being, is not unlike the term 'Methodist' which was also coined by critics of Methodism during the eighteenth century in Britain. John Wesley's adversaries, especially the pseudonymous John Smith with whom Wesley exchanged letters for a period of three years, frequently challenged the plausibility of direct spiritual sensation, which Wesley defended. What does Wesley mean by perceptible inspiration? What does the teaching reveal about the nature and existence of God in Wesley's thinking? What does it suggest about the spiritual nature of humankind? In John Wesley's Pneumatology, it is argued that 'perceptible inspiration' more than a sidebar of Methodist thought, offers a useful model for considering the various features of Wesley's views on the work of the Spirit in relation to human existence, participatory religious knowledge, and moral theology.

As computers proliferate and as the field of computer graphics matures, it has become increasingly important for computer scientists to understand how users perceive and interpret computer graphics. Experimental Design: From User Studies to Psychophysics is an accessible introduction to psychological experiments and experimental design, covering the major components in the design, execution, and analysis of perceptual studies.

The book begins with an introduction to the concepts central to designing and understanding experiments, including developing a research question, setting conditions and controls, and balancing specificity with generality. The book then explores in detail a number of types of experimental tasks: free description, rating scales, forced-choice, specialized multiple choice, and real-world tasks as well as physiological studies. It discusses the advantages and disadvantages of each type and provides examples of that type of experiment from the authors own work. The book also covers stimulus-related issues, including popular stimulus resources. It concludes with a thorough examination of statistical techniques for analyzing results, including methods specific to individual tasks.

Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student's preparation and the mathematical skills that are required to be successful in such a course. Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers. Features Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis Suitable for junior or senior undergraduates majoring in mathematics.

The Growth of English Industry and Commerce, published in its first edition in 1882, was a large-scale economic study by the historian William Cunningham (1849-1919). The ambitious work ultimately grew to encompass two volumes, divided into three parts, and reissued over a period of more than forty years in several revised and expanded editions. This book contains the 1907 fourth edition of the second part of Volume II, dealing with laissez faire in commerce. It covers the period of economic history from about the beginning of the Industrial Revolution to the middle of the nineteenth century.

William Cunningham (1849-1919) was a prominent British economist and economic historian. In this book, which was first published in 1917, Cunningham provides a concise guide to various aspects of political philosophy, with a particular focus on British political institutions. Appendices are included and textual notes are incorporated throughout. This book will be of value to anyone with an interest in political philosophy and the nature of governance.

Originally published in 1886, the Hulsean Lectures for 1885 by William Cunningham deal in detail with the writings and lasting influence of St Augustine (or Austin) from the fourth century AD through the Middle Ages up to eighteenth-century Anglicanism. The text includes a chronology of Augustine's life and writings and is richly footnoted with quotations from important source texts in the original languages. This book will be of use to students of Augustine and anyone interested in the influence of the early Church and Patristic writings.

First published in 1898, as part of the Cambridge Historical Series, this book presents a discussion of the main economic features in the growth and diffusion of Western European culture during ancient times. The text covers a broad range of periods and societies, beginning with Ancient Egypt and moving through to Constantinople and the decline of the Western Roman Empire. Although necessarily dealing with limited information, it draws striking connections between various groups and provides a broad overview of economic change. This book will be of value to anyone with an interest in perspectives on the origins of Western civilization and ancient history.

First published in 1910, as the fourth edition of an 1895 original, this book forms part of the Cambridge Historical Series. The text presents a comprehensive analysis of English industrial development, incorporating discussion of financial systems, immigration, agriculture and the growth of towns, as well as the fundamental changes of the industrial revolution. This broad perspective is rooted in the idea that English industrial history 'is the story of the material side of the life of a great nation'. A bibliography and chronological table are also included. This is a highly readable book that will be of value to anyone with an interest in historiography, British industrial history and economic history.

First published in 1900, as part of the Cambridge Historical Series, this book presents a discussion of the economic and industrial development of Western Europe from medieval times onwards. The text covers a broad range of periods and societies, beginning with the origins of Christendom and moving through to the impact of the Industrial Revolution. Throughout, the intention is 'to show how the material progress of the human race has been carried on and affected by one great polity after another'. Striking connections are drawn during this narrative, providing a comprehensive overview of economic change. This book will be of value to anyone with an interest in perspectives on Western civilization and economic history.

The Growth of English Industry and Commerce, published in its first edition in 1882, was a large-scale economic study by the historian William Cunningham (1849-1919). The ambitious work ultimately grew to encompass two volumes, divided into three parts, and reissued over a period of more than forty years in several revised and expanded editions. This book contains the fifth edition of Volume I, published in 1910. It covers the period of economic history during the Early and Middle Ages.

The Growth of English Industry and Commerce, published in its first edition in 1882, was a large-scale economic study by the historian William Cunningham (1849-1919). The ambitious work ultimately grew to encompass two volumes, divided into three parts, and reissued over a period of more than forty years in several revised and expanded editions. This book contains the 1907 fourth edition of the first part of Volume II, dealing with the mercantile system. It covers the period of economic history from the beginning of the Elizabethan era to about the end of the eighteenth century.

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.

To achieve the complex task of interpreting what we see, our brains rely on statistical regularities and patterns in visual data. Knowledge of these regularities can also be considerably useful in visual computing disciplines, such as computer vision, computer graphics, and image processing. The field of natural image statistics studies the regularities to exploit their potential and better understand human vision. With numerous color figures throughout, Image Statistics in Visual Computing covers all aspects of natural image statistics, from data collection to analysis to applications in computer graphics, computational photography, image processing, and art.

The authors keep the material accessible, providing mathematical definitions where appropriate to help readers understand the transforms that highlight statistical regularities present in images. The book also describes patterns that arise once the images are transformed and gives examples of applications that have successfully used statistical regularities. Numerous references enable readers to easily look up more information about a specific concept or application. A supporting website also offers additional information, including descriptions of various image databases suitable for statistics.

Collecting state-of-the-art, interdisciplinary knowledge in one source, this book explores the relation of natural image statistics to human vision and shows how natural image statistics can be applied to visual computing. It encourages readers in both academic and industrial settings to develop novel insights and applications in all disciplines that relate to visual computing.