Robert Newton's Books

Benjamin Lightbourne/Lightburn of Westmoreland County, Pennsylvania and His Descendants

By: Robert C Lightburn

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Benjamin Lightbourne/Lightburn of Westmoreland County, Pennsylvania and His Descendants

By: Robert C Lightburn

I first became interested in genealogy when I was about twelve. It was then that my paternal grandmother first introduced me to a book entitled Genealogy of the Fell Family in America Descended from Joseph Fell. This book, which was published in 1891, included my grandfather, Charles McConnell Lightburn. I was struck by the time span covered by the book—nearly three hundred years—and was fascinated by the fact that all of the people in that book were related to one another and to me either by blood or marriage! My grandmother later gave me that book, and it became the first book in my genealogical library. My grandfather and my great-aunt Mary told me that their father had fought for the North during the Civil War by the side of his older brother, who was a brigadier general. This fascinated me. They also told me that there was a town in West Virginia called Lightburn. I couldn’t wait to find it on a map! My own genealogical research did not begin until the late 1970s when I requested the Civil War records of my great grandfather, Calvin Luther Lightburn, and his brothers from the National Archives. During the 1980s, I continued my research, albeit at a very low level of activity. It was not until the early 1990s when I moved to the Washington, DC, area that I became intensively involved in—some might even say addicted to—genealogy. The resources in the Washington, DC, area are extensive, and I ended up spending many happy (and sometimes frustrating) hours conducting research in the National Archives, Library of Congress, and the library of the Daughters of the American Revolution. By 1999, I had amassed a great deal of genealogical information, most of which was stuffed in cardboard boxes. I was encouraged to put what I had on paper by Faye M. (Brown) Lightburn, who had published her book, Revolutionary Soldier Samuel Brown and Some of his Family in 1993. So after attending several related sessions at the National Genealogical Society Conference in the States, which was held that year in Providence, Rhode Island, I finally screwed up my courage and plunged in. I published the original book in 2003. This book is the second and probably last edition.

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793

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iUniverse

Published Date

ISBN 10

1532062494

ISBN 13

9781532062490

Illustrated Encyclopedia of Applied and Engineering Physics, Three-Volume Set

By: Robert Splinter

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Illustrated Encyclopedia of Applied and Engineering Physics, Three-Volume Set

By: Robert Splinter

This resource provides a single, concise reference containing terms and expressions used in the study, practice, and application of physical sciences. The reader will be able to identify quickly critical information about professional jargon, important people, and events. The encyclopedia gives self-contained definitions with essentials regarding the meaning of technical terms and their usage, as well as about important people within various fields of physics and engineering, with highlights of technical and practical aspects related to cross-functional integration. It will be indispensable for anyone working on applications in biomedicine, materials science, chemical engineering, electrical engineering, mechanical engineering, geology, astronomy, and energy. It also includes handy tables and chronological timelines organized by subject area and giving an overview on the historical development of ideas and discovery.

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2045

Publisher

CRC Press

Published Date

ISBN 10

1351625632

ISBN 13

9781351625630

Describing the Hand of God

Divine Agency and Augustinian Obstacles to the Dialogue between Theology and Science

By: Robert Brennan

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Describing the Hand of God

Divine Agency and Augustinian Obstacles to the Dialogue between Theology and Science

By: Robert Brennan

The question of divine agency in the world remains one important unresolved underlying obstacle in the dialogue between theology and science. Modern notions of divine agency are shown to have developed out of the interaction of three factors in early modernity. Two are well known: late medieval perfect-being theology and the early modern application of the notion of the two books of God's revelation to the understanding of the natural order. It is argued the third is the early modern appropriation of theAugustinian doctrine of inspiration. This assumes the soul's existence and a particular description of divine agency in humans, which became more generally applied to divine agency in nature. Whereas Newton explicitly draws the parallel between divine agency in humans and that in nature, Darwin rejects its supposed perfection and Huxley raises serious questions regarding the traditional understanding of the soul. This book offers an alternative incarnational description of divine agency, freeing consideration of divine agency from being dependent on resolving the complex issues of perfect-being theology and the existence of the soul. In conversation with Barth's pneumatology, this proposal is shown to remain theologically coherent and plausible while resolving or avoiding a range of known difficulties in the science-theology dialogue.

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302

Publisher

James Clarke & Company

Published Date

ISBN 10

0227905326

ISBN 13

9780227905326

Riding the Windhorse

Manic-Depressive Disorder and the Quest for Wholeness

By: Robert S. Corrington

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Riding the Windhorse

Manic-Depressive Disorder and the Quest for Wholeness

By: Robert S. Corrington

In this moving account of his struggles with manic-depressive disorder, distinguished philosopher Robert S. Corrington, creator of the school of ecstatic naturalism, presents a compelling argument for rethinking the nature of this malady. Having inherited the disorder from his mother, a gifted actress who struggled with her own form of it until her death, he developed crucial survival strategies that he recommends to other sufferers. In Riding the Windhorse, Corrington details the latest medical, psychological, and spiritual thinking about bipolar disease; a disorder characterized by extreme mood swings and responsible for many untimely deaths each year. Surprisingly, however, manic-depression is also found in almost all forms of genius and Corrington presents two detailed case studies showing this correlation. Riding the Windhorse represents one person's eventual triumph over a potentially crippling disease by demonstrating how creativity and the quest for wholeness can support the erratic flight of the windhorse of manic-depression.

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263

Publisher

Hamilton Books

Published Date

ISBN 10

146162679X

ISBN 13

9781461626794

Block by Block

The Historical and Theoretical Foundations of Thermodynamics

By: Robert Hanlon

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Block by Block

The Historical and Theoretical Foundations of Thermodynamics

By: Robert Hanlon

At the heart of many fields - physics, chemistry, engineering - lies thermodynamics. While this science plays a critical role in determining the boundary between what is and is not possible in the natural world, it occurs to many as an indecipherable black box, thus making the subject a challenge to learn. Two obstacles contribute to this situation, the first being the disconnect between the fundamental theories and the underlying physics and the second being the confusing concepts and terminologies involved with the theories. While one needn't confront either of these two obstacles to successfully use thermodynamics to solve real problems, overcoming both provides access to a greater intuitive sense of the problems and more confidence, more strength, and more creativity in solving them. This book offers an original perspective on thermodynamic science and history based on the three approaches of a practicing engineer, academician, and historian. The book synthesises and gathers into one accessible volume a strategic range of foundational topics involving the atomic theory, energy, entropy, and the laws of thermodynamics.

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667

Publisher

Oxford University Press, USA

Published Date

ISBN 10

0198851545

ISBN 13

9780198851547

Reformation without end

Religion, politics and the past in post-revolutionary England

By: Robert G. Ingram

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Reformation without end

Religion, politics and the past in post-revolutionary England

By: Robert G. Ingram

This study provides a radical reassessment of the English Reformation. No one in eighteenth-century England thought that they were living during ‘the Enlightenment’; instead, they saw themselves as facing the religious, intellectual and political problems unleashed by the Reformation, which began in the sixteenth century. Moreover, they faced those problems in the aftermath of two bloody seventeenth-century political and religious revolutions. This book examines how the eighteenth-century English debated the causes and consequences of those revolutions and the thing they thought had caused them, the Reformation. It draws on a wide array of manuscript sources to show how authors crafted and pitched their works.

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375

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Manchester University Press

Published Date

ISBN 10

1526126966

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9781526126962

Wealth and Notoriety: the extraordinary families of William Levy and Charles Lewis of London

By: Robert Ward

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Wealth and Notoriety: the extraordinary families of William Levy and Charles Lewis of London

By: Robert Ward

This book is much more than just a catalogue of genealogical facts, dates and events. It reveals an extraordinary family with noteworthy individuals in almost every branch. Some were wealthy; some were notorious. Their activities frequently surfaced in the courts and in newspapers. Their wealth originated from a London Jewish couple, William and Elizabeth Levy, whose 'disorderly house' attracted the attention of an 1817 House of Commons enquiry. Later generations were able to enter more respectable professions; they became lawyers, businessmen, theatre owners, military heroes, pioneering adventurers, actors, writers and artists. Amongst those mentioned are: William Levy, Charles Lewis, Lawrence Isaac Nathan, Laurence Hanray, Lawrence Levy, Edward Lawrence Levy, Robert Neck, Frank Van Neck, Morrice Levy, Henry Harris, Samuel Harris, Alan King-Hamilton, Edward Dillon Lewis, Charles Wray Lewis, Ernest Lewis, Donald Swain Lewis, Edward Tyrrell Lewis, Somers Reginald Lewis, Arthur Percy Lewis.

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237

Publisher

Lulu.com

Published Date

ISBN 10

1291334777

ISBN 13

9781291334777

Test Equating, Scaling, and Linking

Methods and Practices

By: Michael J. Kolen,Robert L. Brennan

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Test Equating, Scaling, and Linking

Methods and Practices

By: Michael J. Kolen,Robert L. Brennan

By providing an introduction to test equating which both discusses the most frequently used equating methodologies and covering many of the practical issues involved, this volume expands upon the coverage of the first edition by providing a new chapter on test scaling and a second on test linking.

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584

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387400869

ISBN 13

9780387400860

Science, Religion, and Mormon Cosmology

By: Erich Robert Paul

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Science, Religion, and Mormon Cosmology

By: Erich Robert Paul

Merrill, who urged a unique vision of reality that shaped a Mormon eschatology. He shows how authorities eventually retreated from the perception of reality as "true" and adopted a scientifically less secure position in order to protect their theology, an eventuality which ultimately resulted in a reactionary response to science within Mormonism.

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320

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University of Illinois Press

Published Date

ISBN 10

0252018958

ISBN 13

9780252018954

Between Chance and Choice

Interdisciplinry Perspectives on Determinism

By: Harald Atmanspacher,Robert Bishop

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Between Chance and Choice

Interdisciplinry Perspectives on Determinism

By: Harald Atmanspacher,Robert Bishop

Are choice and free will possible in a world governed by deterministic fundamental equations? What sense would determinism make if many events and processes in the world seemed to be governed by chance? These and many other questions emphasize the fact that chance and choice are two leading actors on stage whenever issues of determinism are under discussion. This volume collects essays by accomplished scientists and philosophers, addressing numerous facets of the concept of determinism. The contributions cover viewpoints from mathematics, physics, cognitive science and social science as well as various branches of philosophy. They offer valuable reading for everyone interested in the interdisciplinary relations between determinism, chance and free will. The desire to foster an interdisciplinary dialogue on determinism, chance and free will was the initial impetus leading to an international workshop on determinism taking place at Ringberg Castle near Lake Tegernsee, south of Munich, in June 2001. Representatives from mathematics, physics, cognitive and social science, and various branches of philosophy convened to discuss numerous aspects of determinism from their disciplinary perspectives. This volume is based on elaborated and refereed manuscripts of their lectures.

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517

Publisher

Andrews UK Limited

Published Date

ISBN 10

184540629X

ISBN 13

9781845406295

Masters of Mathematics

The Problems They Solved, Why These Are Important, and What You Should Know about Them

By: Robert A. Nowlan

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Masters of Mathematics

The Problems They Solved, Why These Are Important, and What You Should Know about Them

By: Robert A. Nowlan

The original title for this work was “Mathematical Literacy, What Is It and Why You Need it”. The current title reflects that there can be no real learning in any subject, unless questions of who, what, when, where, why and how are raised in the minds of the learners. The book is not a mathematical text, and there are no assigned exercises or exams. It is written for reasonably intelligent and curious individuals, both those who value mathematics, aware of its many important applications and others who have been inappropriately exposed to mathematics, leading to indifference to the subject, fear and even loathing. These feelings are all consequences of meaningless presentations, drill, rote learning and being lost as the purpose of what is being studied. Mathematics education needs a radical reform. There is more than one way to accomplish this. Here the author presents his approach of wrapping mathematical ideas in a story. To learn one first must develop an interest in a problem and the curiosity to find how masters of mathematics have solved them. What is necessary to be mathematically literate? It’s not about solving algebraic equations or even making a geometric proof. These are valuable skills but not evidence of literacy. We often seek answers but learning to ask pertinent questions is the road to mathematical literacy. Here is the good news: new mathematical ideas have a way of finding applications. This is known as “the unreasonable effectiveness of mathematics.”

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623

Publisher

Springer

Published Date

ISBN 10

9463008934

ISBN 13

9789463008938

Recent Advances in Nonsmooth Optimization

By: Dingzhu Du,Liqun Qi,Robert S. Womersley

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Recent Advances in Nonsmooth Optimization

By: Dingzhu Du,Liqun Qi,Robert S. Womersley

Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.

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488

Publisher

World Scientific

Published Date

ISBN 10

9810222653

ISBN 13

9789810222659

The First Professional Scientist

Robert Hooke and the Royal Society of London

By: Robert D. Purrington

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The First Professional Scientist

Robert Hooke and the Royal Society of London

By: Robert D. Purrington

A contemporary of Christopher Wren, Robert Boyle, and Isaac Newton, and close friend of all but Newton, Robert Hooke (1635-1703), one of the founders of the early scientific revolution, faded into almost complete obscurity after his death and remained there for nearly three centuries. The result has been that his role in the scientific revolution has been almost totally ignored. He was the first professional scientist worthy of the name, working for the young Royal Society of London as its curator of experiments for four decades. He became the Society’s intellectual center, and for a while its Secretary, roles which led to confrontation with Newton. He made important contributions to pneumatics, mechanics, microscopy, astronomy, and geology, and was partner to Wren in rebuilding London after the Fire.

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292

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Springer Science & Business Media

Published Date

ISBN 10

3034600372

ISBN 13

9783034600378

After Certainty

A History of Our Epistemic Ideals and Illusions

By: Robert Pasnau

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After Certainty

A History of Our Epistemic Ideals and Illusions

By: Robert Pasnau

No part of philosophy is as disconnected from its history as is epistemology. After Certainty offers a reconstruction of that history, understood as a series of changing expectations about the cognitive ideal that beings such as us might hope to achieve in a world such as this. The story begins with Aristotle and then looks at how his epistemic program was developed through later antiquity and into the Middle Ages, before being dramatically reformulated in the seventeenth century. In watching these debates unfold over the centuries, one sees why epistemology has traditionally been embedded within a much larger sphere of concerns about human nature and the reality of the world we live in. It ultimately becomes clear why epistemology today has become a much narrower and specialized field, concerned with the conditions under which it is true to say, that someone knows something. Based on a series of lectures given at Oxford University, Robert Pasnau's book ranges widely over the history of philosophy, and examines in some detail the rise of science as an autonomous discipline. Ultimately Pasnau argues that we may have no good reasons to suppose ourselves capable of achieving even the most minimal standards for knowledge, and the final chapter concludes with a discussion of faith and hope.

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393

Publisher

Oxford University Press

Published Date

ISBN 10

0198801785

ISBN 13

9780198801788

Minds-on Physics

By: William J. Leonard,Robert J. Dufresne,William J. Gerace,Jose P. Mestre

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Minds-on Physics

By: William J. Leonard,Robert J. Dufresne,William J. Gerace,Jose P. Mestre

Activities same basic structure Outcomprinciples, and other ideas that will be raised and addressed during the activity. This section also tells students what they are expected to learn Knowledge Neede they should know or be familiar with before attempting the activity. Then, if necessary, we provide any additional background needed to do the activity Main Activity section contains the specific questions and problems that probe students' understanding and prepare them to make sense out of the ideas Reflection finishing the Main Activity, students re-examine their answers to look for patterns. They are also asked to generalize, abstract, and relate concepts to the situations they have studied

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228

Publisher

Kendall Hunt

Published Date

ISBN 10

0787239291

ISBN 13

9780787239299

Selected Essays

By: Robert Palter

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Selected Essays

By: Robert Palter

Versified dinner parties; the cultural significance of wild fruit; a dreamlike trip to Russia on the eve of the breakup of the Soviet Union; parallel lines in Euclid’s geometry; grotesque episodes in recent Jewish history; the role of religion in the 17th-century origins of modern science: all these and many other topics are explored in essays, half of them never published before, composed during a long scholarly career.

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245

Publisher

Easton Studio Press, LLC

Published Date

ISBN 10

1935212303

ISBN 13

9781935212300

Religion, Politics and Dissent, 1660–1832

Essays in Honour of James E. Bradley

By: Robert D. Cornwall

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Religion, Politics and Dissent, 1660–1832

Essays in Honour of James E. Bradley

By: Robert D. Cornwall

The idea of the long eighteenth century (1660-1832) as a period in which religious and political dissent were regarded as antecedents of the Enlightenment has recently been advanced by several scholars. The purpose of this collection is further to explore these connections between religious and political dissent in Enlightenment Britain. Addressing the many and rich connections between political and religious dissent in the long eighteenth century, the volume also acknowledges the work of Professor James E. Bradley in stimulating interest in these issues among scholars. Contributors engage directly with ideas of secularism, radicalism, religious and political dissent and their connections with the Enlightenment, or Enlightenments, together with other important themes including the connections between religious toleration and the rise of the 'enlightenments'. Contributors also address issues of modernity and the ways in which a 'modern' society can draw its inspiration from both religion and secularity, as well as engaging with the seventeenth-century idea of the synthesis of religion and politics and its evolution into a system in which religion and politics were interdependent but separate. Offering a broadly-conceived interpretation of current research from a more comprehensive perspective than is often the case, the historiographical implications of this collection are significant for the development of ideas of the nature of the Enlightenment and for the nature of religion, society and politics in the eighteenth century. By bringing together historians of politics, religion, ideas and society to engage with the central theme of the volume, the collection provides a forum for leading scholars to engage with a significant theme in British history in the 'long eighteenth century'.

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269

Publisher

Routledge

Published Date

ISBN 10

1317067185

ISBN 13

9781317067184

Notitia Cestriensis, or Historical Notices of the Diocese of Chester

Vol. I

By: Francis Robert Raines,Francis Gastrell

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Notitia Cestriensis, or Historical Notices of the Diocese of Chester

Vol. I

By: Francis Robert Raines,Francis Gastrell

Reprint of the original, first published in 1845.

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422

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BoD – Books on Demand

Published Date

ISBN 10

3368876163

ISBN 13

9783368876166

Governing Complexity in the 21st Century

By: Neil E. Harrison,Robert Geyer

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Governing Complexity in the 21st Century

By: Neil E. Harrison,Robert Geyer

Governing Complexity in the 21st Century surveys the ways in which social systems are becoming more complex. It shows how this complexity impacts every aspect of life for individuals, governments and societies in most social systems at individual, regional, national and global scales and explores how embracing ‘complexity thinking’ can greatly improve the art of governance in all policy areas. The book clearly explains the ideas and methods of complexity science—widely accepted in both the natural and social sciences—then demonstrates how ‘complexity thinking’ can be applied to improve our understanding of governance and policy actions. Providing a deep analysis of many governance challenges, including economic development and technological innovation, environment management, climate change and development in the Middle East, the book also compares national responses to the COVID-19 pandemic. Clear and jargon-free, this book is accessible to undergraduates and scholars alike. It is essential reading for policymakers everywhere, showcasing methods for governing effectively and efficiently in our increasingly complex world. It brings together the broad range of social and environmental science fields and will be useful for those studying or working in policy, politics and international relations, environmental issues, business management, philosophy, history and sociology.

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209

Publisher

Routledge

Published Date

ISBN 10

1000466043

ISBN 13

9781000466041

Universe: The Solar System

By: Roger Freedman,Robert Geller,William J. Kaufmann

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Universe: The Solar System

By: Roger Freedman,Robert Geller,William J. Kaufmann

Universe. When it comes to staying current with latest discoveries, clearing away common misconceptions, and harnessing the power of media in the service of students and instructors, no other full-length introduction to astronomy can match it. Now the textbook that has evolved discovery by discovery with the science of astronomy and education technology for over two decades returns in spectacular new edition, thoroughly updated and offering unprecedented media options. Available in Split Volumes Universe: Stars and Galaxies, Fourth Edition, 1-4292-4015-6 Universe: The Solar System, Fourth Edition, 1-4292-4016-4

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859

Publisher

Macmillan

Published Date

ISBN 10

1429240164

ISBN 13

9781429240161

Smoot's Ear

The Measure of Humanity

By: Robert Tavernor

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Smoot's Ear

The Measure of Humanity

By: Robert Tavernor

Measures are the subject of this unusual book, in which Robert Tavernor offers a fascinating account of the various measuring systems human beings have devised over two millennia. He discusses measures in our own time - when space travel presents to humankind a direct encounter with the unfathomable measure of the universe.

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270

Publisher

Yale University Press

Published Date

ISBN 10

0300124929

ISBN 13

9780300124927

World History Readers' Theater, Grades 5-8

By: Robert W. Smith

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World History Readers' Theater, Grades 5-8

By: Robert W. Smith

Why use Readers Theater in history classes? The format gives students a sense of involvement with the human dramas that make up history. Performers can feel the excitement as Archimedes discovers the displacement of water. They can relate to the terrors of a slave s passage from Africa to the Americas. They can imagine the tension of wading through the water at Omaha Beach as bullets strike their buddies. Each script (12 15 per book) is accompanied by background information, literature connections, extension activities, and discussion questions.

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114

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Teacher Created Resources

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ISBN 10

1420639986

ISBN 13

9781420639988

Frame of the Universe

By: Frank Durham,Robert D. Purrington

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Frame of the Universe

By: Frank Durham,Robert D. Purrington

Durham and Purrington approach the history of the universe by exploring the frontiers of physics, while maintaining a long-standing interest in astronomy and cosmology. They stress that man can not fully understand himself until he understands the universe, of which he is a part.

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300

Publisher

Columbia University Press

Published Date

ISBN 10

0231053932

ISBN 13

9780231053938

The Language of Disenchantment

Protestant Literalism and Colonial Discourse in British India

By: Robert A. Yelle

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The Language of Disenchantment

Protestant Literalism and Colonial Discourse in British India

By: Robert A. Yelle

The Language of Disenchantment explores how Protestant ideas about language inspired British colonial critiques of Hindu mythological, ritual, linguistic, and legal traditions.

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322

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Oxford University Press, USA

Published Date

ISBN 10

0199925011

ISBN 13

9780199925018

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

By: Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell

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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

By: Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell

This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

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620

Publisher

SIAM

Published Date

ISBN 10

1611971233

ISBN 13

9781611971231

Fallen Languages

Crises of Representation in Newtonian England, 1660-1740

By: Robert Markley

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Fallen Languages

Crises of Representation in Newtonian England, 1660-1740

By: Robert Markley

Traces the importance of theology to the crisis of representation in English natural philosophy as documented by the writings of Robert Boyle, Isaac Newton, and their contemporaries. Finds that the tension between observed experimental phenomena and established religious and political thought led them to devise innovative theories. Annotation copyright by Book News, Inc., Portland, OR

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292

Publisher

Cornell University Press

Published Date

ISBN 10

0801425883

ISBN 13

9780801425882

Capacity Theory with Local Rationality

The Strong Fekete-Szegö Theorem on Curves

By: Robert Rumely

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Capacity Theory with Local Rationality

The Strong Fekete-Szegö Theorem on Curves

By: Robert Rumely

This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities. Another chapter contains extensions of the theorem, including variants on Berkovich curves. The proof uses both algebraic and analytic methods, and draws on arithmetic and algebraic geometry, potential theory, and approximation theory. It introduces new ideas and tools which may be useful in other settings, including the local action of the Jacobian on a curve, the "universal function" of given degree on a curve, the theory of inner capacities and Green's functions, and the construction of near-extremal approximating functions by means of the canonical distance.

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466

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470409801

ISBN 13

9781470409807

Book's by Robert Newton

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