Greek Mathematical Thought and the Origin of Algebra

Author: Jacob Klein

Publisher: Courier Corporation

ISBN: 0486319814

Category: Mathematics

Page: 384

View: 2656

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Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

From Discrete to Continuous

The Broadening of Number Concepts in Early Modern England

Author: K. Neal

Publisher: Springer Science & Business Media

ISBN: 940170077X

Category: Mathematics

Page: 175

View: 6345

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In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.

The New Yearbook for Phenomenology and Phenomenological Philosophy

Author: Burt Hopkins,John Drummond

Publisher: Routledge

ISBN: 1317547284

Category: Philosophy

Page: 320

View: 6564

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The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer.

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

Author: Ivor Grattan-Guinness

Publisher: Routledge

ISBN: 1134957491

Category: Reference

Page: 1840

View: 1677

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* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics

Repetition and Identity

The Literary Agenda

Author: Catherine Pickstock

Publisher: OUP Oxford

ISBN: 0191506532

Category: Literary Criticism

Page: 240

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The Literary Agenda is a series of short polemical monographs about the importance of literature and of reading in the wider world and about the state of literary education inside schools and universities. The category of 'the literary' has always been contentious. What is clear, however, is how increasingly it is dismissed or is unrecognised as a way of thinking or an arena for thought. It is sceptically challenged from within, for example, by the sometimes rival claims of cultural history, contextualized explanation, or media studies. It is shaken from without by even greater pressures: by economic exigency and the severe social attitudes that can follow from it; by technological change that may leave the traditional forms of serious human communication looking merely antiquated. For just these reasons this is the right time for renewal, to start reinvigorated work into the meaning and value of literary reading. Repetition and Identity offers a theory of the existing thing as such. A thing only has identity and consistency when it has already been repeated, but repetition summons difference and the shadow invocation of a connecting sign. In contrast to the perspectives of Post-structuralism, Catherine Pickstock proposes that signs are part of reality, and that they truthfully express the real. She also proposes that non-identical repetition involves analogy, rather than the Post-structuralist combination of univocity and equivocity, or of rationalism with scepticism. This proposal, which is happy for reality to make sense, involves, however, a subjective decision which is to be poetically performed. A wager is laid upon the possibility of a consistency which sustains the subject, in continuity with the elusive consistency of nature. This wager is played out in terms of a performative argument concerning the existential stances open to human beings. It is concluded that the individual sustains this quest within the context of an inter-subjective search for an historical consistency of culture. But can ethical consistency, and the harmonisation of this with an aesthetic surplus of an 'elsewhere', invoked by the sign, be achieved without a religious gesture? And can this gesture avoid a tragic tension between ethical commitment and religious renunciation? Pickstock suggests a Kierkegaardian re-reading of the Patristic categories of 'recapitulation' and 'reconstitution' can reconcile this tension. The quest for the identity and consistency of the thing leads us from the subject through fiction and history and to sacred history, to shape an ontology which is also a literary theory and a literary artefaction.

Modelling and Mathematics Education

ICTMA 9 - Applications in Science and Technology

Author: J F Matos,S K Houston,W Blum,S P Carreira

Publisher: Elsevier

ISBN: 0857099655

Category: Mathematics

Page: 432

View: 5246

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The articles included in this book are from the ICTMA 9 conference held in Lisbon, attended by delegates from about 30 countries. This work records the 1999 Lisbon Conference of ICTMA. It contains the selected and edited content of the conference and makes a significant contribution to mathematical modelling which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships. Contains the selected and edited content of the 1999 Lisbon Conference of ICTMA Makes a significant contribution to mathematical modelling, which is the significant investigative preliminary to all scientific and technological applications from machinery to satellites and docking of space-ships

Architecture in the Age of Divided Representation

The Question of Creativity in the Shadow of Production

Author: Dalibor Vesely

Publisher: MIT Press

ISBN: 9780262220675

Category: Architecture

Page: 506

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Reclaiming the humanistic role of architecture in the age of technology: an examination of architecture's indispensable role as a cultural force throughout history.

The Politics and Rhetoric of Scientific Method

Historical Studies

Author: J. Schuster,R.R. Yeo

Publisher: Springer Science & Business Media

ISBN: 9400945604

Category: History

Page: 352

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The institutionalization of History and Philosophy of Science as a distinct field of scholarly endeavour began comparatively earl- though not always under that name - in the Australasian region. An initial lecturing appointment was made at the University of Melbourne immediately after the Second World War, in 1946, and other appoint ments followed as the subject underwent an expansion during the 1950s and 1960s similar to that which took place in other parts of the world. Today there are major Departments at the University of Melbourne, the University of New South Wales and the University of Wollongong, and smaller groups active in many other parts of Australia and in New Zealand. "Australasian Studies in History and Philosophy of Science" aims to provide a distinctive publication outlet for Australian and New Zealand scholars working in the general area of history, philosophy and social studies of science. Each volume comprises a group of essays on a connected theme, edited by an Australian or a New Zealander with special expertise in that particular area. Papers address general issues, however, rather than local ones; parochial topics are avoided. Further more, though in each volume a majority of the contributors is from Australia or New Zealand, contributions from elsewhere are by no means ruled out. Quite the reverse, in fact - they are actively encour aged wherever appropriate to the balance of the volume in question.

Routledge History of Philosophy Volume IV

The Renaissance and Seventeenth Century Rationalism

Author: G.H.R. Parkinson

Publisher: Routledge

ISBN: 113493873X

Category: Philosophy

Page: 480

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First published in 1993. Routledge is an imprint of Taylor & Francis, an informa company.

On the Shoulders of Merchants

Exchange and the Mathematical Conception of Nature in Early Modern Europe

Author: Richard W. Hadden

Publisher: SUNY Press

ISBN: 9780791420126

Category: Social Science

Page: 191

View: 9491

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This book shows how the universal quantification of science resulted from the routinization of commercial practices that were familiar in scientist’s daily lives. Following the work of Franz Borkenau and Jacob Klein in the 1930s, the book describes the rise of the mechanistic world-view as a reification of relations of exchange in the sixteenth and seventeenth centuries. Critical of more orthodox, positivist Marxist accounts of the rise of science, it argues that commercial reckoners, in keeping with the social relations in which their activity took place, delivered a new mathematical object, “general magnitude,” to the new mechanics. The book is an historical extension of the sociology of scientific knowledge and develops and refines themes found in the work of Alfred Sohn-Rethel and Gideon Freudenthal.

New Perspectives on Galileo

Papers Deriving from and Related to a Workshop on Galileo held at Virginia Polytechnic Institute and State University, 1975

Author: Robert E. Butts,Joseph C. Pitt

Publisher: Springer Science & Business Media

ISBN: 940099799X

Category: Science

Page: 264

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The essays in this volume (except for the contribution of Dr. Le Grand) are extremely revised versions of papers originally delivered at a workshop on Galileo held in Blacksburg, Virginia in October, 1975. The meeting was organized by Professor Joseph Pitt and sponsored by the Department of Philosophy and Religion, The College of Arts and Sciences, and the Division of Research of Virginia Polytechnic Institute and State University. The papers that follow deal with problems OIf Galileo's philosophy of science, specific and general problems connected with his methodology, and with historical and conceptual questions concerning the relationship of his work to that of contemporaries and both earlier and later scientists. New perspectives take many forms. In this book the 'newness' has, for the most part, two forms. First, in the papers by Wisan, Shea, Le Grand and Wallace (the concerns will also appear in some of the other contributions), greatly enriched historical discoveries of how Galileo's science and its method ology developed are provided. It should be stressed that these papers are attempts to recapture a deep sense of the kind of science Galileo was creating. Other papers in the volume, for example, those by McMullin, Machamer, Butts and Pitt, underscore the importance of this historical venture by discussing various aspects of the philosophical background of Galileo's thought. The historical and philosophical evaluations and analyses compliment one another.

Ten Gifts of the Demiurge

Proclus on Plato's Timaeus

Author: Emilie Kutash

Publisher: A&C Black

ISBN: 1472519825

Category: Philosophy

Page: 320

View: 302

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Proclus' commentary on Plato's "Timaeus" is perhaps the most important surviving Neoplatonic commentary. In it Proclus contemplates nature's mysterious origins and at the same time employs the deductive rigour required to address perennial philosophical questions. Nature, for him, is both divine and mathematically transparent. He renders theories of Time, Eternity, Providence, Evil, Soul and Intellect and constructs an elaborate ontology that includes mathematics and astronomy. He gives ample play to pagan theology too, frequently lapsing into the arcane language of the "Chaldaean Oracles". "Ten Gifts of the Demiurge" is an essential companion to this rich but complex and densely wrought text, providing an analysis of its arguments and showing that it, like the cosmos Proclus reveres, is a living coherent whole. The book provides aides to understanding Proclus' work within the complex background of Neoplatonic philosophy, familiarising the reader with the political context of the Athenian school, analysing Proclus' key terminology, and giving background to the philosophical arguments and ancient sciences upon which Proclus draws.Above all, it helps the reader appreciate the varicoloured light that Proclus sheds on the secrets of nature.

Badiou and Plato

Author: A.J Bartlett

Publisher: Edinburgh University Press

ISBN: 0748688854

Category: Philosophy

Page: 256

View: 9059

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This book will help you to understand Badiou's central concepts, the philosophical relation between Badiou and Plato and will rethink the importance of Badiou's 'Platonic' claim that 'the only education is an education by truths'.

Imagining Numbers

(particularly the square root of minus fifteen)

Author: Barry Mazur

Publisher: Farrar, Straus and Giroux

ISBN: 1429931469

Category: Mathematics

Page: 288

View: 6167

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How the elusive imaginary number was first imagined, and how to imagine it yourself Imagining Numbers (particularly the square root of minus fifteen) is Barry Mazur's invitation to those who take delight in the imaginative work of reading poetry, but may have no background in math, to make a leap of the imagination in mathematics. Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination. It took more than two hundred years for mathematicians to discover a satisfactory way of "imagining" these numbers. With discussions about how we comprehend ideas both in poetry and in mathematics, Mazur reviews some of the writings of the earliest explorers of these elusive figures, such as Rafael Bombelli, an engineer who spent most of his life draining the swamps of Tuscany and who in his spare moments composed his great treatise "L'Algebra". Mazur encourages his readers to share the early bafflement of these Renaissance thinkers. Then he shows us, step by step, how to begin imagining, ourselves, imaginary numbers.

Phenomenological Perspectives

Historical and Systematic Essays in Honor of Herbert Spiegelberg

Author: P.J. Bossert

Publisher: Springer Science & Business Media

ISBN: 9401016461

Category: Philosophy

Page: 279

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Professor H. L. Van Breda had hoped to write this preface, but his recent, unexpected and untimely death has left that task in my hands. Although my remarks will not be as eloquent and insightful as his surely would have been, some few words are clearly in order here; for the phenomenological community has not only lost the leadership of Fr. Van Breda these last years, but also the scholarship and leadership of Aron Gurwitsch and Alden Fisher - both contributors to this volume - as well as that of Dorion Cairns and John Wild. Our leaders are fewer now but Herbert Spiegelberg is still very obviously one of them. This volume thus presents the work of some of the past and presently recognized leaders in phenomenology - e. g. Gurwitsch, Straus, and Fisher - but, more important perhaps, it also presents the work of some of those who are sure to be future leaders of our community of phenomenological philosophers, if in fact they have not already achieved this status. Most, if not all, of the contribu tors to this volume are in some way or another indebted to Herbert Spiegelberg and his work in phenomenology.

The History of Mathematics

A Brief Course

Author: Roger L. Cooke

Publisher: John Wiley & Sons

ISBN: 1118460294

Category: Mathematics

Page: 648

View: 8715

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Praise for the Second Edition "An amazing assemblage of worldwide contributions in mathematicsand, in addition to use as a course book, a valuable resource . . .essential." —CHOICE This Third Edition of The History of Mathematicsexamines the elementary arithmetic, geometry, and algebra ofnumerous cultures, tracing their usage from Mesopotamia, Egypt,Greece, India, China, and Japan all the way to Europe during theMedieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the historyof mathematics for science, engineering, and secondary education,the book focuses on three main ideas: the facts of who, what, when,and where major advances in mathematics took place; the type ofmathematics involved at the time; and the integration of thisinformation into a coherent picture of the development ofmathematics. In addition, the book features carefully designedproblems that guide readers to a fuller understanding of therelevant mathematics and its social and historical context.Chapter-end exercises, numerous photographs, and a listing ofrelated websites are also included for readers who wish to pursue aspecialized topic in more depth. Additional features of TheHistory of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented asindividual lessons New and revised exercises ranging between technical, factual,and integrative Individual PowerPoint presentations for each chapter and a bankof homework and test questions (in addition to the exercises in thebook) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduatestudents, the book also serves as a fascinating reference formathematically inclined individuals who are interested in learningabout the history of mathematics.

An Introduction to Algebraic Structures

Author: Joseph Landin

Publisher: Courier Corporation

ISBN: 9780486659404

Category: Mathematics

Page: 247

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As the author notes in the preface, "The purpose of this book is to acquaint a broad spectrum of students with what is today known as 'abstract algebra.'" Written for a one-semester course, this self-contained text includes numerous examples designed to base the definitions and theorems on experience, to illustrate the theory with concrete examples in familiar contexts, and to give the student extensive computational practice.The first three chapters progress in a relatively leisurely fashion and include abundant detail to make them as comprehensible as possible. Chapter One provides a short course in sets and numbers for students lacking those prerequisites, rendering the book largely self-contained. While Chapters Four and Five are more challenging, they are well within the reach of the serious student.The exercises have been carefully chosen for maximum usefulness. Some are formal and manipulative, illustrating the theory and helping to develop computational skills. Others constitute an integral part of the theory, by asking the student to supply proofs or parts of proofs omitted from the text. Still others stretch mathematical imaginations by calling for both conjectures and proofs.Taken together, text and exercises comprise an excellent introduction to the power and elegance of abstract algebra. Now available in this inexpensive edition, the book is accessible to a wide range of students, who will find it an exceptionally valuable resource. Unabridged, corrected Dover (1989) republication of the edition published by Allyn and Bacon, Boston, 1969.

Advanced Calculus of Several Variables

Author: Charles Henry Edwards

Publisher: Courier Corporation

ISBN: 9780486683362

Category: Mathematics

Page: 457

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Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.

Illustrating Nature

How to Paint and Draw Plants and Animals

Author: Dot Barlowe,Sy Barlowe

Publisher: Courier Corporation

ISBN: 9780486299211

Category: Art

Page: 111

View: 5228

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The thrill of recapturing scenes from nature can translate into a rewarding career or an invigorating pastime. Both professionals and hobbyists will benefit from this expert, step-by-step guide, which shows how to draw every aspect of nature, from lush swampland vegetation to shy forest dwellers and even prehistoric creatures. You'll find expert discussions of a variety of media--pencil, watercolors, oils, acrylics, scratch board, and pen-and-ink--along with practical advice on how to choose the best method of portraying a particular subject, especially for book or magazine illustration. The authors also consider the difficulties of combining artistic effect with scientific accuracy in rendering color, texture, and form. Helpful individual demonstration projects carefully guide the reader toward mastery of specific techniques. Enhanced with over 400 illustrations and a wealth of tips and suggestions for improving style and presentation, this book is a rich and engaging resource for amateurs and professionals alike. Unabridged Dover (1997) republication of the work published by the Viking Press, New York, 1982.