GREEK MATHEMATICAL THOUGHT AND THE ORIGIN OF ALGEBRA

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Greek Mathematical Thought And The Origin Of Algebra

Author : Jacob Klein
ISBN : 9780486319810
Genre : Mathematics
File Size : 79.3 MB
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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.
Category: Mathematics

Descartes S Mathematical Thought

Author : C. Sasaki
ISBN : 9789401712255
Genre : Mathematics
File Size : 45.74 MB
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Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.
Category: Mathematics

Revolutions And Continuity In Greek Mathematics

Author : Michalis Sialaros
ISBN : 9783110565959
Genre : History
File Size : 26.72 MB
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This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.
Category: History

Classics In The History Of Greek Mathematics

Author : Jean Christianidis
ISBN : 1402000812
Genre : Mathematics
File Size : 44.58 MB
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The twentieth century is the period during which the history of Greek mathematics reached its greatest acme. Indeed, it is by no means exaggerated to say that Greek mathematics represents the unique field from the wider domain of the general history of science which was included in the research agenda of so many and so distinguished scholars, from so varied scientific communities (historians of science, historians of philosophy, mathematicians, philologists, philosophers of science, archeologists etc. ), while new scholarship of the highest quality continues to be produced. This volume includes 19 classic papers on the history of Greek mathematics that were published during the entire 20th century and affected significantly the state of the art of this field. It is divided into six self-contained sections, each one with its own editor, who had the responsibility for the selection of the papers that are republished in the section, and who wrote the introduction of the section. It constitutes a kind of a Reader book which is today, one century after the first publications of Tannery, Zeuthen, Heath and the other outstanding figures of the end of the 19th and the beg- ning of 20th century, rather timely in many respects.
Category: Mathematics

Mathematical Thought From Ancient To Modern Times

Author : Morris Kline
ISBN : 9780199770465
Genre : Mathematics
File Size : 38.91 MB
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The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.
Category: Mathematics

From Discrete To Continuous

Author : K. Neal
ISBN : 9789401700771
Genre : Mathematics
File Size : 41.24 MB
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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.
Category: Mathematics

Repetition And Identity

Author : Catherine Pickstock
ISBN : 9780191506536
Genre : Literary Criticism
File Size : 61.12 MB
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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.
Category: Literary Criticism

Modelling And Mathematics Education

Author : J F Matos
ISBN : 9780857099655
Genre : Mathematics
File Size : 61.29 MB
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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
Category: Mathematics

An Introduction To Algebraic Structures

Author : Joseph Landin
ISBN : 0486659402
Genre : Mathematics
File Size : 38.56 MB
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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.
Category: Mathematics