Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean PDF Download
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Author: Victor J. Katz
Publisher: Princeton University Press
ISBN: 0691202818
Category : Mathematics
Languages : en
Pages : 720
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Book Description
"In recent decades, there has been extensive research on Greek mathematics that has considerably enlarged the scope of this area of inquiry. Traditionally, "Greek mathematics" has referred to the axiomatic work of Archimedes, Apollonius, and others in the first three centuries BCE. However, there is a wide body of mathematical work that appeared in the eastern Mediterranean during the time it was under Greek influence (from approximately 400 BCE to 600 CE), which remains under-explored in the existing scholarship. This sourcebook provides an updated look at Greek mathematics, bringing together classic Greek texts with material from lesser-known authors, as well as newly uncovered texts that have been omitted in previous scholarship. The book adopts a broad scope in defining mathematical practice, and as such, includes fields such as music, optics, and architecture. It includes important sources written in languages other than Greek in the eastern Mediterranean area during the period from 400 BCE to 600 CE, which show some influence from Greek culture. It also includes passages that highlight the important role mathematics played in philosophy, pedagogy, and popular culture. The book is organized topically; chapters include arithmetic, plane geometry, astronomy, and philosophy, literature, and education. Within each chapter, the (translated) texts are organized chronologically. The book weaves together ancient commentary on classic Greek works with the works themselves to show how the understanding of mathematical ideas changed over the centuries"--
Author: Victor J. Katz
Publisher: Princeton University Press
ISBN: 0691202818
Category : Mathematics
Languages : en
Pages : 720
Get Book Here
Book Description
"In recent decades, there has been extensive research on Greek mathematics that has considerably enlarged the scope of this area of inquiry. Traditionally, "Greek mathematics" has referred to the axiomatic work of Archimedes, Apollonius, and others in the first three centuries BCE. However, there is a wide body of mathematical work that appeared in the eastern Mediterranean during the time it was under Greek influence (from approximately 400 BCE to 600 CE), which remains under-explored in the existing scholarship. This sourcebook provides an updated look at Greek mathematics, bringing together classic Greek texts with material from lesser-known authors, as well as newly uncovered texts that have been omitted in previous scholarship. The book adopts a broad scope in defining mathematical practice, and as such, includes fields such as music, optics, and architecture. It includes important sources written in languages other than Greek in the eastern Mediterranean area during the period from 400 BCE to 600 CE, which show some influence from Greek culture. It also includes passages that highlight the important role mathematics played in philosophy, pedagogy, and popular culture. The book is organized topically; chapters include arithmetic, plane geometry, astronomy, and philosophy, literature, and education. Within each chapter, the (translated) texts are organized chronologically. The book weaves together ancient commentary on classic Greek works with the works themselves to show how the understanding of mathematical ideas changed over the centuries"--
Author: Roger L. Cooke
Publisher: John Wiley & Sons
ISBN: 1118030249
Category : Mathematics
Languages : en
Pages : 630
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Book Description
This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
Author: Peter Green
Publisher: Univ of California Press
ISBN: 0520914147
Category : History
Languages : en
Pages : 999
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Book Description
The Hellenistic Age, the three extraordinary centuries from the death of Alexander in 323 B. C. to Octavian's final defeat of Antony and Cleopatra at the Battle of Actium, has offered a rich and variegated field of exploration for historians, philosophers, economists, and literary critics. Yet few scholars have attempted the daunting task of seeing the period whole, of refracting its achievements and reception through the lens of a single critical mind. Alexander to Actium was conceived and written to fill that gap. In this monumental work, Peter Green—noted scholar, writer, and critic—breaks with the traditional practice of dividing the Hellenistic world into discrete, repetitious studies of Seleucids, Ptolemies, Antigonids, and Attalids. He instead treats these successor kingdoms as a single, evolving, interrelated continuum. The result clarifies the political picture as never before. With the help of over 200 illustrations, Green surveys every significant aspect of Hellenistic cultural development, from mathematics to medicine, from philosophy to religion, from literature to the visual arts. Green offers a particularly trenchant analysis of what has been seen as the conscious dissemination in the East of Hellenistic culture, and finds it largely a myth fueled by Victorian scholars seeking justification for a no longer morally respectable imperialism. His work leaves us with a final impression of the Hellenistic Age as a world with haunting and disturbing resemblances to our own. This lively, personal survey of a period as colorful as it is complex will fascinate the general reader no less than students and scholars.
Author: Jran Friberg
Publisher: World Scientific
ISBN: 9812708847
Category : Mathematics
Languages : en
Pages : 497
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Book Description
A sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the authorOCOs intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian OC metric algebra, OCO a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets. The bookOCOs use of OC metric algebra diagramsOCO in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract OC lettered diagramsOCO in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The authorOCOs comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics."
Author: Peter Michael Harman
Publisher: Cambridge University Press
ISBN: 9780521892667
Category : Biography & Autobiography
Languages : en
Pages : 552
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Book Description
A collection of twenty original essays on the history of science and mathematics. The topics covered embrace the main themes of Whiteside's scholarly work, emphasising Newtonian topics: mathematics and astronomy to Newton; Newton's manuscripts; Newton's Principia; Newton and eighteenth-century mathematics and physics; after Newton: optics and dynamics. The focus of these themes gives the volume considerable coherence. This volume of essays makes available important original work on Newton and the history of the exact sciences. This volume has been published in honour of D. T. Whiteside, famous for his edition of The Mathematical Papers of Isaac Newton.
Author: Anil Nerode
Publisher: Springer Science & Business Media
ISBN: 1468402110
Category : Computers
Languages : en
Pages : 383
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Book Description
In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
Author: Karoly Bezdek
Publisher: CRC Press
ISBN: 1000000338
Category : Mathematics
Languages : en
Pages : 307
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Book Description
Volume of geometric objects plays an important role in applied and theoretical mathematics. This is particularly true in the relatively new branch of discrete geometry, where volume is often used to find new topics for research. Volumetric Discrete Geometry demonstrates the recent aspects of volume, introduces problems related to it, and presents methods to apply it to other geometric problems. Part I of the text consists of survey chapters of selected topics on volume and is suitable for advanced undergraduate students. Part II has chapters of selected proofs of theorems stated in Part I and is oriented for graduate level students wishing to learn about the latest research on the topic. Chapters can be studied independently from each other. Provides a list of 30 open problems to promote research Features more than 60 research exercises Ideally suited for researchers and students of combinatorics, geometry and discrete mathematics
Author: Jean Christianidis
Publisher: Springer Science & Business Media
ISBN: 9781402000812
Category : Mathematics
Languages : en
Pages : 502
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Book Description
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.
Author: June Barrow-Green
Publisher: American Mathematical Society
ISBN: 1470466767
Category : Mathematics
Languages : en
Pages : 505
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Book Description
The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the first volume of the two-volume set, takes readers from the beginning of counting in prehistory to 1600 and the threshold of the discovery of calculus. It is notable for the extensive engagement with original—primary and secondary—source material. The coverage is worldwide, and embraces developments, including education, in Egypt, Mesopotamia, Greece, China, India, the Islamic world and Europe. The emphasis on astronomy and its historical relationship to mathematics is new, and the presentation of every topic is informed by the most recent scholarship in the field. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
Author: Amos Funkenstein
Publisher: Princeton University Press
ISBN: 0691184267
Category : Science
Languages : en
Pages : 442
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Book Description
Theology and the Scientific Imagination is a pioneering work of intellectual history that transformed our understanding of the relationship between Christian theology and the development of science. Distinguished scholar Amos Funkenstein explores the metaphysical foundations of modern science and shows how, by the 1600s, theological and scientific thinking had become almost one. Major figures like Descartes, Leibniz, Newton, and others developed an unprecedented secular theology whose debt to medieval and scholastic thought shaped the trajectory of the scientific revolution. The book ends with Funkenstein’s influential analysis of the seventeenth century’s “unprecedented fusion” of scientific and religious language. Featuring a new foreword, Theology and the Scientific Imagination is a pathbreaking and classic work that remains a fundamental resource for historians and philosophers of science.
