The Crest of the Peacock

Non-European Roots of Mathematics (Third Edition)
Author: George Gheverghese Joseph
Publisher: Princeton University Press
ISBN: 9780691135267
Category: Mathematics
Page: 561
View: 5311

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"Enthralling ... After reading it, we cannot see the past in the same comforting haze of age-old stories, faithfully and uncritically retold from teacher to pupil down the years ... Invaluable for mathematics teachers at all levels."--New Scientist.

The Crest of the Peacock

Non-European Roots of Mathematics, Third Edition
Author: George Gheverghese Joseph
Publisher: Princeton University Press
ISBN: 1400836360
Category: Science
Page: 584
View: 9305

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From the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour of the roots and shoots of non-European mathematics. He shows us the deep influence that the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China. The third edition emphasizes the dialogue between civilizations, and further explores how mathematical ideas were transmitted from East to West. The book's scope is now even wider, incorporating recent findings on the history of mathematics in China, India, and early Islamic civilizations as well as Egypt and Mesopotamia. With more detailed coverage of proto-mathematics and the origins of trigonometry and infinity in the East, The Crest of the Peacock further illuminates the global history of mathematics.

The Crest of the Peacock

The Non-European Roots of Mathematics
Author: George Gheverghese Joseph
Publisher: N.A
ISBN: 9780691006598
Category: Education
Page: 455
View: 2113

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The author guides a breathtaking multicultural tour of the roots and shoots of non-European mathematics, revealing the deep influence the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China.

A Passage to Infinity

Medieval Indian Mathematics from Kerala and Its Impact
Author: George Gheverghese Joseph
Publisher: SAGE Publications India
ISBN: 8132104811
Category: Mathematics
Page: 236
View: 6804

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This book traces the first faltering steps taken in the mathematical theorisation of infinity which marks the emergence of modern mathematics. It analyses the part played by Indian mathematicians through the Kerala conduit, which is an important but neglected part of the history of mathematics. Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact begins with an examination of the social origins of the Kerala School and proceeds to discuss its mathematical genesis as well as its achievements. It presents the techniques employed by the School to derive the series expansions for sine, cosine, arctan, and so on. By using modern notation but remaining close to the methods in the original sources, it enables the reader with some knowledge of trigonometry and elementary algebra to follow the derivations. While delving into the nature of the socio-economic processes that led to the development of scientific knowledge in pre-modern India, the book also probes the validity or otherwise of the conjecture of the transmission of Kerala mathematics to Europe through the Jesuit channel. The book straddles two domains: science and social sciences. It will appeal to those interested in mathematics, statistics, medieval history, history of science and technology, links between mathematics and culture and the nature of movements of ideas across cultures.

Women in Mathematics

The Addition of Difference
Author: Claudia Henrion
Publisher: Indiana University Press
ISBN: 9780253114990
Category: Social Science
Page: 328
View: 5217

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"... a wonderful addition to any mathematics teacher's professional bookshelf." -- The Mathematics Teacher "The individual biographies themselves make for enthralling, often inspiring, reading... this volume should be compelling reading for women mathematics students and professionals. A fine addition to the literature on women in science... Highly recommended." -- Choice "... it makes an important contribution to scholarship on the interrelations of gender, mathematics, and culture in the U.S. in the second half of the twentieth century." -- Notices of the AMS "Who is the audience for this book? Certainly women who are interested in studying mathematics and women already in mathematics who have become discouraged will find much to interest and help them. Faculty who teach such women would put it to good use. But it would be a loss to relegate the book to a shelf for occasional reference to an interested student or beginning mathematician. Everyone in the mathematics community in which each of Henrion's subjects struggled so hard to find a place could benefit by a thoughtful reading." -- Society for Industrial and Applied Mathematics (SIAM) News Mathematics is often described as the purest of the sciences, the least tainted by subjective or cultural influences. Theoretically, the only requirement for a life of mathematics is mathematical ability. And yet we see very few women mathematicians. Why? Based upon a series of ten intensive interviews with prominent women mathematicians throughout the United States, this book investigates the role of gender in the complex relationship between mathematician, the mathematical community, and mathematics itself.

The Mathematics of Egypt, Mesopotamia, China, India, and Islam

A Sourcebook
Author: Victor J. Katz
Publisher: Princeton University Press
ISBN: 9780691114859
Category: Mathematics
Page: 685
View: 4966

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In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.

The Historical Roots of Elementary Mathematics


Author: Lucas N. H. Bunt,Phillip S. Jones,Jack D. Bedient
Publisher: Courier Corporation
ISBN: 0486139689
Category: Mathematics
Page: 336
View: 5730

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Exciting, hands-on approach to understanding fundamental underpinnings of modern arithmetic, algebra, geometry and number systems examines their origins in early Egyptian, Babylonian, and Greek sources.

A History of Chinese Mathematics


Author: Jean-Claude Martzloff
Publisher: Springer
ISBN: 3540337830
Category: Mathematics
Page: 487
View: 8482

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This book is made up of two parts, the first devoted to general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. The book is uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike.

Ethnomathematics

A Multicultural View of Mathematical Ideas
Author: Marcia Ascher
Publisher: Routledge
ISBN: 1351449508
Category: Mathematics
Page: 214
View: 8188

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In this truly one-of-a-kind book, Ascher introduces the mathematical ideas of people in traditional, or ""small-scale"", cultures often omitted from discussion of mathematics. Topics such as ""Numbers: Words and Symbols"", ""Tracing Graphs in the Sand"", ""The Logic of Kin Relations"", ""Chance and Strategy in Games and Puzzles"", and ""The Organization and Modeling of Space"" are traced in various cultures including the Inuit, Navajo, and Iroquois of North America; the Inca of South America; the Malekula, Warlpiri, Maori, and Caroline Islanders of Oceania, and the Tshokwe, Bushoong, and Kpelle of Africa. As Ascher explores mathematical ideas involving numbers, logic, spatial configuration, and the organization of these into systems and structures, readers gain both a broader understanding and anappreciation for the idease of other peoples.

Taming the Unknown

A History of Algebra from Antiquity to the Early Twentieth Century
Author: Victor J. Katz,Karen Hunger Parshall
Publisher: Princeton University Press
ISBN: 1400850525
Category: Mathematics
Page: 504
View: 2822

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What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra’s remarkable growth through different epochs around the globe.

Indian Mathematics

Engaging with the World from Ancient to Modern Times
Author: George Gheverghese Joseph
Publisher: World Scientific
ISBN: 1786340631
Category: Mathematics
Page: 512
View: 9195

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Indian Mathematics gives a unique insight into the history of mathematics within a historical global context. It builds on research into the connection between mathematics and the world-wide advancement of economics and technology. Joseph draws out parallel developments in other cultures and carefully examines the transmission of mathematical ideas across geographical and cultural borders. Accessible to those who have an interest in the global history of mathematical ideas, for the historians, philosophers and sociologists of mathematics, it is a book not to be missed.

Multicultural Mathematics


Author: David Nelson,George Gheverghese Joseph,Julian Williams
Publisher: Oxford University Press, USA
ISBN: N.A
Category: Education
Page: 228
View: 2992

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The history of mathematics is one of creation and discovery in many parts of the world, and yet few people realize that Pythagoras' Theorem was known to the Babylonians a thousand years before the Greeks. Similarly, Pascal's Triangle of 1645 was actually used in practical ways much earlier in China. Indeed, there is a rich field of African, Middle Eastern, and Asian mathematics that is often ignored in the teaching of the subject. Mathematics, then, is an international language and field of study that knows no barriers between race, culture, or creed. How can we exploit this rich heritage not only to improve the teaching of mathematics, but to prepare our children for life in a multicultural society? This pioneering book is the first to explore ways of helping schoolchildren understand the universality of mathematics, and at the same time making it a more enjoyable, relevant, and rewarding enterprise. Multicultural Mathematics brings together the experience of three well-known teachers and researchers who offer suggestions and guidance for an important new approach to education. Written for parents, teachers, and administrators, and with technical mathematics kept to a minimum, this book discusses the theories behind multicultural mathematics, shows how this method can be applied within the core of any elementary curriculum, and explores the educational and social benefits of this new approach to teaching mathematics.

Mathematics in India


Author: Kim Plofker
Publisher: Princeton University Press
ISBN: 9780691120676
Category: History
Page: 357
View: 7783

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Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning. Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. Mathematics in India provides a rich and complex understanding of the Indian mathematical tradition. **Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (Interdisciplinary Science Reviews 28, 2003, 1-13).

Mathematics Elsewhere

An Exploration of Ideas Across Cultures
Author: Marcia Ascher
Publisher: Princeton University Press
ISBN: 0691187649
Category: Mathematics
Page: N.A
View: 9581

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Mathematics Elsewhere is a fascinating and important contribution to a global view of mathematics. Presenting mathematical ideas of peoples from a variety of small-scale and traditional cultures, it humanizes our view of mathematics and expands our conception of what is mathematical. Through engaging examples of how particular societies structure time, reach decisions about the future, make models and maps, systematize relationships, and create intriguing figures, Marcia Ascher demonstrates that traditional cultures have mathematical ideas that are far more substantial and sophisticated than is generally acknowledged. Malagasy divination rituals, for example, rely on complex algebraic algorithms. And some cultures use calendars far more abstract and elegant than our own. Ascher also shows that certain concepts assumed to be universal--that time is a single progression, for instance, or that equality is a static relationship--are not. The Basque notion of equivalence, for example, is a dynamic and temporal one not adequately captured by the familiar equal sign. Other ideas taken to be the exclusive province of professionally trained Western mathematicians are, in fact, shared by people in many societies. The ideas discussed come from geographically varied cultures, including the Borana and Malagasy of Africa, the Tongans and Marshall Islanders of Oceania, the Tamil of South India, the Basques of Western Europe, and the Balinese and Kodi of Indonesia. This book belongs on the shelves of mathematicians, math students, and math educators, and in the hands of anyone interested in traditional societies or how people think. Illustrating how mathematical ideas play a vital role in diverse human endeavors from navigation to social interaction to religion, it offers--through the vehicle of mathematics--unique cultural encounters to any reader.

Numbers

Their History and Meaning
Author: Graham Flegg
Publisher: Courier Corporation
ISBN: 0486166511
Category: Mathematics
Page: 304
View: 6066

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Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

Poetry of the Universe


Author: Robert Osserman
Publisher: Anchor
ISBN: 0307790584
Category: Science
Page: 224
View: 7879

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In the bestselling literary tradition of Lewis Thomas's Lives of a Cell and James Watson's The Double Helix, Poetry of the Universe is a delightful and compelling narrative charting the evolution of mathematical ideas that have helped to illuminate the nature of the observable universe. In a richly anecdotal fashion, the book explores teh leaps of imagination and vision in mathematics that have helped pioneer our understanding of the world around us.

Studies in the History of Indian Mathematics


Author: C. S. Seshadri
Publisher: Springer
ISBN: 9386279495
Category: Mathematics
Page: 404
View: 9103

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This volume is the outcome of a seminar on the history of mathematics held at the Chennai Mathematical Institute during January-February 2008 and contains articles based on the talks of distinguished scholars both from the West and from India. The topics covered include: (1) geometry in the oulvasatras; (2) the origins of zero (which can be traced to ideas of lopa in Paoini's grammar); (3) combinatorial methods in Indian music (which were developed in the context of prosody and subsequently applied to the study of tonal and rhythmic patterns in music); (4) a cross-cultural view of the development of negative numbers (from Brahmagupta (c. 628 CE) to John Wallis (1685 CE); (5) Kunnaka, Bhavana and Cakravala (the techniques developed by Indian mathematicians for the solution of indeterminate equations); (6) the development of calculus in India (covering the millennium-long history of discoveries culminating in the work of the Kerala school giving a complete analysis of the basic calculus of polynomial and trigonometrical functions); (7) recursive methods in Indian mathematics (going back to Paoini's grammar and culminating in the recursive proofs found in the Malayalam text Yuktibhaua (1530 CE)); and (8) planetary and lunar models developed by the Kerala School of Astronomy. The articles in this volume cover a substantial portion of the history of Indian mathematics and astronomy. This book will serve the dual purpose of bringing to the international community a better perspective of the mathematical heritage of India and conveying the message that much work remains to be done, namely the study of many unexplored manuscripts still available in libraries in India and abroad.

Women of mathematics

a biobibliographic sourcebook
Author: Louise S. Grinstein
Publisher: Greenwood Pub Group
ISBN: N.A
Category: Biography & Autobiography
Page: 292
View: 4165

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"A unique resource. Each of the 43 articles contains a biography, a summary of achievements, and a bibliography of works by and about the woman mathematician. . . . The articles are well written and the bibliographies appear to include all the major works by or about the biographees. Numerous appendixes and indexes enhance the value of this bibliography. This very thorough reference is highly recommended for all libraries." Choice "...a valuable collection, with most of the biographies proving entertaining as well as educational." Library Journal

Women in Mathematics


Author: Lynn M. Osen
Publisher: MIT Press
ISBN: 9780262650090
Category: Biography & Autobiography
Page: 185
View: 9404

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Examines the lives and scholarly endeavors of women who have profoundly affected mathematical thought since antiquity