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: 6918

"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: 3040

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: 2844

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: 8790

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: 9534

"... 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: 678

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.

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: 1391

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.

A History of Chinese Mathematics

Author: Jean-Claude Martzloff

Publisher: Springer

ISBN: 3540337830

Category: Mathematics

Page: 487

View: 2047

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.

The History of Mathematics: A Very Short Introduction

Author: Jacqueline Stedall

Publisher: OUP Oxford

ISBN: 0191633968

Category: Mathematics

Page: 144

View: 8997

Mathematics is a fundamental human activity that can be practised and understood in a multitude of ways; indeed, mathematical ideas themselves are far from being fixed, but are adapted and changed by their passage across periods and cultures. In this Very Short Introduction, Jacqueline Stedall explores the rich historical and cultural diversity of mathematical endeavour from the distant past to the present day. Arranged thematically, to exemplify the varied contexts in which people have learned, used, and handed on mathematics, she also includes illustrative case studies drawn from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Mathematics in India

Author: Kim Plofker

Publisher: Princeton University Press

ISBN: 9780691120676

Category: History

Page: 357

View: 6162

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).

Ethnomathematics

A Multicultural View of Mathematical Ideas

Author: Marcia Ascher

Publisher: Routledge

ISBN: 1351449508

Category: Mathematics

Page: 214

View: 6996

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.

Multicultural Mathematics

Author: David Nelson,George Gheverghese Joseph,Julian Williams

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Education

Page: 228

View: 1268

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 Elsewhere

An Exploration of Ideas Across Cultures

Author: Marcia Ascher

Publisher: Princeton University Press

ISBN: 0691187649

Category: Mathematics

Page: N.A

View: 6936

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: 883

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.

Women of mathematics

a biobibliographic sourcebook

Author: Louise S. Grinstein

Publisher: Greenwood Pub Group

ISBN: N.A

Category: Biography & Autobiography

Page: 292

View: 2764

"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: 5164

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

Sourcebook in the Mathematics of Medieval Europe and North Africa

Author: Victor J. Katz,Menso Folkerts,Barnabas Hughes,Roi Wagner,J. Lennart Berggren

Publisher: Princeton University Press

ISBN: 1400883202

Category: Mathematics

Page: 592

View: 7301

Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.

The Book

The Life Story of a Technology

Author: Nicole Howard

Publisher: Greenwood Publishing Group

ISBN: 9780313330285

Category: History

Page: 171

View: 3818

Introduces the history of the book, beginning with papyrus in ancient Egypt, through the development of the printing press, to current computer-based technologies, including its influence on societies and cultures around the world.

A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Author: Sarah P. Otto,Troy Day

Publisher: Princeton University Press

ISBN: 1400840910

Category: Science

Page: 744

View: 5895

Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available