Chinese Mathematics in the Thirteenth Century
Chinese Mathematics in the Thirteenth Century

Author: Ulrich Libbrecht

Publisher: Courier Corporation

Published: 2005-01-01

Total Pages: 594

ISBN-13: 0486446190

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An exploration of the life and work of the thirteenth-century mathematician Ch'in, this fascinating book examines a range of mathematical issues that reflect Chinese life of a millennium ago. Its first part consists of four closely related studies of Ch'in and his work. The first study brings together what is known of the mathematician's life and of the history of his only extant work, the Shu-shu chiu-chang. Subsequent studies examine the entire range of mathematical techniques and problems found within Ch'in's book. The core of this book consists of an in-depth study of what modern mathematicians still refer to as the Chinese remainder theorem for the solution of indeterminate equations of the first degree. This was Ch'in's most original contribution to mathematics--so original that no one could correctly explain Ch'in's procedure until the early nineteenth century. This volume's concluding study unites information on artisanal, economic, administrative, and military affairs dispersed throughout Ch'in's writings, providing rare insights into thirteenth-century China.

A History of Chinese Mathematics
A History of Chinese Mathematics

Author: Jean-Claude Martzloff

Publisher: Springer

Published: 2007-08-17

Total Pages: 491

ISBN-13: 3540337830

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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.

Chinese Mathematics in the Thirteenth Century
Chinese Mathematics in the Thirteenth Century

Author: Ulrich Libbrecht

Publisher: MIT Press (MA)

Published: 1973

Total Pages: 596

ISBN-13:

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The essence of the book is its insight into Chinese thought and life, as revealed by the general concepts that emerge and interrelate and by the practical mathematical problems posed by Ch'in that tie into the everyday realities of his time.

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

Author: Victor J. Katz

Publisher: Princeton University Press

Published: 2007-08-05

Total Pages: 712

ISBN-13: 9780691114859

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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.

Fibonacci’s Liber Abaci
Fibonacci’s Liber Abaci

Author: Laurence Sigler

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 736

ISBN-13: 1461300797

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First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.

The Chinese Roots of Linear Algebra
The Chinese Roots of Linear Algebra

Author: Roger Hart

Publisher: JHU Press

Published: 2011-01-01

Total Pages: 304

ISBN-13: 0801899583

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A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts—the classic ancient Chinese mathematics text—and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards. By "cross multiplying" these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions. Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.

The Crisis of the 14th Century
The Crisis of the 14th Century

Author: Martin Bauch

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-12-16

Total Pages: 420

ISBN-13: 3110657961

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Pre-modern critical interactions of nature and society can best be studied during the so-called "Crisis of the 14th Century". While historiography has long ignored the environmental framing of historcial processes and scientists have over-emphasized nature's impact on the course of human history, this volume tries to describe the at times complex modes of the late-medieval relationship of man and nature. The idea of 'teleconnection', borrowed from the geosciences, describes the influence of atmospheric circulation patterns often over long distances. It seems that there were 'teleconnections' in society, too. So this volumes aims to examine man-environment interactions mainly in the 14th century from all over Europe and beyond. It integrates contributions from different disciplines on impact, perception and reaction of environmental change and natural extreme events on late Medieval societies. For humanists from all historical disciplines it offers an approach how to integrate written and even scientific evidence on environmental change in established and new fields of historical research. For scientists it demonstrates the contributions scholars from the humanities can provide for discussion on past environmental changes.