Computation in Ancient India

Computation in Ancient India
Title Computation in Ancient India PDF eBook
Author T. R. N. Rao
Publisher
Pages
Release 2016-07
Genre
ISBN 9781988207124

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The material in this book presents an introduction to the Indian contributions to the science of computing. The book starts with an overview of Indian science. The next three chapters deal with the description of binary numbers, the Katapayadi notation and its equivalence to hashing that is used in computer systems, and the Panini-Backus form to describe a high-level computer language based on the ideas of the great grammarian Panini. The next two chapters describe some technical aspects of Panini's grammar and Indian logic. The Paninian structure (5th century BCE) has been shown to be equivalent to the Turing machine. The rise of mathematical logic in India took place centuries before its rediscovery in Europe. The next chapter shows how one needs ingenuity in decoding Indian texts. It is shown that Indian myths represent information regarding the motions of the planets. The last two chapters deal with cosmology and cognitive science.




Computing Science in Ancient India

Computing Science in Ancient India
Title Computing Science in Ancient India PDF eBook
Author Thammavarapu R. N. Rao
Publisher
Pages 128
Release 2000
Genre Computer science
ISBN

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Description: Not only the sign for zero, but also the binary number system, the ideas of metarules, algebraic transformation, recursion, hashing, mathematical logic, formal grammars, and high level language description arose first in India. Indian mathematical science had already reached dizzying heights about 2,500 years ago by the time of Panini and Pingala, considered by tradition to have been brothers. Panini's grammar for Sanskrit, which is equivalent in its computing power to the most powerful computing machine, has not yet been matched for any other language, while Pingala described the binary number system. This classic book of contributions by the leading scholars in the world presents an overview of these seminal contributions to computer science. It also includes chapters on models and computation in astronomy and cognitive science.




Cultures of Computation and Quantification in the Ancient World

Cultures of Computation and Quantification in the Ancient World
Title Cultures of Computation and Quantification in the Ancient World PDF eBook
Author Karine Chemla
Publisher Springer Nature
Pages 764
Release 2023-01-01
Genre Science
ISBN 3030983617

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This book sheds light on the variety of mathematical cultures in general. To do so, it concentrates on cultures of computation and quantification in the ancient world, mainly in ancient China, South Asia, and the Ancient Near East and offers case studies focused on numbers, quantities, and operations, in particular in relation to mathematics as well as administrative and economic activities. The various chapters focus on the different ways and contexts of shaping numbers and quantities, and on the procedures applied to them. The book places special emphasis on the processes of emergence of place-value number systems, evidenced in the three geographical areas under study All these features yield essential elements that will enable historians of mathematics to further capture the diversity of computation practices in their contexts, whereas previous historical approaches have tended to emphasize elements that displayed uniformity within “civilizational” blocks. The book includes editions and translations of texts, some of them published here for the first time, maps, and conventions for editions of ancient texts. It thereby offers primary sources and methodological tools for teaching and learning. The volume is aimed at historians and philosophers of science and mathematics, historians of the ancient worlds, historians of economics, sinologists, indologists, assyriologists, as well as undergraduate, graduate students and teachers in mathematics, the history and philosophy of science and mathematics, and in the history of ancient worlds.




Ancient Computing

Ancient Computing
Title Ancient Computing PDF eBook
Author Michael Woods
Publisher Twenty-First Century Books
Pages 98
Release 2000-01-01
Genre Juvenile Nonfiction
ISBN 9780822529972

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Discusses the methods of computation developed in various civilizations around the world, from prehistoric times up until the end of the Roman Empire.




Ancient Computing Technology

Ancient Computing Technology
Title Ancient Computing Technology PDF eBook
Author Mary B. Woods
Publisher Twenty-First Century Books
Pages 100
Release 2011-01-01
Genre Young Adult Nonfiction
ISBN 0761372717

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Did you know . . . • Ancient cultures measured time accurately with water clocks? • An engineer in the first century B.C. designed an odometer to calculate distance traveled? • People computed the first values of pi about four thousand years ago? Computing technology is as old as human society itself. The first humans on Earth used basic computing skills. They counted by carving tally marks in bone. They used body parts and basic tools to measure. Over the centuries, ancient peoples learned more about computing. People in the ancient Middle East used scales to measure goods for trading. The ancient Egyptians wrote textbooks including multiplication and division problems. The ancient Chinese developed an abacus for speedy calculations. Ancient Greeks made advances in geometry. What kinds of tools and techniques did ancient mathematicians use? Which of their inventions and discoveries have stood the test of time? And how did the ancients set the stage for our own modern computing? Learn more in Ancient Computing Technology.




Ancient Indian Leaps into Mathematics

Ancient Indian Leaps into Mathematics
Title Ancient Indian Leaps into Mathematics PDF eBook
Author B.S. Yadav
Publisher Springer Science & Business Media
Pages 230
Release 2011-01-20
Genre Mathematics
ISBN 0817646957

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This book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. Although the translations of some Sanskrit mathematical texts are available in the literature, Indian contributions are rarely presented in major Western historical works. Yet some of the well-known and universally-accepted discoveries from India, including the concept of zero and the decimal representation of numbers, have made lasting contributions to the foundation of modern mathematics. Through a systematic approach, this book examines these ancient mathematical ideas that were spread throughout India, China, the Islamic world, and Western Europe.




Contributions to the History of Indian Mathematics

Contributions to the History of Indian Mathematics
Title Contributions to the History of Indian Mathematics PDF eBook
Author Gerard G. Emch
Publisher Springer
Pages 293
Release 2005-10-15
Genre Mathematics
ISBN 9386279258

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This volume consists of a collection of articles based on lectures given by scholars from India, Europe and USA at the sessions on 'History of Indian Mathematics' at the AMS-India mathematics conference in Bangalore during December 2003. These articles cover a wide spectrum of themes in Indian mathematics. They begin with the mathematics of the ancient period dealing with Vedic Prosody and Buddhist Logic, move on to the work of Brahmagupta, of Bhaskara, and that of the mathematicians of the Kerala school of the classical and medieval period, and end with the work of Ramanaujan, and Indian contributions to Quantum Statistics during the modern era. The volume should be of value to those interested in the history of mathematics.