# Download Ebook Free Mathematical Achievements Of Pre-modern Indian Mathematicians

## Mathematical Achievements of Pre-modern Indian Mathematicians

Publisher : Newnes

Release Date : 2012

Category : Mathematics

Total pages :743

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Mathematics in India has a long and impressive history. Presented in chronological order, this book discusses mathematical contributions of Pre-Modern Indian Mathematicians from the Vedic period (800 B.C.) to the 17th Century of the Christian era. These contributions range across the fields of Algebra, Geometry and Trigonometry. The book presents the discussions in a chronological order, covering all the contributions of one Pre-Modern Indian Mathematician to the next. It begins with an overview and summary of previous work done on this subject before exploring specific contributions in exemplary technical detail. This book provides a comprehensive examination of pre-Modern Indian mathematical contributions that will be valuable to mathematicians and mathematical historians. Contains more than 160 original Sanskrit verses with English translations giving historical context to the contributions Presents the various proofs step by step to help readers understand Uses modern, current notations and symbols to develop the calculations and proofs

## Mathematics in India

Publisher : Princeton University Press

Release Date : 2009-01-18

Category : History

Total pages :357

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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).

## A Passage to Infinity

Publisher : SAGE Publications India

Release Date : 2009-12-10

Category : Mathematics

Total pages :236

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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.

## Collected Papers of Srinivasa Ramanujan

Publisher : Cambridge University Press

Release Date : 2015-12-03

Category : Mathematics

Total pages :392

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Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887-1920), with editorial contributions from G. H. Hardy (1877-1947). Detailed notes are incorporated throughout and appendices are also included. This book will be of value to anyone with an interest in the works of Ramanujan and the history of mathematics.

## Studies in the History of Indian Mathematics

Publisher : Springer

Release Date : 2010-08-15

Category : Mathematics

Total pages :404

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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.

## How Europe Made the Modern World

Publisher : Bloomsbury Publishing

Release Date : 2019-10-03

Category : History

Total pages :248

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One thousand years ago, a traveler to Baghdad or the Chinese capital Kaifeng would have discovered a vast and flourishing city of broad streets, spacious gardens, and sophisticated urban amenities; meanwhile, Paris, Rome, and London were cramped and unhygienic collections of villages, and Europe was a backwater. How, then, did it rise to world preeminence over the next several centuries? This is the central historical conundrum of modern times. How Europe Made the Modern World draws upon the latest scholarship dealing with the various aspects of the West's divergence, including geography, demography, technology, culture, institutions, science and economics. It avoids the twin dangers of Eurocentrism and anti-Westernism, strongly emphasizing the contributions of other cultures of the world to the West's rise while rejecting the claim that there was nothing distinctive about Europe in the premodern period. Daly provides a concise summary of the debate from both sides, whilst also presenting his own provocative arguments. Drawing on a wide range of primary and secondary sources, and including maps and images to illuminate key evidence, this book will inspire students to think critically and engage in debates rather than accepting a single narrative of the rise of the West. It is an ideal primer for students studying Western Civilization and World History courses.

## Geometry in Ancient and Medieval India

Publisher : Motilal Banarsidass Publ.

Release Date : 1999

Category : Geometry

Total pages :277

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This book is a geometrical survey of the Sanskrit and Prakrt scientific and quasi-scientific literature of India, beginning with the Vedic literature and ending with the early part of the 17th century. It deals in detail with the Sulbasutras in the Vedic literature, with the mathematical parts of Jaina Canonical works and of the Hindu Siddhantas and with the contributions to geometry made by the astronomer mathematicians Aryabhata I & II, Sripati, Bhaskara I & II, Sangamagrama Madhava, Paramesvara, Nilakantha, his disciples and a host of others. The works of the mathematicians Mahavira, Sridhara and Narayana Pandita and the Bakshali Manuscript have also been studied. The work seeks to explode the theory that the Indian mathematical genius was predominantly algebraic and computational and that it eschewed proofs and rationales. There was a school in India which delighted to demonstrate even algebraical results geometrically. In their search for a sufficiently good approximation for the value of pie Indian mathematicians had discovered the tool of integration. Which they used equally effectively for finding the surface area and volume of a sphere and in other fields. This discovery of integration was the sequel of the inextricable blending of geometry and series mathematics.

## The Mathematics of India

Publisher : Springer

Release Date : 2018-09-19

Category : Mathematics

Total pages :441

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This book identifies three of the exceptionally fruitful periods of the millennia-long history of the mathematical tradition of India: the very beginning of that tradition in the construction of the now-universal system of decimal numeration and of a framework for planar geometry; a classical period inaugurated by Aryabhata’s invention of trigonometry and his enunciation of the principles of discrete calculus as applied to trigonometric functions; and a final phase that produced, in the work of Madhava, a rigorous infinitesimal calculus of such functions. The main highlight of this book is a detailed examination of these critical phases and their interconnectedness, primarily in mathematical terms but also in relation to their intellectual, cultural and historical contexts. Recent decades have seen a renewal of interest in this history, as manifested in the publication of an increasing number of critical editions and translations of texts, as well as in an informed analytic interpretation of their content by the scholarly community. The result has been the emergence of a more accurate and balanced view of the subject, and the book has attempted to take an account of these nascent insights. As part of an endeavour to promote the new awareness, a special attention has been given to the presentation of proofs of all significant propositions in modern terminology and notation, either directly transcribed from the original texts or by collecting together material from several texts.

## From Zero to Infinity

Publisher : CRC Press

Release Date : 2006-01-16

Category : Mathematics

Total pages :208

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From Zero to Infinity is a combination of number lore, number history, and sparkling descriptions of the simply stated but exceedingly difficult problems posed by the most ordinary numbers that first appeared in 1955 and has been kept in print continuously ever since. With the fifth edition this classic has been updated to report on advances in num

## Mathematics and Its History

Publisher : Springer Nature

Release Date : 2020-11-07

Category : Mathematics

Total pages :400

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This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

## Gaṇitānanda

Publisher : Springer Nature

Release Date : 2019-11-08

Category : Mathematics

Total pages :639

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This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses.

## A History of Mathematics

Publisher : OUP Oxford

Release Date : 2013-02-21

Category : Mathematics

Total pages :296

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A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

## Contributions to the History of Indian Mathematics

Publisher : Springer

Release Date : 2005-10-15

Category : Mathematics

Total pages :296

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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.

## Harmonic Analysis on Semisimple Lie Groups

Publisher : Unknown

Release Date : 1969

Category : Harmonic analysis

Total pages :31

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## Lost Discoveries

Publisher : Simon and Schuster

Release Date : 2010-05-11

Category : Science

Total pages :464

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Lost Discoveries, Dick Teresi's innovative history of science, explores the unheralded scientific breakthroughs from peoples of the ancient world -- Babylonians, Egyptians, Indians, Africans, New World and Oceanic tribes, among others -- and the non-European medieval world. They left an enormous heritage in the fields of mathematics, astronomy, cosmology, physics, geology, chemistry, and technology. The mathematical foundation of Western science is a gift from the Indians, Chinese, Arabs, Babylonians, and Maya. The ancient Egyptians developed the concept of the lowest common denominator, and they developed a fraction table that modern scholars estimate required 28,000 calculations to compile. The Babylonians developed the first written math and used a place-value number system. Our numerals, 0 through 9, were invented in ancient India; the Indians also boasted geometry, trigonometry, and a kind of calculus. Planetary astronomy as well may have begun with the ancient Indians, who correctly identified the relative distances of the known planets from the sun, and knew the moon was nearer to the earth than the sun was. The Chinese observed, reported, dated, recorded, and interpreted eclipses between 1400 and 1200 b.c. Most of the names of our stars and constellations are Arabic. Arabs built the first observatories. Five thousand years ago, the Sumerians said the earth was circular. In the sixth century, a Hindu astronomer taught that the daily rotation of the earth on its axis provided the rising and setting of the sun. Chinese and Arab scholars were the first to use fossils scientifically to trace earth's history. Chinese alchemists realized that most physical substances were merely combinations of other substances, which could be mixed in different proportions. Islamic scholars are legendary for translating scientific texts of many languages into Arabic, a tradition that began with alchemical books. In the eleventh century, Avicenna of Persia divined that outward qualities of metals were of little value in classification, and he stressed internal structure, a notion anticipating Mendeleyev's periodic chart of elements. Iron suspension bridges came from Kashmir, printing from India; papermaking was from China, Tibet, India, and Baghdad; movable type was invented by Pi Sheng in about 1041; the Quechuan Indians of Peru were the first to vulcanize rubber; Andean farmers were the first to freeze-dry potatoes. European explorers depended heavily on Indian and Filipino shipbuilders, and collected maps and sea charts from Javanese and Arab merchants. The first comprehensive, authoritative, popularly written, multicultural history of science, Lost Discoveries fills a crucial gap in the history of science.