Studies in the History of Indian Mathematics
Studies in the History of Indian Mathematics

Author: C. S. Seshadri

Publisher: Springer

Published: 2010-08-15

Total Pages: 395

ISBN-13: 9386279495

DOWNLOAD EBOOK

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.

The Mathematics of India
The Mathematics of India

Author: P. P. Divakaran

Publisher: Springer

Published: 2018-09-19

Total Pages: 441

ISBN-13: 9811317747

DOWNLOAD EBOOK

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.

Studies in Indian Mathematics and Astronomy
Studies in Indian Mathematics and Astronomy

Author: Aditya Kolachana

Publisher: Springer

Published: 2019-05-29

Total Pages: 754

ISBN-13: 9811373264

DOWNLOAD EBOOK

This volume presents a collection of some of the seminal articles of Professor K. S. Shukla who made immense contributions to our understanding of the history and development of mathematics and astronomy in India. It consists of six parts: Part I constitutes introductory articles which give an overview of the life and work of Prof. Shukla, including details of his publications, reminiscences from his former students, and an analysis of his monumental contributions. Part II is a collection of important articles penned by Prof. Shukla related to various aspects of Indian mathematics. Part III consists of articles by Bibhutibhusan Datta and Avadhesh Narayan Singh—which together constitute the third unpublished part of their History of Hindu Mathematics—that were revised and updated by Prof. Shukla. Parts IV and V consist of a number of important articles of Prof. Shukla on different aspects of Indian astronomy. Part VI includes some important reviews authored by him and a few reviews of his work. Given the sheer range and depth of Prof. Shukla’s scholarship, this volume is essential reading for scholars seeking to deepen their understanding of the rich and varied contributions made by Indian mathematicians and astronomers.

Mathematics in India
Mathematics in India

Author: Kim Plofker

Publisher: Princeton University Press

Published: 2009-01-18

Total Pages: 386

ISBN-13: 9780691120676

DOWNLOAD EBOOK

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).

Contributions to the History of Indian Mathematics
Contributions to the History of Indian Mathematics

Author: Gerard G. Emch

Publisher: Springer

Published: 2005-10-15

Total Pages: 293

ISBN-13: 9386279258

DOWNLOAD EBOOK

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.

Leonhard Euler
Leonhard Euler

Author: Robert E. Bradley

Publisher: Elsevier

Published: 2007-03-20

Total Pages: 543

ISBN-13: 0080471293

DOWNLOAD EBOOK

The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment's most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world's best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler's life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler's philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler's innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science.- Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Writing the History of Mathematics: Its Historical Development
Writing the History of Mathematics: Its Historical Development

Author: Joseph W. Dauben

Publisher: Springer Science & Business Media

Published: 2002-09-23

Total Pages: 776

ISBN-13: 9783764361679

DOWNLOAD EBOOK

As an historiographic monograph, this book offers a detailed survey of the professional evolution and significance of an entire discipline devoted to the history of science. It provides both an intellectual and a social history of the development of the subject from the first such effort written by the ancient Greek author Eudemus in the Fourth Century BC, to the founding of the international journal, Historia Mathematica, by Kenneth O. May in the early 1970s.

The Bakhshālī Manuscript
The Bakhshālī Manuscript

Author: Takao Hayashi

Publisher: Groningen Oriental Studies

Published: 1995

Total Pages: 608

ISBN-13:

DOWNLOAD EBOOK

This volume offers a fresh translation of the Bakhshālī Manuscript. It presents the first English translation of the whole text based on a systematic study of linguistic peculiarities, and a mathematical commentary based on a comparative study of the Bakhshālī work and other Sanskrit mathematical texts.