The mathematics of India : concepts, methods, connections / P.P. Divakaran.

Format:

Book

Author/Creator:

Divakaran, P. P., author.

Series:

Sources and studies in the history of mathematics and physical sciences

Sources and studies in the history of mathematics and physical sciences.

Language:

English

Subjects (All):

Mathematics--India--History.

Mathematics.

History.

India.

Mathematics--History.

Mathematics--Study and teaching.

Genre:

History.

Physical Description:

xi, 441 pages : illustrations ; 24 cm.

Place of Publication:

Singapore : Springer ; New Dehli : Hindustan Book Agency, [2018].

Summary:

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 highlights 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 translation 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.

Contents:

I. Beginnings

Background : culture and language

Vedic geometry

Antecedents? Mathematics in the Indus Valley

Decimal numbers

Numbers in the vedic literature

II. The aryabhatan revolution

From 500 BCE to 500 CE

The mathematics of the Gaṇitapāda

From brahmagupta to bhaskara II to narayana

III. Madhava and the invention of calculus

The nila phenomenon

Nila mathematics

general survey

The (pie symbol) series

The sine and cosine series

The (pie symbol) series revisited : algebra in analysis

IV. Connections

What is Indian about the mathematics of India?

What is Indian...? The question of proofs

Upasaṃhāra.

Notes:

Includes bibliographical references (pages 423-426) and index.

Other Format:

Online version: Divakaran, P. P. Mathematics of India.

ISBN:

9811317739

9789811317736

OCLC:

1042083302