Subject Code: HS4L014	Subject Name: Mathematics in India: Ancient to Modern Times	L-T-P: 3-0-0	Credit: 3
Pre-Requisite(s): Prior exposure is not required Objective of Course: A study of the evolution of mathematical concepts is one of the most engaging and fascinating topics, as it is tantamount to the study of some of the finest intellectual achievements of humanity. This course ‘Mathematics in India: From the Vedic to the Modern period’ aims to provide a glimpse of how various important mathematical ideas got evolved in India over several millennia. This would indeed be an eye-opener to most of the students of science and engineering, as they would get an opportunity to learn how some of the most fundamental concepts and ideas in mathematics--- starting from the decimal-place-value system to expressing a finite quantity in terms of an infinite series, as well as the foundations of calculus---got originated in India. Along with the technical aspects of mathematics, the course also aims to introduce in a balanced manner the primary source material (Sanskrit text) in which they have been expressed. This would give an idea as to how mathematics and its practice are deeply connected with culture. Suggested Books: NPTEL Lectures by M.D. Srinivas, M.S. Sriram and K. Ramasubramanian B. Datta and A.N. Singh, History of Hindu Mathematics 2 parts, Reprint, Bharatiya Kala Prakashan, New Delhi, 2004. Supplementary material revised by K.S. Shukla in issues of Indian Journal of History of Science, INSA, New Delhi, India (spread and over Vols.15, 18, 19, 27 and 28), 1980-1984, 2004 C.N. Srinivasa Iyengar, History of Indian Mathematics, World Press, Calcutta, 1967 T.A. Saraswati Amma, Geometry in Ancient and Medieval India, Motilal Banarsidass, Varanasi; Reprint 2007, 1979 A.K. Bag, Mathematics in Ancient and Medieval India, Choukhambha, Varanasi, 1979 K.V. Sarma, K.Ramasubramanian, M.D. Srinivas and M.S. Sriram, Ganitayuktibhasa of Jyesthadeva: Rationales in MathematicalAstronomy, Vol. 1. Mathematics, Vol.2. Astronomy, Hindustan Book Agency, New Delhi; Springer reprint, 2009., 2008/09 George Gheverghese Joseph, Indian Mathematics: Engaging with the world from Ancient to Modern times, World Scientific, 2016 K.S. Shukla and K.V. Sarma, Aryabhatiya of Aryabhata, edited, translated with explanatory notes, INSA, New Delhi, 1976 H.T. Colebrooke, Classics of Indian Mathematics, Algebra, Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhaskara, London: Reprint, Sharada Publishing House, Delhi, 2005., 1817 M. Rangacarya, Ganitasarasangraha of Mahaviracarya, with translation and notes, Govt. of Madras, 2012 Paramananda Singh, Ganita Kaumudi of Narayana Pandita, Translation and notes in Ganita Bharati, New Delhi, Vols. 20- 24, 1998-2001 G.G. Joseph, The Crest of the Peacock, The Non-European Roots of Mathematics, Penguin, 1990, 3rd Ed. Princeton, 2011, 1990 Kim Plofker, Mathematics in India, Princeton University Press; Indian Reprint, Hindustan Book Agency, New Delhi, 2012., 2009 G.G. Emch, M.D. Srinivas and R. Sridharan, Eds. Contributions to the History of Mathematics in India, Hindustan Book Agency, New Delhi., 2005 C.S. Seshadri, Ed. Studies in History of Indian Mathematics, Hindustan Book Agency, New Delhi., 2011 S. Balachandra Rao, Indian Mathematics and Astronomy: Some Landmarks, 3rd Edn., Bhavan's Gandhi Centre, Bangalore., 2004 P.P. Divakaran, The Mathematics of India: Concepts, Methods, Connections, Hindustan Book Agency, New Delhi., 2018

Subject Code: HS4L014

Subject Name: Mathematics in India: Ancient to Modern Times

L-T-P: 3-0-0

Credit: 3

Pre-Requisite(s): Prior exposure is not required

Objective of Course:

A study of the evolution of mathematical concepts is one of the most engaging and fascinating topics, as it is tantamount to the study of some of the finest intellectual achievements of humanity. This course ‘Mathematics in India: From the Vedic to the Modern period’ aims to provide a glimpse of how various important mathematical ideas got evolved in India over several millennia. This would indeed be an eye-opener to most of the students of science and engineering, as they would get an opportunity to learn how some of the most fundamental concepts and ideas in mathematics--- starting from the decimal-place-value system to expressing a finite quantity in terms of an infinite series, as well as the foundations of calculus---got originated in India. Along with the technical aspects of mathematics, the course also aims to introduce in a balanced manner the primary source material (Sanskrit text) in which they have been expressed. This would give an idea as to how mathematics and its practice are deeply connected with culture.

Suggested Books:

NPTEL Lectures by M.D. Srinivas, M.S. Sriram and K. Ramasubramanian
B. Datta and A.N. Singh, History of Hindu Mathematics 2 parts, Reprint, Bharatiya Kala Prakashan, New Delhi, 2004. Supplementary material revised by K.S. Shukla in issues of Indian Journal of History of Science, INSA, New Delhi, India (spread and over Vols.15, 18, 19, 27 and 28), 1980-1984, 2004
C.N. Srinivasa Iyengar, History of Indian Mathematics, World Press, Calcutta, 1967
T.A. Saraswati Amma, Geometry in Ancient and Medieval India, Motilal Banarsidass, Varanasi; Reprint 2007, 1979
A.K. Bag, Mathematics in Ancient and Medieval India, Choukhambha, Varanasi, 1979
K.V. Sarma, K.Ramasubramanian, M.D. Srinivas and M.S. Sriram, Ganitayuktibhasa of Jyesthadeva: Rationales in MathematicalAstronomy, Vol. 1. Mathematics, Vol.2. Astronomy, Hindustan Book Agency, New Delhi; Springer reprint, 2009., 2008/09
George Gheverghese Joseph, Indian Mathematics: Engaging with the world from Ancient to Modern times, World Scientific, 2016
K.S. Shukla and K.V. Sarma, Aryabhatiya of Aryabhata, edited, translated with explanatory notes, INSA, New Delhi, 1976
H.T. Colebrooke, Classics of Indian Mathematics, Algebra, Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhaskara, London: Reprint, Sharada Publishing House, Delhi, 2005., 1817
M. Rangacarya, Ganitasarasangraha of Mahaviracarya, with translation and notes, Govt. of Madras, 2012
Paramananda Singh, Ganita Kaumudi of Narayana Pandita, Translation and notes in Ganita Bharati, New Delhi, Vols. 20- 24, 1998-2001
G.G. Joseph, The Crest of the Peacock, The Non-European Roots of Mathematics, Penguin, 1990, 3rd Ed. Princeton, 2011, 1990
Kim Plofker, Mathematics in India, Princeton University Press; Indian Reprint, Hindustan Book Agency, New Delhi, 2012., 2009
G.G. Emch, M.D. Srinivas and R. Sridharan, Eds. Contributions to the History of Mathematics in India, Hindustan Book Agency, New Delhi., 2005
C.S. Seshadri, Ed. Studies in History of Indian Mathematics, Hindustan Book Agency, New Delhi., 2011
S. Balachandra Rao, Indian Mathematics and Astronomy: Some Landmarks, 3rd Edn., Bhavan's Gandhi Centre, Bangalore., 2004
P.P. Divakaran, The Mathematics of India: Concepts, Methods, Connections, Hindustan Book Agency, New Delhi., 2018