This should be the start of the narrative of Hindu History of Mathematics, a narrative yet to be told to the students and researchers all over the world.
With the anugraham of Devi Sarasvati, this course should be a resounding harbinger of a renaissance of a great civilization with a remarkable mathematical heritage. Chandogya Upanishad calls mathematics, rāśi (Śankara's commentary).
Kalyanaraman
Prof. M.D.Srinivas Centre for Policy Studies, Chennai.
Prof.M.S.Sriram University of Madras, Chennai 
Prof.K.Ramasubramanian IIT Bombay 
Mathematics in India - From Vedic Period to Modern Times (Video)COURSE OUTLINE Download Syllabus in PDF format Course Co-ordinated by IIT Bombay
The Course would cover the development of mathematical ideas and techniques , starting from the Vedic period to modern times. While the treatment would be historical, we would be focusing mainly on the mathematical contents of various texts. We would be covering topics such as –the discussion of numbers in the Vedas, details of construction of geometrical figures and altars as given in Sulvasutras, discovery of zero and the place value system, and also details of arithmetic, algebra, geometry, trigonometry and combinatorics, as discussed in the works of Aryabhata, Brahmagupta, Mahavira, Bhaskaracharya and Narayana Pandita. Development of ideas and techniques of calculus and spherical trigonometry as found in the Kerala school of astronomy and mathematics will also be discussed. Detailed proofs of mathematical results as contained in the famous workYuktibhasa will be presented. At the end of the course, we briefly sketch the development of mathematics in modern India , especially highlighting the workof Srinivasa Ramanujan which seems to be in continuation both in methods and philosophy, with several aspects of the older tradition of mathematics in India.
COURSE DETAIL
Lectures Topics
1. Introductory Overview (MDS)
2. Mathematics in the Vedas and Sulva Sutras 1 (KR)
3. Mathematics in the Vedas and Sulva Sutras 2 (KR)
4. Panini (MDS)
5. Pingala (MDS)
6. Mathematics in the Jaina Texts (KR)
7. Development of Place Value System (KR)
8. Aryabhatiya of Aryabhata 1(KR)
9. Aryabhatiya of Aryabhata 2(KR)
10. Aryabhata and Bhaskara I (KR)
11. Brahmasphutasiddhanta of Brahmagupta 1 (MSS)
12. Brahmasphutasiddhanta of Brahmagupta 2 (MSS)
13. Brahmasphutasiddhanta of Brahmagupta 3(KR)
14. Bakshali Manuscript (KR)
15. Ganitasarasangraha of Mahavira 1 (MSS)
16. Ganitasarasangraha of Mahavira 2 (MSS)
17. Ganitasarasangraha of Mahavira 3 (MSS)
18. Development of Combinatorics 1 (MDS)
19. Development of Combinatorics 2 (MDS)
20. Lilavati of Bhaskara II 1 (MSS)
21. Lilavati of Bhaskara II2 (MSS)
22. Lilavati of Bhaskara III3 (MSS)
23. Bijaganita of Bhaskara II 1 (MDS)
24. Bijaganita of Bhaskara II2(MDS)
25. Ganita Kaumudi of Narayana Pandita 1 (MSS)
26. Ganita Kaumudi of Narayana Pandita 2 (MSS)
27. Ganita Kaumudi of Narayana Pandita 3 (MDS)
28. Magic Squares 1 (KR)
29. Magic Squares 2 (KR)
30. Kerala School of Astronomy and Development of Calculus 1 (MDS)
31. Kerala School of Astronomy and Development of Calculus 2 (MDS)
32. Computation of Accurate Sine Tables (KR)
33. Trigonometry and Spherical Trigonometry 1 (MSS)
34. Trigonometry and Spherical Trigonometry 2 (MSS)
35. Trigonometry and Spherical Trigonometry 3 (MSS)
36. Proofs in Indian Mathematics 1(MDS)
37. Proofs in Indian Mathematics 2(KR)
38. Proofs in Indian Mathematics 3 (MDS)
39. Mathematics in Modern India 1(MDS)
40. Mathematics in Modern India 2 (MDS)
PREREQUISITES
• Mathematics at +2 level
• Desirable : Sanskrit as second language or Optional subject at the school level.
REFERENCES
1. 1.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 over Vols. 15, 18, 19, 27 and 28,1980-1984.
2. 2.C.N.Srinivasa Iyengar, History of Indian Mathematics, World Press, Calcutta, 1967.
3. 3.T.A.Saraswati Amma, Geometry in Ancient and Medieval India, Motilal Banarsidass, Varanasi, 1079.
4. 4.A.K.Bag, Mathematics in Ancient and Medieval India, Choukhambha, Varanasi, 1979.
5. 5.K.V.Sarma, K.Ramasubramanian, M.D.Srinivas and M.S.Sriram, Ganitayuktibhasa of Jyesthadeva : Rationales in Mathematical Astronomy , Vol.1. Mathematics, Vol.2. Astronomy, Hindustan Book Agency, New Delhi, 2008/2009 ; Springer Reprint, 2009.
ADDITIONAL READINGS
1. K.S.Shukla and K.V.Sarma,Aryabhatiya of Aryabhata, Edited, translated with explanatory notes, INSA, New Delhi, 1976.
2. H.T.Colebrooke,Classics of Indian Mathematics, Algebra, Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhascara, London, 1817; Reprint: Sharada Publishing House, Delhi, 2005.
3. M.Rangacarya,Ganitasarasangraha of Mahaviracarya, with Translation and notes, Govt. of Madras, Madras, 2012.
4. Paramananda Singh,Ganita Kaumudi of Narayana Pandita, Translation and notes in Ganita Bharati, New Delhi, Vols. 20-24 , 1998-2001.
5. G.G.Joseph,The Crest of the Peacock : The Non-European Roots of Mathematics, Penguin 1990, 3rd Ed, Princeton, 2011.
6. Kim Plofker,Mathematics in India, Princeton Univ. Press, 2009; Indian Reprint : Hindustan Book Agency, New Delhi, 2012.
7. G.G.Emch, M.D.Srinivas and R.Sridharan, Eds,Contributions to the History of Mathematics in India, Hindustan Book Agency, Delhi, 2005.
8. C.S.Seshadri Ed.,Studies in History of Indian Mathematics, Hindustan Book Agency, Delhi, 2011.
9. S.Balachandra Rao,Indian Mathematics and Astronomy : Some Landmarks , 3rd Edn., Bhavan's Gandhi Centre, Bangalore, 2004.
10. C.K.Raju,Cultural Foundations of Mathematics : the Nature of Mathematical Proof and the Transmission of the Calculus from Indian to Europe in the 16th c. CE, Pearson, Delhi, 2007.
11. K.Ramasubramanian and M.S.Sriram,Tantrasangraha of Nilakantha Somayaji, Hindustan Book Agency, 2011; Springer Reprint , 2011.
http://nptel.iitm.ac.in/syllabus/syllabus.php?subjectId=111101080
Mathematics in India - From Vedic Period to Modern Times (Video)
COURSE OUTLINE
The Course would cover the development of mathematical ideas and techniques , starting from the Vedic period to modern times. While the treatment would be historical, we would be focusing mainly on the mathematical contents of various texts. We would be covering topics such as –the discussion of numbers in the Vedas, details of construction of geometrical figures and altars as given in Sulvasutras, discovery of zero and the place value system, and also details of arithmetic, algebra, geometry, trigonometry and combinatorics, as discussed in the works of Aryabhata, Brahmagupta, Mahavira, Bhaskaracharya and Narayana Pandita. Development of ideas and techniques of calculus and spherical trigonometry as found in the Kerala school of astronomy and mathematics will also be discussed. Detailed proofs of mathematical results as contained in the famous workYuktibhasa will be presented. At the end of the course, we briefly sketch the development of mathematics in modern India , especially highlighting the workof Srinivasa Ramanujan which seems to be in continuation both in methods and philosophy, with several aspects of the older tradition of mathematics in India.
COURSE DETAIL
Lectures Topics
1. Introductory Overview (MDS)
2. Mathematics in the Vedas and Sulva Sutras 1 (KR)
3. Mathematics in the Vedas and Sulva Sutras 2 (KR)
4. Panini (MDS)
5. Pingala (MDS)
6. Mathematics in the Jaina Texts (KR)
7. Development of Place Value System (KR)
8. Aryabhatiya of Aryabhata 1(KR)
9. Aryabhatiya of Aryabhata 2(KR)
10. Aryabhata and Bhaskara I (KR)
11. Brahmasphutasiddhanta of Brahmagupta 1 (MSS)
12. Brahmasphutasiddhanta of Brahmagupta 2 (MSS)
13. Brahmasphutasiddhanta of Brahmagupta 3(KR)
14. Bakshali Manuscript (KR)
15. Ganitasarasangraha of Mahavira 1 (MSS)
16. Ganitasarasangraha of Mahavira 2 (MSS)
17. Ganitasarasangraha of Mahavira 3 (MSS)
18. Development of Combinatorics 1 (MDS)
19. Development of Combinatorics 2 (MDS)
20. Lilavati of Bhaskara II 1 (MSS)
21. Lilavati of Bhaskara II2 (MSS)
22. Lilavati of Bhaskara III3 (MSS)
23. Bijaganita of Bhaskara II 1 (MDS)
24. Bijaganita of Bhaskara II2(MDS)
25. Ganita Kaumudi of Narayana Pandita 1 (MSS)
26. Ganita Kaumudi of Narayana Pandita 2 (MSS)
27. Ganita Kaumudi of Narayana Pandita 3 (MDS)
28. Magic Squares 1 (KR)
29. Magic Squares 2 (KR)
30. Kerala School of Astronomy and Development of Calculus 1 (MDS)
31. Kerala School of Astronomy and Development of Calculus 2 (MDS)
32. Computation of Accurate Sine Tables (KR)
33. Trigonometry and Spherical Trigonometry 1 (MSS)
34. Trigonometry and Spherical Trigonometry 2 (MSS)
35. Trigonometry and Spherical Trigonometry 3 (MSS)
36. Proofs in Indian Mathematics 1(MDS)
37. Proofs in Indian Mathematics 2(KR)
38. Proofs in Indian Mathematics 3 (MDS)
39. Mathematics in Modern India 1(MDS)
40. Mathematics in Modern India 2 (MDS)
PREREQUISITES
• Mathematics at +2 level
• Desirable : Sanskrit as second language or Optional subject at the school level.
REFERENCES
1. 1.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 over Vols. 15, 18, 19, 27 and 28,1980-1984.
2. 2.C.N.Srinivasa Iyengar, History of Indian Mathematics, World Press, Calcutta, 1967.
3. 3.T.A.Saraswati Amma, Geometry in Ancient and Medieval India, Motilal Banarsidass, Varanasi, 1079.
4. 4.A.K.Bag, Mathematics in Ancient and Medieval India, Choukhambha, Varanasi, 1979.
5. 5.K.V.Sarma, K.Ramasubramanian, M.D.Srinivas and M.S.Sriram, Ganitayuktibhasa of Jyesthadeva : Rationales in Mathematical Astronomy , Vol.1. Mathematics, Vol.2. Astronomy, Hindustan Book Agency, New Delhi, 2008/2009 ; Springer Reprint, 2009.
ADDITIONAL READINGS
1. K.S.Shukla and K.V.Sarma,Aryabhatiya of Aryabhata, Edited, translated with explanatory notes, INSA, New Delhi, 1976.
2. H.T.Colebrooke,Classics of Indian Mathematics, Algebra, Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhascara, London, 1817; Reprint: Sharada Publishing House, Delhi, 2005.
3. M.Rangacarya,Ganitasarasangraha of Mahaviracarya, with Translation and notes, Govt. of Madras, Madras, 2012.
4. Paramananda Singh,Ganita Kaumudi of Narayana Pandita, Translation and notes in Ganita Bharati, New Delhi, Vols. 20-24 , 1998-2001.
5. G.G.Joseph,The Crest of the Peacock : The Non-European Roots of Mathematics, Penguin 1990, 3rd Ed, Princeton, 2011.
6. Kim Plofker,Mathematics in India, Princeton Univ. Press, 2009; Indian Reprint : Hindustan Book Agency, New Delhi, 2012.
7. G.G.Emch, M.D.Srinivas and R.Sridharan, Eds,Contributions to the History of Mathematics in India, Hindustan Book Agency, Delhi, 2005.
8. C.S.Seshadri Ed.,Studies in History of Indian Mathematics, Hindustan Book Agency, Delhi, 2011.
9. S.Balachandra Rao,Indian Mathematics and Astronomy : Some Landmarks , 3rd Edn., Bhavan's Gandhi Centre, Bangalore, 2004.
10. C.K.Raju,Cultural Foundations of Mathematics : the Nature of Mathematical Proof and the Transmission of the Calculus from Indian to Europe in the 16th c. CE, Pearson, Delhi, 2007.
11. K.Ramasubramanian and M.S.Sriram,Tantrasangraha of Nilakantha Somayaji, Hindustan Book Agency, 2011; Springer Reprint , 2011.
http://nptel.iitm.ac.in/syllabus/syllabus.php?subjectId=111101080
NPTEL COURSE ON MATHEMATICS IN INDIA: FROM VEDIC PERIOD TO MODERN TIMES (IIT MADRAS, MAY 15-28, 2013)
This Course proposes to give a detailed overview of the development of mathematics in India from the Vedic period to the modern times. While the treatment of the subject is historical, the focus will be mainly on the mathematical ideas and techniques discussed in the major texts dealing with mathematics in India. The purpose is to highlight the explicitly algorithmic and constructive approach that is characteristic of Indian mathematics, and showcase some of the extremely novel and interesting examples through which the subject is presented in the classic texts, for the benefit of the students, teachers and researchers in mathematics in India.
The first few lectures are being devoted to the development of mathematics in the ancient and early classical periods. They shall deal with the details of construction of geometrical figures and altars as given in the oldest textbooks of geometry, Śulvasūtras; the discovery of zero and the development of place value system; and the mathematical ideas found in the early Jaina texts. An introduction shall also be given to the recursive, algorithmic and symbolic techniques developed in the Indian grammatical tradition culminating in the seminal work of Pāõini, and the combinatorial ideas developed in the pioneering work of Piïgala on Sanskrit prosody.
A major part of the course is being devoted to the development of Indian mathematics in the later classical period (500 CE-1250 CE). This would include details of the mathematical ideas and techniques discussed in the classic texts of Āryabhaña (c.499), Bhāskara I (c.629), Brahmagupta (c.628) and Mahāvīra (c.850). By the time of Āryabhañīya, the Indian mathematicians had systematised most of the basic procedures of arithmetic, algebra, geometry and trigonometry that are generally taught in schools to-day, and many more that are more advanced (such as kuññaka and sine-tables) and are of importance in astronomy. The culmination of all these developments may be seen in the canonical works of Bhāskarācārya II (c.1150), Līlāvatī and Bījagaõita, which
will be discussed in considerable detail. The classical period also saw remarkable developments in combinatorial techniques, which are found in the texts of prosody and music, and some of them would be highlighted in the course.
An important feature of this course is the extensive coverage of developments in Indian
mathematics in the medieval period (c.1250-1750). This has indeed been made possible by the pioneering scholarly investigations carried out mainly in the recent decades. The seminal work Gaõitakaumudī of Nārāyaõa Paõóita (c.1356) will be discussed in detail, especially as it introduces several new ideas and techniques in arithmetic, algebra and geometry, and also devotes an entire chapter each to novel topics such as factorisation, combinatorics and magic squares. The other most important development in the medieval period is the work of the Kerala School (c.1350-1825), pioneered by Mādhava (c.1350-1420). Particularly noteworthy are their contributions to the development of calculus and spherical trigonometry, and they will be
discussed along with details of the proofs contained in the famous Malayalam work Yuktibhāùā.
While discussing the tradition of proofs (upapatti) in Indian mathematics, some of the crucial aspects in which it differs from the Greco-European tradition shall be indicated.
The final couple of lectures are devoted to the development of mathematics in India in the modern period. Unlike the continued and almost uninterrupted developments seen over the previous two millennia, the later part of the eighteenth and much of the nineteenth century saw a serious erosion of traditional learning in India. It is only with the onset of the 20th century that some work in modern sciences and mathematics got initiated. However, soon there arose a natively grown genius, Srinivasa Ramanujan (1887-1920), whose work continues to have a major impact even in contemporary times. A brief introduction shall be given to the life and work of Ramanujan indicating how his work can be viewed to be clearly in continuation, particularly in methodology and philosophy, with the earlier tradition of mathematics in India. While summarizing the significant developments in mathematics in post-Independent India, a brief mention shall also be made of the recent studies which seem to show a somewhat halting growth in mathematics (and scientific research) in India in the last few decades, especially in comparison with many other developing countries.
INSTRUCTORS
1. Prof. K. Ramasubramanian, Cell for Indian Science & Technology in Sanskrit, Dept of
Humanities, IIT Bombay, Mumbai 400076
2. Prof. M. S. Sriram, Dept of Theoretical Physics, University of Madras, Guindy Campus, Chennai 600025
3. Prof. M .D. Srinivas, Centre for Policy Studies, Mylapore, Chennai 600004
Pre-requisites: Mathematics at + 2 level, Basic Knowledge of Sanskrit
Desirable: Sanskrit as a Second Language or Optional subject at School Level
For further details on the course, please visit
http://nptel.iitm.ac.in/syllabus/syllabus.php?subjectId=111101080
Those desirous of attending the course may contact Prof. M. S. Sriram at
sriram.physics@gmail.com
Source: http://nptel.iitm.ac.in/syllabus/syllabus_pdf/111101080.pdf