The Spread of Indian Mathematics

We find the use of mathematics from the early Vedic age. Śulbasūtras (9 th c. B.C. -5 th c. B.C.), written specially for making alters (vedis) for the rituals of Hindus, are the manuals of geometric constructions which could not have come into existence overnight. It seems more probable that Indian geometry developed gradually into the Śulvasūtra stage with the intervening links buried in the sands of time. Āryabhata I (475A.D.), Brahmagupta (7 th century) and Bhāskarācārya (1150 A.D.) did works in many fields of mathematics which were applied in many fields including astronomy and geography. Brahmagupta's theorems on cyclic quadrilaterals are the great achievements in the mathematical history of India. Mathematicians from Kerala added more advancement in mathematics and broke the finite barrier and soared to infinite. Their infinite series expansions may have anticipated other mathematicians to work on that field. Because of their works, the period between 13 th and 18 th century A.D. is known as the golden age of Indian mathematics. Pingalacchandasūtram is a book related to prosody in Sanskrit but it uses some advanced mathematical expressions which may attract the interest of a mathematician.

Knowledge Traditions & Practices of India, 2013

A module for the CBSE course "Knowledge Traditions & Practices of India", published in a textbook by the same name, Kapil Kapoor and Michel Danino, (eds), Vol. 1, for Class XI, CBSE, New Delhi, 2013

Pedagogical Research

The educationists and the statesmen of different eras have casted mathematics education in different forms, and it has swayed to and from the elites to the commoners several times. The vision of the educationists always took tolls on mathematics curriculum, which survived the maximum change during the past one century. Several unorganized or partially organized ventures of mathematics education planning were seen in the pre-colonial era whereas the colonial period displayed some extremely organized, target-oriented decisions regarding the education system as a whole, taking mathematics in and out of focus. In this article, we have focused on the change in mathematics curriculum at the secondary school level in India.

Mathematics research in India, as reflected by papers indexed in Mathsci 1990 and 1994, is quantified and mapped. There were 1319 papers originating in India and indexed in the!990disc of Mathsci CD-ROM version, and 1391 papers indexed in 1994. Of these 2710 papers, 2549 had appeared in 467 journals, 221 of which were indexed in Journal Citation Reports 1994. Indian researchers had published 999 papers in these two years in 62 Indian journals, 503 papers in 108 US journals, 254 papers in 40 journals from the Netherlands, and 155 papers in 42 British journals. 188 institutions located in 110 cities/towns and 23 states/union territories had contributed to India's research output indexed in Mathsci, although only three have contributed more than a hundred papers in the two years, and another nine had contributed 50 or more papers. Academic institutions had published 87% of all papers and central government funded research councils and departments accounted for 12.6%. Four cities, viz. Calcutta, New Delhi, Bombay, and Madras had published more than 200 papers each in the two years. Five states, viz. West Bengal, Uttar Pradesh, Maharashtra, Tamil Nadu, and Delhi had published more than 250 papers each. More than 53% of journal papers were published in journals not indexed in Journal Citation Reports. Only 81 papers had appeared in journals of impact factor greater than 2.000, and these are mostly physics journals. Of the 61 subfields in Mathsci, Indian researchers had been most active in Statistics, General topolgy, Quantum theory, and Special functions. India has a high activity index for Special functions and General topology and a moderately high activity index for Statistics, Integral transforms and Operational calculus, and Sequences, series and summability. The activity is low in Prtial differential equations, Ordinary differential equations, Numerical analysis, K-theory, and Computer science. The future of mathematics in India seems to rest with DAE, TIFR and ISI. Universities seem to be losing momentum.

Mathematics in India , 2014

arXiv: History and Philosophy of Physics, 2015

Mathematics is probably the only subject that can be classified both as art as well as science - former, because it is not constrained by the real world and latter because it is a logical system with precisely defined rules as well as primitives that lead to unambiguous nontrivial theorems. Indian (and of Indian origin) mathematicians have continued to do seminal work till present times, culminating in Manjul Bhargava receiving the Fields Medal last year. In such fabulous times, a non-mathematician ponders about the nature of mathematics, and revisits the question: why are fundamental laws of Nature inherently mathematical?

With my roots in a rural based agriculture family of simple people of our country, where the following preachings: (i) “सर्वे भवन्तु सुखिनः सर्वे सन्तु निरामया ! सर्वे भद्राणि पश्यन्तु, मा कश्चिद दुःख-भाग भवेत् !!” (Be all happy and free from maladies. Let all witness nice events and none be ever miserable.) (ii) “सम शीतल नहिं त्यागहिं नीती ! सरल सुभाउ, सबहिं संग प्रीती !!” (Behave uniformly and coolly without setting aside morality. Maintaining simplicity, extend your affection to all.) (iii) "बड़े भये तो क्या भये, जैसे पेड़ खजूर ! पंक्षी को छाया नहीं, फल लागैं अति दूर !!" (Attaining heights like a palm tree becomes meaningless as the latter provides no shelter even to a bird and bears the fruits not in easy reach.) (iv) “रहिमन देखि बड़ेन को लघु न दीजिये डारि ! जहाँ काम आवै सुई काह करै तरवारि !!” [Do not underestimate the contributions of insignificant people while admiring achievements of their counterparts. A (mighty) sword cannot be a substitute of a (tiny) needle.] could still be dominant, and the instructions received from my visionary father (though without alphabets due to his poor economic conditions after having lost his father at a tender age of 9) to respect everyone especially elder and of his social status, the roots of real socialism and fraternity were installed in me quite early. I have described such philosophy of these village folks in detail in the biography of my father [9]1. I detailed almost all the mathematics brethren, whom I met or heard about them, during my long service of 22 years put up at the Department of Mathematics, University of Allahabad, Allahabad in my another article “Mathematics and Mathematicians at Prayag (Allahabad)”, Lambert Academic Publishers, Saarbrücken (Germany), 2011, ISBN 978-3-8443-0102-1, also available on the internet [10], in the form of a saga. In the following, I endeavour mentioning all the faculty members who taught mathematics at UoA2, its constituent Colleges including present day’s MNNIT (earlier MLN Regional Engg. College), SHUATS (erstwhile Allahabad Agricultural Institute), HRI (earlier Mehta Research Institute) and teachers of V.S. Mehta P-G College, Bharwari, staying in Allahabad city. The list starts with the first Indian mathematician (Prof. Dr. Ganesh Prasad), who could be termed as the first mathematics researcher at least in North India [4], and ends up to the faculty members appointed till my stay at UoA (1985). The main contents are presented in four sections: first offering tributes to already gone noble souls, followed by untraceable ones, superannuated ones and, thereafter few those who are still in active service. In addition, the last three sections deal with the miscellaneous information, list of abbreviations used, references and the photo gallery. The brief information about their educational merit, the highest rank achieved (either at Allahabad or elsewhere, in case of migration), dates of joining / leaving the institution or the date / location of passing away or the present place of living etc. are given. In spite of my untiring and continued efforts in contacting over more than hundred people, hardly few of them responded to my call.

Journal of Emerging Technologies and Innovative Research (JETIR), 2019

This study examines the lack of Mathematics knowledge in two-year B.Ed. curriculum from the year 2015. Teachers-Educational Institutions can play a significant role in bringing changes to the Education System and can develop a Nation. Teacher Training Institute is a Teacher-Making Factory, which has been playing an important role in the formation of a nation and a nation for a long time. Here teachers of various pedagogy subjects are trained. For example-Bengali, Sanskrit, English, History, Geography, Education, Biology, Fine-Arts, Physical Education, Physics, Mathematics and Chemistry, etc. Mathematics is one of them. While studying Pedagogy on a specific subject in two year's Bed. Course, students also have to study other subjects and Pedagogics. In general two years B.Ed. courses can be divided into three categories, a) Theory Part, b) Practicum and c) Internship. This study focuses on the practical work and use of mathematical knowledge on the overview of two universities, one of which is WBSU and the other is WBUTTPA in West Bengal, India. The methodology of the study is a mixed type involving an interpretative, interview, observation and study secondary sources, like books, articles, journals, thesis, university news, expert opinion and websites etc. Finally, meaningful suggestions are offered.

2016

The existing studies on the origin and history of mathematical economics are euro-centric and cover only the past two centuries. It is intended to show that 1) mathematical economics has an ancient origin. Kautilya wrote The Arthashastra during the fourth century BCE and used discrete marginal analysis and combinatory rules to sharpen economic analysis. 2) It is indicated that in the West, image of mathematics has changed directly and that of economics indirectly as the theology/philosophy of the church changed. 3) It is claimed that in India the developments in both economics and mathematics have always been simple, secular and user-friendly to solve problems related to agriculture, construction, navigation and trade.

The article tells about the history of the formation of mathematics fabibibg and numbers in the state of ancient India. In the early days of the theme of Mecca, historical sources of the ancient Indian state of kadimgi were used.