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Studies in Indian Mathematics and Astronomy
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...
Gaṇitānanda
This book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses.
Tantrasaṅgraha of Nīlakaṇṭha Somayājī
Tantrasangraha, composed by the renowned Kerala astronomer Nīlakantha Somayājī (c.1444-1545 AD) ranks along with Āryabhatīya of Āryabhata and Siddhāntaśiromani of Bhāskarācārya as one of the major works which significantly influenced further work on astronomy in India. One of the distinguishing features is the introduction of a major revision of the traditional Indian planetary model. Nīlakantha arrived at a unified theory of planetary latitudes and a better formulation of the equation of centre for the interior planets (Mercury and Venus) than was previously available. In preparing the translation and explanatory notes, K. Ramasubramanian and M. S. Sriram have used authentic Sanskrit editions of Tantrasangraha by Surand Kunjan Pillai and K V Sarma. All verses have been translated into English, which have been supplemented with detailed explanations including all necessary mathematical relations, illustrative examples, figures and tables using modern mathematical notation.
Karaṇapaddhati of Putumana Somayājī
This book is an important text of the Kerala school of astronomy and mathematics, probably composed in the 16th century. In the Indian astronomical tradition, the karaṇa texts are essentially computational manuals, and they often display a high level of ingenuity in coming up with simplified algorithms for computing planetary longitudes and other related quantities. Karaṇapaddhati, however, is not a karaṇa text. Rather, it discusses the paddhati or the rationale for arriving at suitable algorithms that are needed while preparing a karaṇa text for a given epoch. Thus the work is addressed not to the almanac maker but to the manual maker. Karaṇapaddhati presents the theoretical basis...
Energy-Efficient Modular Exponential Techniques for Public-Key Cryptography
Cryptographic applications, such as RSA algorithm, ElGamal cryptography, elliptic curve cryptography, Rabin cryptosystem, Diffie -Hellmann key exchange algorithm, and the Digital Signature Standard, use modular exponentiation extensively. The performance of all these applications strongly depends on the efficient implementation of modular exponentiation and modular multiplication. Since 1984, when Montgomery first introduced a method to evaluate modular multiplications, many algorithmic modifications have been done for improving the efficiency of modular multiplication, but very less work has been done on the modular exponentiation to improve the efficiency. This research monograph addresses...
Astronomy in India: A Historical Perspective
India has a strong and ancient tradition of astronomy, which seamlessly merges with the current activities in Astronomy and Astrophysics in the country. While the younger generation of astronomers and students are reasonably familiar with the current facilities and the astronomical research, they might not have an equally good knowledge of the rich history of Indian astronomy. This particular volume, brought out as a part of the Platinum Jubilee Celebrations of Indian National Science Academy, concentrates on selected aspects of historical development of Indian astronomy in the form of six invited chapters. Two of the chapters – by Balachandra Rao and M.S. Sriram – cover ancient astronomy and the development of calculus in the ancient Kerela text Yuktibhasa. The other four chapters by B.V. Sreekantan, Siraj Hasan, Govind Swarup and Jayant Narlikar deal with the contemporary history of Indian astronomy covering space astronomy, optical astronomy, radio astronomy and developments in relativistic astrophysics. These chapters, written by experts in the field, provide an in-depth study of the subject and make this volume quite unique.
MVT: A Most Valuable Theorem
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of ca...
500 Years of Tantrasangraha
`Tantrasangraha` By The Renowned Kerala Astronomer Nilakantha Somayaji (C. 1444-1545 Ad) Ranks Along With `Aryabhatiya` Of Aryabhata And Siddhantasiromani (C. 1150 Ad) Of Bhaskaracharya As One Of The Major Works Which Significantly Influenced All Further Work On Astronomy In India.
The Great Mathematicians of Bharat
"The Great Mathematicians of Bharat" emerges as a seminal work, aligning perfectly with the vision of the National Education Policy (NEP) 2020, which emphasizes the integration and appreciation of Indian Knowledge Systems (IKS) in contemporary education. This book meticulously documents the rich legacy of India's mathematical geniuses, serving as a crucial resource in rekindling interest and respect for Bharat's profound mathematical traditions. It underscores the symbiotic relationship between cultural ethos and scientific inquiry, highlighting how Indian mathematicians not only contributed to the field of mathematics but also how their work was deeply interwoven with Hindu spiritual and cultural practices. By chronicling the journey from ancient sages to modern masters, the book provides a comprehensive view of the evolution of mathematical thought in Bharat, thus fulfilling NEP 2020's objective of integrating indigenous knowledge with modern academic frameworks. In doing so, it not only educates but also inspires, setting a precedent for future academic endeavours to explore and celebrate India's rich intellectual heritage.
