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 Part III consists of articles by Bibhutibhusan Datta and Avadhesh Narayan Singh-which together constitute the third unpublished part of their History of Hindu Mathematics-that were revised and updated by Prof. Shukla. Parts IV and V consist of a number of important articles of Prof. Shukla on different aspects of Indian astronomy. Part VI includes some important reviews authored by him and a few reviews of his work. Given the sheer range and depth of Prof. Shukla's scholarship, this volume is essential reading for scholars seeking to deepen their understanding of the rich and varied contributions made by Indian mathematicians and astronomers.

Tantrasangraha, composed by the renowned Kerala astronomer N lakantha Somay j (c.1444-1545 AD) ranks along with ryabhat ya of ryabhata and Siddh nta iromani of Bh skar c rya 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. N lakantha 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.

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 karana 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. Karanapaddhati, however, is not a karana text. Rather, it discusses the paddhati or the rationale for arriving at suitable algorithms that are needed while preparing a karana text for a given epoch. Thus the work is addressed not to the almanac maker but to the manual maker. Karanapaddhati presents the theoretical basis for the vakya system, where the true longitudes of the planet are calculated directly by making use of certain auxiliary notions such as the khanda, mandala and dhruva along with tabulated values of changes in the true longitude over certain regular intervals which are expressed in the form of vakyas or mnemonic phrases. The text also discusses the method of vallyupasamhara, which is essentially a technique of continued fraction expansion for obtaining optimal approximations to the rates of motion of planets and their anomalies, involving ratios of smaller numbers. It also presents a new fast convergent series for which is not mentioned in the earlier works of the Kerala school. As this is a unique text presenting the rationale behind the vakya system and the computational procedures used in the karana texts, it would serve as a useful companion for all those interested in the history of astronomy. The authors have provided a translation of the text followed by detailed notes which explain all the computational procedures, along with their rationale, by means of diagrams and equations.

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 karana 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. Karanapaddhati, however, is not a karana text. Rather, it discusses the paddhati or the rationale for arriving at suitable algorithms that are needed while preparing a karana text for a given epoch. Thus the work is addressed not to the almanac maker but to the manual maker. Karanapaddhati presents the theoretical basis for the vakya system, where the true longitudes of the planet are calculated directly by making use of certain auxiliary notions such as the khanda, mandala and dhruva along with tabulated values of changes in the true longitude over certain regular intervals which are expressed in the form of vakyas or mnemonic phrases. The text also discusses the method of vallyupasamhara, which is essentially a technique of continued fraction expansion for obtaining optimal approximations to the rates of motion of planets and their anomalies, involving ratios of smaller numbers. It also presents a new fast convergent series for which is not mentioned in the earlier works of the Kerala school. As this is a unique text presenting the rationale behind the vakya system and the computational procedures used in the karana texts, it would serve as a useful companion for all those interested in the history of astronomy. The authors have provided a translation of the text followed by detailed notes which explain all the computational procedures, along with their rationale, by means of diagrams and equations.

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 third unpublished part of their History of Hindu Mathematics-that were revised and updated by Prof. Shukla. Parts IV and V consist of a number of important articles of Prof. Shukla on different aspects of Indian astronomy. Part VI includes some important reviews authored by him and a few reviews of his work. Given the sheer range and depth of Prof. Shukla's scholarship, this volume is essential reading for scholars seeking to deepen their understanding of the rich and varied contributions made by Indian mathematicians and astronomers.

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.

Ganita-yukti-bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva (c.1530) is a seminal text of the Kerala school of astronomy. It is composed in the Malayalam language and presents detailed yuktis or explanations and demonstrations for the results and processes of mathematical astronomy. The text, comprising fifteen chapters, is naturally divided into two parts, mathematics and astronomy, and purports to give an exposition of the techniques and theories employed in the computation of planetary motions as set forth in the great treatise Tantrasangraha (c.1500) of Nilakantha Somayaji. Even though the importance of Ganita-yukti-bhasa was brought to the attention of modern scholarship by C.M Whish in the 1830s, a critical edition of the entire Malayalam text is published here for the first time along with an English translation and detailed explanatory notes.