भारतीयगणितम् - सद्रत्नमाला- भाग १

Indian Mathematics has a glorious tradition of more than 2 millenia. Sadratnamala is a treatise in Samskrita written by Shankaravarma, an astronomer-mathematician of the Kerala school of mathematics, in 1819. This text is ideal for beginners to understand the basic terms and approach of Indian Mathematics. In this course, Dr. Chandrasekharan Raman explains the verses of first two chapters of the text in simple Samskrita, covering the basic operations and technical terms of the shastra.

**What will you gain from this course? (Key Benefits / Learning Outcomes):**

- Learn the Samskrita terms and definitions of 8 basic Mathematical operations - addition, subtraction, multiplication, division, finding squares, square roots, cubes and cube roots.
- Learn through examples the traditional method of carrying out these operations.
- Learn the terms used in ancient Indian texts for powers of 10 upto 10
^{17 } - Learn about many technical concepts and terms of Indian astronomy, such as divisions of time, divisions of a circle, units of distance, volume & weight, components of panchanga, etc.

**What are the materials/support you get?**

- Approximately 16 live classes, along with the video and audio recordings of the class which you can access anytime, from any device.
- PDFs of the presentations used in the class.
- Doubt clarifications through Email.

**What are the pre-requisites to get the best out of this course? (Eligibility)**

- Understand Spoken Samskritam.
- The students should have the knowledge of Samskritam upto the level of doing padanvaya of shlokas.
- Interest to understand the Indian Knowledge System.

Sadratnamala is an astronomical-mathematical treatise in Samskritam written by Shankaravarma in 1819.

Shankaravarma was an astronomer-mathematician of the Kerala school of mathematics, who lived in the late 18th - early 19th century CE. He was a younger prince in the principality of Katathanad in North Malabar of Kerala. He was known by the name ‘Appu Thampuran’ by the local people.

The book contains six chapters (prakaranas) which in turn cumulatively contain 212 verses. Chapters are referred as prakarana-s here.

परिकर्माष्टकप्रकरणम् - Basic Mathematical Operations

परिभाषाप्रकरणम् - Technical terms of measurement

पञ्चाङ्गप्रकरणम् - Katapayadi system, astronomical calculations

ज्याचापादिप्रकरणम् - Various measurements related to circles, arcs and jya

पञ्चबोधप्रकरणम् - Discussion on the 5 elements (chaya, vyatipata, etc)

गणितपरिष्करणप्रकरणम् - Methods of computation of planetary positions, orbits, circumference of earth, etc

The first two chapters introduce basic arithmetic operations and measurements in 33 verses and these two chapters will be covered in this course.

First chapter of the text contains 19 verses on the 8 basic mathematical operations. Second chapter contains 14 verses on technical terms of measurement. In this course, the teacher would introduce the students to read and understand the shlokas directly in Samskritam, rather than using a translation. This would help participants to explore the vast treasure of Indian Mathematics further.

Yes, there will be homework assessments at the end of each class. Learners who complete all assignments and gain over 60% of marks will get a certificate from Vyoma Labs.

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- What is the objective of this course? The objective of this course is to introduce participants to reading Sanskrit texts in Mathematics directly in Sanskrit, and not through translations.
- Why not teach completely in English? There is a good translation already available. It can be understood with high school level Mathematics knowledge. This course is an attempt to understand the text directly in Sanskrit, thereby understanding the Mathematics technical terms in Sanskrit.
- Why is it important to understand the Mathematics texts in Sanskrit? Below is an excerpt from a scholarly article titled “The Untapped Wealth of Manuscripts in Indian Astronomy and Mathematics” by Dr. M. D. Srinivas, CPS Chennai. While significant progress has been achieved by the modern scholarship in Indian Astronomy and Mathematics during the last seventy years, we are as yet far from achieving a comprehensive understanding of the fundamental concepts and techniques, theories and methodologies and even the historical development of Indian Astronomy and Mathematics. This is mainly because: 1. Only 450 (or 5%) of the estimated 9,000 source-texts (which are available in manuscript form) have been edited and published so far. 2. Further, even among the 450 or so published works, only about 96 texts have been seriously studied and explicated via translations and explanatory commentaries with a view to bring out their technical (mathematical-astronomical) content. 3. Most of these editions and studies have been brought out during the last seventy years or so; and this is largely due to the voluntary and dedicated efforts of a number of Indian scholars, as there has been little scope or support for such work in our institutions of higher learning. There is thus an urgent need to reorient our national priorities and give due importance to the Preservation, Digitization, Listing and Cataloguing, Editing & Publishing, and Promoting Systematic Studies of the large corpus of source-works of the great tradition of Science and Technology in India. Training young scholars for undertaking all these tasks should indeed form an integral part of the courses and research conducted in our institutions of higher learning. If the texts are not studied and understood in the language they are written, it is impossible to preserve the treasure of ancient Indian Mathematics.
- What is the textbook for the course? Sarma, K. V., “Sadratnamala of Sankaravarman”, Sanskrit Text with Introduction in English (available at https://web.archive.org/web/20150402140113/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b67_s1.pdf) Reference book – “Sadratnamala of Sankaravarman”, with English translation and notes by Dr. S. Madhavan, published in 2011 by KSRI, Chennai.

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