1. Start with Ancient Indian Mathematics:

- The study of ancient Indian mathematics can begin with the Vedic period, where the oldest known mathematical text, the "Sulba Sutras," was composed. These texts contain rules and techniques for performing geometric constructions and calculations.

- Explore the contributions of mathematicians from the classical period, such as Aryabhata, whose work focused on algebra, astronomy, and trigonometry. His book "Aryabhatiya" is an essential text to study.

- Another significant mathematician of this period is Brahmagupta, known for his work on number systems and algebraic solutions.

2. Delve into the Contributions of the Kerala School:

- The Kerala School, which flourished between the 14th and 16th centuries, made significant advancements in mathematics and astronomy.

- Explore the works of mathematicians like Madhava and Nilakantha, who developed infinite series and trigonometric functions before European mathematicians.

- Learn about the famous "Kerala school approximation," also known as the "Madhava series," which accurately calculates the values of trigonometric functions.

3. Study Indian Astronomical Contributions:

- Ancient Indian astronomers made remarkable discoveries and calculations in astronomy.

- Learn about the influential text "Aryabhatiya," which includes knowledge of planetary motion, eclipses, and the determination of celestial constants.

- Dig deeper into "Siddhanta Shiromani" by Bhaskara II, a comprehensive treatise on astronomy that covers various astronomical phenomena.

4. Understand Indian Scientific Discoveries:

- Explore the works of renowned scientists such as Srinivasa Ramanujan, who made substantial contributions to mathematical analysis, number theory, and continued fractions.

- Learn about the modern developments and achievements of Indian scientists in various scientific fields, including physics, chemistry, and biology.

- Familiarize yourself with the contributions of Homi J. Bhabha, C. V. Raman, Jagadish Chandra Bose, and other notable Indian scientists.

5. Utilize Resources and References:

- Read books and research papers dedicated to the history of Indian mathematics and science, such as "The Crest of the Peacock" by George Gheverghese Joseph.

- Access online resources, scholarly articles, and academic websites that provide in-depth knowledge about the history of Indian mathematics and science.

- Explore relevant museum exhibits, documentaries, and lectures available online or at local institutions.