Foundation of Indian Knowledge & Mathematics
- 30 Hours
-
2 Credits
*(T&C Apply) Credits applicable only for Undergraduate and Postgraduate students enrolling for SIKSHA courses through academic institutions based in India.
- UG
- Upcoming Courses
₹5,000.00(GST additional)
About The Course
This course offers a structured introduction to the foundations of Indian knowledge and mathematics by bringing together philosophical, textual, and computational perspectives. Beginning with the Indian concept of knowledge and the centrality of the Vedas and Vedāṅgas, it then explores traditional applied sciences preserved in the Upavedas and related śāstras. The mathematical component presents the richness of Indian contributions to arithmetic, fractions, zero, progressions, combinatorics, geometry through the Śulbasūtras, algebraic methods such as Kuṭṭaka and Vargaprakṛti, and the development of trigonometry. Through this integrated approach, students gain both historical insight and problem-solving skills, appreciating how Indian intellectual traditions have shaped and enriched global mathematical thought.
Syllabus
- Unit 1: Indian Knowledge Traditions – The Concept of Knowledge
- • Importance and stature of knowledge in the Indian worldview
- • Definition and scope of knowledge (vidyā, jñāna)
- • Vedas as foundational texts; structure and content
- • The idea of śabda pramāṇa and its role in the epistemology of Indian knowledge systems
- • Introduction to Vedāṅgas
- Unit 2: Knowledge Systems in Practice – Upavedas and Applied Sciences
- • Introduction to Upaveda-s: Ayurveda, Dhanurveda, Gandharvaveda, Arthashastra
- • Applied sciences and their textual foundations:
- • Gandharvaveda (Music and performing arts)
- • Dhatuvada (Alchemy and Metallurgy)
- • Gandhashastra (Perfumery), Alekhyavidya (Painting), Ratnapariksha (Gemology), Yantramatrka (Mechanics)
- • Indian architecture and town planning
- Unit 3: Introduction to Indian Mathematics
- Sub-Unit 1. Introduction to Indian Mathematics
- 1.1 Importance of Indian Mathematics
- 1.2 Contents of some important texts in Indian mathematics
- 1.3 Indian Decimal Place value system and Zero.
- Sub-Unit 2. Eight Operations on Numbers
- 2.1. Three Saṅkhyā systems in Sanskrit.
- 2.2. Operations on Natural Numbers
- 2.3. Operations on Fractions.
- 2.4. Operations on Zero.
- Sub-Unit 3. Pāṭīgaṇitam – Arithmetic
- 3.1. Reverse Process, Finding unknown.
- 3.2. Rule of Three, Inverse Proportion, Rule of Five etc.
- 3.3. Rule of Barter, Simple Interest.
- Unit 4: Some Important Topics
- Sub-Unit 4. Some Important topics
- 4.1. Średhī- Progressions.
- 4.2. Aṅkapāśa-Combinatorics part 1
- 4.3. Combinatorics part 2
- Sub-Unit 5. Geometry – Śulbasūtras
- 5.1. Śulbasūtras, introduction.
- 5.2. Śulba constructions.
- 5.3.Śulba Transformations.
- Sub-Unit.6. Kṣetragaṇita –Geometry
- 6.1. Results and examples on Triangles.
- 6.2. Interesting examples under Śulba theorem
- 6.3. Results and examples on Quadrilaterals.
- 6.4. Results and examples on Circles.
- Unit 5: Algebra
- Sub-Unit 7. Algebra
- 7.1. Operations on Integers, surds
- 7.2. Algebraic expressions. Equations : Ekavarṇa
- 7.3. Equations - Anekavarṇa, Bhāvita, Quadratic
- Sub-Unit 8. Kuṭṭaka- Indeterminate Equations of degree one
- 8.1. Methods of Āryabhaṭa I and Bhāskara II
- 8.2. Varieties of Kuṭṭaka
- 8.3. Applications in Astronomy
- Sub-Unit 9. Vargaprakṛti-Indeterminate Equations of degree2
- 9.1. Bhāvanā method.
- 9.2. Solving Equations of type Nx² ± C = y²
- 9.3. Cakravāla Method
- Sub-Unit 10. Trigonometry
- 10.1. Brief History of Indian Trigonometry.
- 10.2. Trigonometric Functions and Identities
- 10.3. Trigonometric series.
More Information
- Learning Objectives
- ● To introduce the foundational concepts of Indian knowledge traditions, including the Indian worldview on knowledge, Vedas and Vedāṅgas as a source of valid knowledge.
- ● To familiarize students with major traditional knowledge systems and applied sciences (Upavedas and associated śāstras) such as Ayurveda, Dhanurveda, Gandharvaveda, architecture, alchemy, perfumery, painting, mechanics, and gemology
- ● To develop a conceptual and procedural understanding of important ideas in Indian mathematics—arithmetic, algebra, geometry, combinatorics, progressions, indeterminate equations, and trigonometry—through classical texts and methods.
- Intended Outcomes
- ● Students will be able to explain key concepts and texts of Indian knowledge systems and articulate their role in shaping Indian intellectual traditions.
- ● Students will be able to analyze and interpret important techniques from Indian mathematics, including operations on numbers and fractions, Śulbasūtra geometry, Średhī (progressions), Aṅkapāśa (combinatorics), Kuṭṭaka, Vargaprakṛti, and early trigonometry.
- ● Students will be able to apply methods from Indian arithmetic, algebra, geometry, and trigonometry to solve relevant mathematical problems and reflect on their relevance to modern mathematics, science, and technology.
