The course is designed to have glimpses of the vast mathematical knowledge that Indians had in ancient/medieval times. The learner is encouraged to learn, understand and practice the different methods given by Indian mathematicians for solving various problems. From basic Arithmetic and Geometry to the
higher Math concepts like Combinatorics and Calculus, the contribution of Indian mathematicians is notable and the learner is expected to develop justified pride about their own ancestors and gain some motivation towards furthering the subject by contributing via research.
Curriculum
- 1 Section
- 14 Lessons
- Lifetime
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- Module 1: Arithmetic, Algebra and CombinatoricsCourse Objectives (CO): This course provides an introduction to the work of Indian mathematicians and its relevance in todays world. It aims to provide knowledge to students about contribution and innovations of Indian Mathematicians. This course is designed with following objectives. CO1: To introduce students to the significant mathematical contributions of ancient Indian scholars, including Aryabhata, Brahmagupta, Bhaskara and Madhava. CO2: To study mathematical concepts found in Vedic texts, including the Sulba Sutras, and their applications in geometry, algebra, and number theory. CO3: To analyze the development of the Indian decimal number system, place value notation, and the invention of zero.Course Outcomes (OC): After completion of the course, students will be able to OC1: understand and recall the methods of obtaining square roots and cube roots, results related radius and diameter and the contributions of Indian Mathematicians OC2: explain Pythagorean triplets as appeared in Shulbasootras, impossibility of square root of negative numbers, expressed by Indian mathematicians, Varga-Sankramana, etc. OC3: apply Indian ancient methods to find squares and cubes, volume of a sphere given by Bhaskaracharya, volume of pyramid given by Brahmagupta etc. OC4: analyse the problem of Kuttaka and the methods given by Brahmagupta and Bhaskaracharya, the problem of Varga Prakriti and the method given by Bhaskaracharya.14
- 1.1Lecture 1: The Zero and the Decimal System: The early appearance of Zero
- 1.2Lecture 2: Terms for the multiples of ten like 10, 20, 30 etc. in Rigveda. Terms for the higher powers of 10, given by Aryabhat, Mahaviracharya and Bhaskaracharya
- 1.3Lecture 3: The elementary operations like addition, subtraction, multiplication, division. Operations with fractions. Operations with zero. Squares and Cubes.
- 1.4Lecture 4: Methods to Obtain Square Roots and Cube Roots in Indian Mathematics
- 1.5Lecture 5: Solved Examples: Square and Cube Roots by Aryabhata & Bhaskaracharya
- 1.6Lecture 6: Impossibility of square root of negative numbers, expressed by Indian mathematicians
- 1.7Lecture 7: Varga-Sankramana, Quadratic Equation
- 1.8Lecture 8: Trairashik, Vyasta-Trairashik, Paanchrashik, Saaptarashik
- 1.9Lecture 9: The problem of Kuttaka and the methods given by Brahmagupta and Bhaskaracharya
- 1.10Lecture 10: The Problem of Varga Prakriti and the Method Given by Bhaskaracharya
- 1.11Lecture 11: Step-by-Step Solution Using Chakravala Method
- 1.12Lecture 12: Progressions and Series in Indian Mathematics
- 1.13Lecture 13: Combinatorics in Ancient Indian Mathematics
- 1.14Lecture 14: Some examples from ancient Indian combinatorics with their original Sanskrit verses, followed by modern translations and explanations
