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Gujarat University and Anaadi Foundation
Jointly offer
Foundational Course on Indian Mathematics
(Certificate Course in Bharatiya Ganita 101)
Duration : 30 Hrs | Course Fee: Rs. 1000

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Course trailer video

About the Course


Various civilizations around the world have contributed their original thought processes to advance humanity’s collective knowledge. The subject of Bhāratīya Gaṇita refers to a particular domain that helps us understand how the knowledge tradition in India advanced in the field of mathematics, blossoming in the cultural and scientific context of the Indian ethos. The history of Bhāratīya Gaṇita spans all the way from the Vedic era to until a few centuries back, where this knowledge tradition thrived in its own unique way and made significant breakthroughs. 
There is indeed a treasure trove of mathematical ideas, pedagogical tools and nuanced reasoning in Indian mathematics that can certainly augment and elevate education of mathematics. One can find inspiration to overcome apprehensions towards math and go on to enjoy mastering various techniques and approaches unique to Bhāratīya Gaṇita. The genesis of various mathematical ideas, concepts, demonstrative proofs, branching of divisions and advanced reasoning of ancient Indian mathematicians are presented in this course. Moreover, children would rejoice in knowing how scholarly works of mathematics were composed as lucid verses in Sanskrit.

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Course Objectives:


Understanding the mathematical heritage of Bharat and the key mathematical breakthroughs pioneered in the global development of mathematics
Developing conceptual clarity by studying Indian mathematical constructs
Understanding the monumental contributions of Bodhayana, Aryabhata, Bhaskaracharya, Narayana Pandita, Madhava, Nilakantha Somayaji and many more Indian mathematicians in order to gain inspiration from their methodologies, problem-solving approach and demonstrative proofs
Drawing concepts and pedagogical tools from Bharatiya Ganita that are highly relevant to aid the cognitive development of learners in current times as well​

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Course Contents: 
10 Hours of Video Lectures | 10 Hours Assigned Reading | 10 Hours Swadhyaya & Quiz

Modules Covered

Unit 

Topics and Sub-topics

Unit 1  -  History of Indian mathematical development

  • Key achievements of Vedic Era (pre 500 BCE)

  • Key achievements of Classical Era (500 BCE - 1300 CE)

  • Key achievements of Medieval Era (1300 CE - 1750 CE)
     

Unit 2  -  Geometry in Shulbasutras

  • The extant Shulbasutras

  • Sutras and properties from Bodhayana Shulbasutras

  • Bhuja-Koti-Karana-Nyaya (Pythogorean Theorem)

  • Geometrical constructions of Citis

  • Earliest exploration of Pi and Surds
     

Unit 3   -  Mathematics in Chandas-Shastra

  • Binary Arithmetic approach in Chandas-Shastra

  • Mathematical patterns in Sanskrit poetry 

  • 6 Pratyayas or Algorithms 

  • Meru Prastara (Pascal’s Triangle)
     

Unit 4  -  Indian Place Values and Number Representation

  • Indian Decimal Number System 

  • Kaṭapayādi Number System

  • Āryabhaṭiya Number System

  • Bhūtasaṅkhyā Number System
     

Unit 5   -  Aryabhata’s excellence in math

  • The Āryabhaṭīya - Overview

  • Āryabhaṭa’s Square Root Technique

  • Contributions in Planar Geometry
     

Unit 6   -  Glimpses of Bhāskarācārya’s Līlāvatī

  • Overview of Bhāskarācārya and Līlāvatī

  • Computing Cubes

  • Computing Cuberoots

  • Gaṇeśa Daivajña’s upapattis for some rules in the Līlāvatī
     

Unit 7   -  Puzzles in Indian Mathematics - Part 1

  • Trairāśika - Rule of Three

  • Theorem of the Diagonal

  • Applications of Theorem of the Diagonal

  • Mensuration of quadrilaterals in the Līlāvatī 
     

Unit 8   -  Puzzles in Indian Mathematics - Part 2

  • Śreḍhī-vyavahāra - Progressions

  • Iṣṭakarma and Vargakarma
     

Unit 9   -   Magic Squares and other contributions of Narayana Pandita

  • History of Magic Squares in India

  • Construction of odd-order magic squares by Narayana

  • Construction of Pandiagonal magic squares with mnemonics

  • Turagagati algorithm by Narayana Pandita

  • Other contributions by Narayana Pandita
     

Unit 10   -  Conclusion and Reflection

  • Summary of development & important breakthroughs

  • Glimpses of other advanced concepts

  • Impact of Bharatiya Ganita on pedagogy

  • Scope in Research and Teaching

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