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
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.
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, problemsolving 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
Course Contents:
10 Hours of Video Lectures  10 Hours Assigned Reading  10 Hours Swadhyaya & Quiz
Modules Covered
Unit
Topics and Subtopics
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

BhujaKotiKaranaNyaya (Pythogorean Theorem)

Geometrical constructions of Citis

Earliest exploration of Pi and Surds
Unit 3  Mathematics in ChandasShastra

Binary Arithmetic approach in ChandasShastra

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

Śreḍhīvyavahāra  Progressions

Iṣṭakarma and Vargakarma
Unit 9  Magic Squares and other contributions of Narayana Pandita

History of Magic Squares in India

Construction of oddorder 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