Course Overview

Bhārata has treated mathematics as a core discipline since the Vedic era. This course traces the Gaṇita-Gaṅgā—the unbroken river of mathematical knowledge flowing from Baudhāyana through Ramanujan.

You will learn to solve first-degree indeterminate equations (linear Diophantine equations) using the Kuṭṭaka method, and second-degree equations (Varga Prakṛti) using Brahmagupta's Bhāvanā and Bhāskara's Chakravāla.

Each algorithm is presented in its original Sanskrit formulation, translated into modern notation, and implemented step-by-step so you can verify results computationally. The course bridges historical scholarship with practical mathematical skill.

The Mathematical Lineage

Baudhāyana Āryabhaṭa (499) Brahmagupta (628) Mahāvīra (850) Bhāskara II (1150) Nārāyaṇa Paṇḍita (1356) Mādhava Ramanujan

What You Will Learn

1. Linear Indeterminate Equations (Kuṭṭaka)
Solve equations of the form ax ± by = c using successive division. Understand why this "pulverising" approach works and how it relates to the Euclidean algorithm—while going further to construct actual solutions.

2. The Vallī (Column) Method
Learn the tabular arrangement Indian mathematicians used to track calculations. This elegant bookkeeping system makes complex computations tractable without modern notation.

3. Remainder Problems
Master the Chinese Remainder Theorem's Indian precursor: finding numbers that leave specific remainders when divided by multiple divisors.

4. Quadratic Indeterminate Equations (Varga Prakṛti)
Advance to Nx² + k = y², including the special case Nx² + 1 = y² (Pell's equation). Learn Brahmagupta's Bhāvanā composition law and Bhāskara's cyclic Chakravāla method.

5. Historical Context & Modern Relevance
Understand how these algorithms were used for astronomical calculations and why they matter for contemporary number theory and cryptography.