Page 17 - Guidelines for Training/ Orientation of Faculty on IKS

B. ELECTIVE COURSES ON SELECTED DISCIPLINES/ TOPICS
THAT ARE PART OF IK

I. MATHEMATICS IN INDIA: FROM VEDIC PERIOD TO MODERN TIMES

1. Introductory Overview
Mahāvīrācārya on the all-pervasiveness of Ganita. The algorithmic approach of Indian Mathematics.
Overview of development of Mathematics in India during the ancient and early classical Period (till
500 CE), later classical period (500-1250) medieval period (1250-1750) and the modern periods
(1750- present). Proofs in Indian Mathematics. The genius of Srinivasa Ramanujan (1887-1920).

Lessons from History.

2. Mathematics in the Vedas and Śulva Sūtras

Mathematical references in Vedas. The extant Śulbasūtra texts & their commentaries. The meaning of
the word Śulbasūtra. Qualities of a Śulbakāra. Finding the cardinal directions. Methods for obtaining
perpendicular bisector. Bodhāyana’s method of constructing a square. The Bodhāyana Theorem (so
called Pythagoras Theorem)

Applications of Bodhāyana Theorem. Constructing a square that is the difference of two squares.
Transforming a rectangle into a square. To construct a square that is n times a given square.
Transforming a square into a circle (approximately measure preserving). Rational approximation for
√2. Construction of Citis. Details of fabrication of bricks, etc.

3. Pāṇini’s Aṣṭādhyāyī

Development of Vyākaraṇa or Śabadaśāstra. Pāṇini and Euclid. Method of Pāṇini’s Aṣṭādhyāyī. Śiva-
sūtras and Pratyāhāras. Context-sensitive rules and other techniques of Aṣṭādhyāyī. Pāṇini and zero.
Patañjali on the method of Aṣṭādhyāyī. Vākyapadīya on Aṣṭādhyāyī as an upāya.

4. Piṅgala’s Chandaḥśāstra
Development of Prosody or Chandaḥśāstra. Long (guru) and short (laghu) syllables. Scanning of
Varṇavṛtta and the eight Gaṇas. Pratyayas in Piṅgala’s Chandaḥśāstra. Prastāra or enumeration in the
form of an array. Saṅkhyā or the total number of metrical forms of n syllables. Naṣṭa and Uddiṣṭa (the
association between a metrical form and the row-number in the prastāra through binary expansion).
Lagakriyā or the number of metrical forms in the prastāra with a given number of Laghus. Varṇameru
and the so called “Pascal Triangle”.

5. Mathematics in the Jaina Texts

Place of Mathematics in Jaina literature. Important Jaina mathematical works. Jaina geometry.
Circumference of a circle. Area of a circle. Relation between chord, śara (arrow) and diameter,
etc. Approximation for the value of π. Notion of different types of infinity. The law of indices.
Permutations and Combinations.

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Guidelines for Incorporating Indian Knowledge in Higher Education Curricula