# Bachelor in vedic mathematics

# Syllabus –SEMSETER-I

MODULES

MODULE NAME

Module- 1

Introduction; Sutras & Sub-Sutras of Vedic Mathematics and its application.

Module -2

Place-Value Principles in Number Systems of Different Civilizations

[Babylonian Place- value Principle; Chinese numerals and Place-value principle; Mayan numerals and Place-value Principle].

[Babylonian Place- value Principle; Chinese numerals and Place-value principle; Mayan numerals and Place-value Principle].

Module -3

Vedic Hindu Place-value System, Numbers and Fractions.

[Place values of digits in numbers from different Sanskrit texts fractions in Sanskrit texts]

[Place values of digits in numbers from different Sanskrit texts fractions in Sanskrit texts]

Module -4

Glimpses of Mathematics from

[Multiplication, Division, Square & Square root 5 &6, Cube & Cube root, Summation of Arithematics series & Geomatric series]

*Ganitasara Sangraha*[Multiplication, Division, Square & Square root 5 &6, Cube & Cube root, Summation of Arithematics series & Geomatric series]

Module- 5

Poetic Mathematical Slokas from BijaGanita and

[Autobiographical Lyrical slokas, examples of fractions in lyrical slokas, permutation, combination, square root of a perfect square surd, extension of the rule to find square root of a complex number, etc]

*Lilavati*of*Bhaskara*–II[Autobiographical Lyrical slokas, examples of fractions in lyrical slokas, permutation, combination, square root of a perfect square surd, extension of the rule to find square root of a complex number, etc]

Module- 6

Zero and Infinity in Vedic Mathematics.

[Shunya (Zero) and Infinity in Vedas and Tantra literatures, Vedic Zero- a multifaceted concept & its etymology, Mahaviracharya’s rule on operations involving zero, Rule of Bhaskara- II on operations involving zero; Concept of Infinite in Bijaganita of Bhaskara - II]

[Shunya (Zero) and Infinity in Vedas and Tantra literatures, Vedic Zero- a multifaceted concept & its etymology, Mahaviracharya’s rule on operations involving zero, Rule of Bhaskara- II on operations involving zero; Concept of Infinite in Bijaganita of Bhaskara - II]

Module- 7

Surds and their approximate Values in Sulva Sutra and other Sanskrit texts.

[Approximate value of , Baudhana Theorem, Pythagoras of Samos, A Theorem of Manava Sulva Sutra, Geometrical method to get , Verification of Sulva sutra value of (i) by Thibaut, (ii) Rodet’s approximation, Geometrical method to find Trikarni त्रिकरत्रि and Tritiya Karni तृतीय करत्रि in Katyayana-Shulva Sutra, Katyayana’s Shulva Sutra method to get the length of चत्वाररशत्करत्रि ( ), Bhavana of Brahmagupta & Justification of Bhavana Process etc.]

[Approximate value of , Baudhana Theorem, Pythagoras of Samos, A Theorem of Manava Sulva Sutra, Geometrical method to get , Verification of Sulva sutra value of (i) by Thibaut, (ii) Rodet’s approximation, Geometrical method to find Trikarni त्रिकरत्रि and Tritiya Karni तृतीय करत्रि in Katyayana-Shulva Sutra, Katyayana’s Shulva Sutra method to get the length of चत्वाररशत्करत्रि ( ), Bhavana of Brahmagupta & Justification of Bhavana Process etc.]

# Syllabus –SEMSETER-II

MODULES

MODULE NAME

Module- 8

Approximate Values to the ratio of circumference of a circle to its diameter.

[From Baudhayana Sulva sutra, Need for its near approximate value, Analgorithm to double the number of sides of an inscribed regular polygon of n-sides, approximate value of by Aryabhatta-I, Mahaveeracharya’s approximation to , Approximate value of by Bhaskara-II, Power series of by Madhava & G W Leibnitz]

[From Baudhayana Sulva sutra, Need for its near approximate value, Analgorithm to double the number of sides of an inscribed regular polygon of n-sides, approximate value of by Aryabhatta-I, Mahaveeracharya’s approximation to , Approximate value of by Bhaskara-II, Power series of by Madhava & G W Leibnitz]

Module -9

Trigonometric Functions.

[Trigonometric terms as lengths in Sanskrit texts, Eymology of the term ‘Sine’, Basic Trigonometric terms as lengths in other civilizations, Trigonometric terms as ratios, Aryabhattiya’s Algorithm to find desired number of Rsines, Algorithm in Sanskrit to find 6-Rsines, Generalization of the algorithm to find N-Rsines, Radian measure in Aryabhattiyan.]

[Trigonometric terms as lengths in Sanskrit texts, Eymology of the term ‘Sine’, Basic Trigonometric terms as lengths in other civilizations, Trigonometric terms as ratios, Aryabhattiya’s Algorithm to find desired number of Rsines, Algorithm in Sanskrit to find 6-Rsines, Generalization of the algorithm to find N-Rsines, Radian measure in Aryabhattiyan.]

Module -10

Cryptographic Numerals.

[Sanskrit words as numerals, Value of in words as numerals in Shishyadhivruddhita Tantra/Lilavati of Bhaskara-II, Radian measure of words as numerals by Suryadeva yajvan, Sanskrit alphabets as numerals, Nagarjuna’s Magic Square using Sanskrit Alphabets as numberals.]

[Sanskrit words as numerals, Value of in words as numerals in Shishyadhivruddhita Tantra/Lilavati of Bhaskara-II, Radian measure of words as numerals by Suryadeva yajvan, Sanskrit alphabets as numerals, Nagarjuna’s Magic Square using Sanskrit Alphabets as numberals.]

Module -11

Approximate Values to the ratio of circumference of a circle to its diameter.

[From Baudhayana Sulva sutra, Need for its near approximate value, Analgorithm to double the number of sides of an inscribed regular polygon of n-sides, approximate value of by Aryabhatta-I, Mahaveeracharya’s approximation to , Approximate value of by Bhaskara-II, Power series of by Madhava & G W Leibnitz]

[From Baudhayana Sulva sutra, Need for its near approximate value, Analgorithm to double the number of sides of an inscribed regular polygon of n-sides, approximate value of by Aryabhatta-I, Mahaveeracharya’s approximation to , Approximate value of by Bhaskara-II, Power series of by Madhava & G W Leibnitz]

Module- 12

Module- 12 SriYantra based Vedic Mathematics –II

Module- 13

Vedic Computing ; Maharshi Pingala Chandasutram& Computer Binary Algorithms

Module- 14

Vedic BioMathematics

Module- 15

Vedic Mathematics in ancient Non-Sanskrit Literatures

Module- 16

Research Papers on Vedic Mathematics.