# DIPLOMA / P.G. DIPLOMA IN VEDIC MATHEMATICS

MODULES

MODULE NAME

Module I

Introduction to Vedic Mathematics

Module II

Place-Value Principles in Number Systems of Different Civilizations

[Hindu Place-value System, Numbers and Fractions, Babylonian Place- value Principle; Chinese numerals and Place-value principle; Mayan numerals and Place-value Principle].

[Hindu Place-value System, Numbers and Fractions, Babylonian Place- value Principle; Chinese numerals and Place-value principle; Mayan numerals and Place-value Principle].

Module III

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 IV

Vedic Mathematics- Sutras & Subsutras

Module IV-A

Arithmetic, Digital sums & the nine-point circle, Large numbers, Digit Sum Check, Number Nine, Number with Shapes, Geometry, Symmetry, Angles & Triangles

Module IV-B

MAGIC SQUARES

By the Completion or Non-completion, Doubling and Halving, Divisibility, Short Multiplication & Division, Powers of Ten & Decimals, Number Splitting, Polygons & Coordinates, Regular Polygons and Perimeters, All from the 9 & the last from 10

By the Completion or Non-completion, Doubling and Halving, Divisibility, Short Multiplication & Division, Powers of Ten & Decimals, Number Splitting, Polygons & Coordinates, Regular Polygons and Perimeters, All from the 9 & the last from 10

Module IV-C

PASCAL’s TRIANGLE

Bar Numbers, On the Flag, Prime & Composite numbers, Proportionately, By one more than the one before, Algebra, Area, Volume, Planets.

Bar Numbers, On the Flag, Prime & Composite numbers, Proportionately, By one more than the one before, Algebra, Area, Volume, Planets.

Module IV-D

FLEXAGONS

Module IV-E

Nikhilam Multiplication, Doubling & Halving, Fractions, Spirals, Fractions & Decimals, The Arithematic of Bar Numbers, General Multiplication, Algebric Multiplication, Squaring.

Module IV-F

THE MOEBIUS STRIP

Sequences, Probability, Equations, Angles & Triangles, Percentages, Forming Equations, 2 and 3- Dimensional shapes, Straight Line Graphs, Charts

Sequences, Probability, Equations, Angles & Triangles, Percentages, Forming Equations, 2 and 3- Dimensional shapes, Straight Line Graphs, Charts

Module IV-G

FRACTALS

Divisibility, Further Multiplication, Combining Fractions, Arithmetical Operations, Special Division, Percentage Changes, Transformations, Constructions, Parallel Lines & Bearings.

Divisibility, Further Multiplication, Combining Fractions, Arithmetical Operations, Special Division, Percentage Changes, Transformations, Constructions, Parallel Lines & Bearings.

Module IV-H

RANGOLI PATTERS

Module IV-I

Recurring Decimals; Formulae; Squares, Cubes & Roots; Straight Division; Equations; Polygons; Similar Figures; The Musical Scale; Nets & Networks

Module IV-J

THE VEDIC SQUARE

Probability; Pi; Volumes of Prisms & Pyramids, Parabolic Curves; Sequences; Loci; Motion; Auxiliary Fractions, Surveys

Probability; Pi; Volumes of Prisms & Pyramids, Parabolic Curves; Sequences; Loci; Motion; Auxiliary Fractions, Surveys

Module IV-K

CODES

Vectors; Simultaneous Equations; Divisibility & Simple Osculators; Square Roots; Quadratic Equations; Pythagoras Theorem; Triples; Proof; Coordinate Geometry

Vectors; Simultaneous Equations; Divisibility & Simple Osculators; Square Roots; Quadratic Equations; Pythagoras Theorem; Triples; Proof; Coordinate Geometry

Module IV-L

THE PLATONIC SOLIDS

Module V

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 VI

Poetic Mathematical Slokas from

[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]

*BijaGanita*and*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 VII

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.]

Module VIII

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

[From Baudhayana Sulva sutra, Need for its near approximate value, An algorithm 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, An algorithm 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 IX

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 X

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 XI

Aryabhatiya Numerals.

[Svara denoting place values in powers of ten Vargaakshara & Avargakshara denoting numbers, Number of revolutions of Geocentric Planets in a Yuga (43,20,000) years in Aryabhattiya numerals]

[Svara denoting place values in powers of ten Vargaakshara & Avargakshara denoting numbers, Number of revolutions of Geocentric Planets in a Yuga (43,20,000) years in Aryabhattiya numerals]