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].
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]
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
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
Bar Numbers, On the Flag, Prime & Composite numbers, Proportionately, By one more than the one before, Algebra, Area, Volume, Planets.
Module IV-D
Module IV-E
Nikhilam Multiplication, Doubling & Halving, Fractions, Spirals, Fractions & Decimals, The Arithematic of Bar Numbers, General Multiplication, Algebric Multiplication, Squaring.
Module IV-F
Sequences, Probability, Equations, Angles & Triangles, Percentages, Forming Equations, 2 and 3- Dimensional shapes, Straight Line Graphs, Charts
Module IV-G
Divisibility, Further Multiplication, Combining Fractions, Arithmetical Operations, Special Division, Percentage Changes, Transformations, Constructions, Parallel Lines & Bearings.
Module IV-H
Module IV-I
Recurring Decimals; Formulae; Squares, Cubes & Roots; Straight Division; Equations; Polygons; Similar Figures; The Musical Scale; Nets & Networks
Module IV-J
Probability; Pi; Volumes of Prisms & Pyramids, Parabolic Curves; Sequences; Loci; Motion; Auxiliary Fractions, Surveys
Module IV-K
Vectors; Simultaneous Equations; Divisibility & Simple Osculators; Square Roots; Quadratic Equations; Pythagoras Theorem; Triples; Proof; Coordinate Geometry
Module IV-L
Module V
Glimpses of Mathematics from Ganitasara Sangraha
[Multiplication, Division, Square & Square root 5 &6, Cube & Cube root, Summation of Arithematics series & Geomatric series]
Module VI
Poetic Mathematical Slokas from 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.]
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]
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.]
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.]
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]