Course 7

The Crowning Gem -

Powers, Roots, Equations Course

**Description**: This online course
shows one beautiful Vedic Master-Formula (Vertically and Crosswise pattern) to
find general powers and roots of numbers (and polynomial expressions) and
solution of quadratic, cubic and higher order equations.

Course participants need only have a basic knowledge of algebra. There are no other prerequisites for joining the course, but knowledge of straight division and use of Duplexes to find squares and square roots is beneficial.

When Sri Bharati Krishna Tirthaji (1884-1960)
reconstructed the ancient system of Vedic Mathematics he left us with
one book on the subject, "Vedic Mathematics" (and a great many
questions). In his book he describes a division technique which he
called the "Crowning Gem" of Vedic Mathematics, the essential feature
being that the first digit of the divisor is used to provide all
subsequent digits when combined appropriately with the other digits
involved. This idea has been developed in this course.

12 video lessons with one test per lesson.

**Details:**

- 100% online, and self-paced: the course is always open and anyone can join

- Courses are available world-wide

- Prior knowledge of Vedic Mathematics is not required

- 12 video lessons

- A trainer is available to answer questions

- Regular tests and discussion forum

- A certificate for those who pass

**Course created by**
Kenneth Williams.

**Prices: **these depend on country so you will need to register at the Math2Shine link below to see this.

There are options for enroling for 2, 6 or 12 months.

Testimonials from previous courses

CLICK
HERE for more details and enrollment (goes to Math2Shine website)

**Course created and conducted by**
Kenneth Williams.

Any queries can be sent to academy@vedicmaths.org

**Course Content: **

SECTION 1: The Duplex and Beyond

1 The Duplex

❖ What the Duplex is, its notation, and how to calculate it.

❖ How the Duplex gives squares of numbers and polynomials.

❖ How each of the Duplexes can be generated from the one before it.

2 Obtaining the Coefficients

❖ What ‘factorials’ are and how to evaluate them.

❖ How to divide factorials by cancelling

❖ How to use factorials to obtain coefficients of terms.

3 The Triplex and Beyond

❖ What the Triplex is, and how to calculate it.

❖ How each of the Triplexes can be generated from the one before it.

❖ How we can work just as easily from right to left.

❖ How to predict the number of Duplexes, Triplexes etc. in an expansion

❖ What Quadruplexes are, and how to generate them.

SECTION 2: Powers

4 The Crowning Gem

❖ How differentiation works.

❖ How to get the important 'multipliers’.

❖ How to use the multipliers to find squares and cubes.

❖ A proof of the pattern for cubing quadratics

5 Powers from Both Ends

❖ How to get powers of polynomials and numbers more easily by working from both ends.

6 Fourth, Fifth Powers and
Beyond

❖ A brief introduction to Pascal's Triangle.

❖ How to get the multipliers more easily.

❖ How to get higher powers of numbers and polynomials, working from both ends.

SECTION 3: Roots

7 Cube Root, Square Root

❖ How the powers pattern from previously can be reversed to find cube and square roots.

❖ How a slight rearrangement can make the process even easier.

8 Fourth, Fifth Roots and Beyond

❖ How the same pattern can be applied to find higher roots.

9 Roots of
Polynomials

❖ How the pattern can give roots of perfect powers of polynomials.

❖ How the pattern gives any root of any polynomial whether perfect or not.

SECTION 4: polynomial equations

10 Quadratic Equations

❖ How to use the pattern to find a solution to quadratic equations.

❖ How to get the other root.

11 Cubic Equations and Beyond

❖ How to solve cubics, quartics, quintics etc. with the same pattern.

12 Change of
Roots

❖ Ways in which the roots of an equation can be changed

❖ How the roots of an equation can be divided or multiplied by some factor

❖ How the signs of the roots can be changed