# Preliminaries

## An Overview

We are giving here the topics that we would be covering with a short introduction for each. The student can go to any section of his choice and start learning. Later we would also be including self testing modules by which the students can test their own understanding of difficult concepts

Let us also mention that we are making certain assumption about the students. It should be made clear that a love for mathematics is what we are assuming the student has. He or She also must have an inquisitive spirit about learning more and finding about unknown aspects of the subject. Let it also be said that our effort will also be there to ensure that the love for the subject is further enhanced by our creative methods of teaching and we would also endeavour to enhance the questioning spirit of the student by creative treatment of the subject.

## ARITHMETIC

As such, arithmetic is the least important of all the subjects that we are going to cover. Algebra is the soul of Mathematics and Geometry is where Mathematics really unfolds. Trigonometry and Coordinate Geometry are tools to understand Geometry better.

However, we must learn about numbers and how to deal with them in the shortest possible time. Thus, in the Arithmetic section we will look at easy and fast methods to deal with Addition, Subtraction, Multiplication and Division. We will also show you how to square a two digit number and multiply two 2-digit numbers very very fast and accurately. And many other things which are very entertaining.

​We have taken up Arithmetic as an aid for Mathematics only in the Preliminaries Section and thus, there will be no section for Arithmetic in the Advanced Section of this site

## GEOMETRY & TRIGONOMETRY

This is where we intend to provide the maximum value to the student. Geometry is nothing but a close look at drawings that we make. We look at triangles and squares and quadrilaterals and polygons. Geometry deals with straight lines and circles, to put it simply. To understand clearly all the aspects of these geometrical entities like triangles, rectangles etc., we will constantly use basic trigonometry. This makes geometry very interesting and provides a 360 degree view on very many aspects.

Here again we would be assuming that the student knows the basics of trigonometry like Tan x, Sin x and Cos x, nothing more. We will be taking up other concepts of trigonometry and show you how it applies to Geometry.

## ALGEBRA

The soul of mathematics is Algebra. Almost everything we do in Mathematics requires the help of algebra. Thus, this is very important. However, we are assuming that the student knows the basics well i.e. the student must be very thorough with Simple Equations so much so that he ought to develop the skill to do simple equations almost verbally. We will deal with that a bit.

Further, we want to take the students to realize how a mathematician’s mind works, how he asks natural questions and seeks to find their solutions. And this is how mathematics grows and mathematical knowledge increases. We are not here to finish a syllabus but rather to embark on a voyage of discovery.

In the Preliminaries Section, our Algebra section is designed to be short. We will take up more complex structures in the Advanced sections. But our real interest lies in Geometry.

## COORDINATE GEOMETRY

Descartes was the brilliant mathematician who combined algebra with geometry to formulate Coordinate Geometry. We are eternally grateful to Descartes for this service to mankind.

The geometrical drawings and shapes are put on a background which is like a graph paper. And then the shapes are reexamined with reference to the graph paper and this is where we can convert any geometrical shape into algebra. We will see how in this section and it is very very interesting.

Not only that, this is the doorway to higher mathematics because once we can express any geometrical shape as algebraic expressions, simultaneously we can also see the geometric shape of any algebraic expression.

This opens up a huge door to a world of mathematics called Functions. In the Advanced section we would be looking into this concept of Function through the Quadratic function. Students may be aware of the quadratic equation but wait till you see the immense beauty that higher mathematics can show you.