Thursday, 2 April 2009

Algebra | Moving Forward in Usage

In the study of algebra, symbolic representation of number or unknown is key concept to solving mathematical equations.

The letter "x" or "y" are examples.
Other symbols can also be used as long as the usages are understood.

In the expression, x + 0.5 = 3.
This meant that the unknown "x" added to 0.5 will give a total of 3.

"x" here is nothing other than an unknown item to be solved.
It should be a number that relates to that maths equation. Nothing more, nothing less.

Another example:
x2 + 2x - 1 = 0

This "x" again is an unknown number to be found out.

Thus this algebraic expression and its "x" are just mathematical item representing a relationship.

Many students learning maths, when faced with this "x" always look puzzled.
With this post, the queries of this "x" (or "y", etc) should be cleared.

With this knowledge of the symbolic representation of unknowns, other areas of maths can be explained easily.

Topics like the trigonometry and logarithm will be expanded from this symbolic concept.

Cos A and log B will thus be finalised to a number, with this "A" and "B" yet to be solved.

Equation like
cos A + 2 = 2.4
will then be nothing more than to relate this unknown "A" to the expression.

It is also an easier way to explain and express this relationship between the unknown (A) and the other number (2 and 2.4).

log x + log 2 = 3
means that "x" is related to the 2 and 3 according to the given equation.

From the above few examples, the question now of what really is this "letter" doing forms meaning, right?

Maths starts off easy when this concept is clear.
Alot of the maths study involves this simple "trick" of presenting unknowns.

You notice how clever past mathematicians were now?
The use of simple symbol to pass off as number to carry on with maths solving.
Without this algebraic presentation, maths will not be as interesting as now.
Alot of guessing will have to be done and .... guess what? Maths will be HELL then.

Enjoy this symbolic concept in maths.
Enjoy your maths.

:-) (-:

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