Maths Symbol in Our Applications

.
There are many symbols in maths.
To learn and understand maths, we need to know the meaning of the symbols.

This is very much like talking to a foreigner. Without understanding each other's language, no communication can be carried out (other than the international body language!)

Hence, knowing the usage of the symbols in a mathematical expression helps.

But is it really so?

Partially.

Why do I say that?

Yes, you may know the symbol while doing maths, but if the same symbol is used elsewhere, do you still understand?

One example is:

y = x + 1
This means x is added by one and their total is represented by the variable "y".
This is for the maths operator "+".

But what about the expression x++ ?
This looks odd, isn't it?

To the maths learner, this may be a typo error, or something is missing.

"x++" is actually commonly used in C programming.

What it means is   x = x + 1.
It is a short-cut way of writing the addition of x and replacing it by the same variable "x".

Thus this example showed the use of "+" in another application.

It is still maths in some sense, but written in another form.

Maths is therefore always around us. It is a matter of us applying them and understanding them.

Only by learning their "language", can we communicate with them.

Interesting?  I bet you agree!

Other applications can be " += ", " :-) " and " x>>4 ". 
Can you find their meaning?

:D

Area Displacement Theory

.
Maths is not all about calculation.

There are always more to it than meet the eyes.

This is especially true when you are doing geometrical questions where you are involved with area, perimeter and so on.

Displacement theory or its equivalent is always done without the knowledge of many people.

What is this theory about?

Let's look at one example below.

In the diagram above, you will see a path (white coloured) going across a blue platform.
If you are asked to find the area of this path, what can you do to obtain this area?

If no data of dimension is given, it is definitely not possible.

Now if the width of the path and the vertical length of the blue platform is given, can you compute the answer?

Again , this need a bit of thinking.

Displacement theory kicks in here. Look at the diagram on the right.

It is the displaced or closed up portion of the blue platform that does the trick.
Here you will notice the dashed line forming a white rectangluar area on the right-most side of the white blue platform.

Are you able to find the area of this white rectangular piece?
The width of this rectangle piece is ACTUAL the width of the white path!

You should now be able to calculate the area of this rectangular piece since the path width and length of the rectangular block is known or deduced now.

How this is possibe is through the "hidden" clue or step of closing up the path revealing the simpler rectangular area that any decent maths student can calculate.

Hence, maths is wonderful in that it tests you not only about applcations of maths tools, but your other "intelligence".

Having known displacement theory here, I believe you are really for the Math Challenge 23.
Go there and answer the question, and be quick before others grap the position one ... 

:-D
.

Purpose of Graph

.
What is the purpose of graph?
This may be the question every learners first ask when they were exposed to this maths topic.

When do we use graph as opposed to using, for example, Argand diagram or vectors sketch?

Graph by nature is a graphical presentation of data that collectively form into information that reflects the trend of some parameters.

It shows the past, current and possibly the future (prediction).

Graph is a relative as well as an absolute maths tool for people using it.

An example of graph application is that in stock market data prediction.
Using past records, people tends to forecast the future through looking at the graph.

Another example is in engineering work.
Collecting data of a certain electrical system behaviour, engineers can predict the failure or potential life of its operation.

A simple graph is plotted with normally 2 parameters.
But this is not always true.
Graph may come in 3 dimensional. The x, y and z direction.

Knowing graph is an alternative problem solving skill or prediction skill.
It allows users to see an overview of the relation between specific targets.

Graph is wonderful if you let it be.
Enjoy it.

:D

Application of Boolean OR operation

'
Besides the Boolean AND operation and its application, Boolean OR operation also serves a special application.

For the AND operation, which is equivalent to the maths multiplication, the use is for it to pull any untied input to a system to zero state.

For the OR operation, the concept is similar, except that now it is the maths addition.
Instead of pulling the untied input to the system to zero, you can set it to the other Boolean state, which is the "1".

In base 2 number system (Boolean), if the input is 000101, and you need the data to be all 1, just OR the input with 111111.

What you will get after this OR (adding) operation is 111111.

This is so due to the fact that 1 + 0 = 1.

Here you will see that option to set the untied input to 0 or 1 can be done using either the AND or OR operation of the Boolean system.

This is maths, if you are aware.
This is the application of maths after understanding the principles of maths operation.

Any comment?

:D

Application of Boolean AND operation

'
Boolean, though, of 2 states, can still be useful.

The concepts of multiplication in this AND operation can be used to perform cancellation of unknowns.

Anything times zero gives zero.
This is a common knowledge.

Here we are talking about basic fundamental maths. Nothing difficult.

Cancellation of unknowns in the AND operation means that we are able to mask out the unwanted or redefine the unknowns to a definite state.
Here the unknown become a zero, a known state or condition.

A more specific application is in the masking of unconnected inputs to a processing system. If the inputs are scanned and compared for status updates, the inputs have to be accurate or of a known status. Otherwise, comparison results become meaningless.

Here the Boolean multiplication (AND) forces the unconnected input to a zero. This is then an accurate input status for comparison.

Here, maths is applied to technical application, and its usefulness become apparent.
This is the power of understanding maths , and is exactly what makes maths interesting.

.