Applications are Essential

tsjeyaganesh — Mon, 11 Jan 2010 07:54:07 +0000

Mathematics is a tool, not just a concept. In order to handle the tool, we should know where it is useful. From school days, we are taught like mathematics as concept, without educating with its applications.

Each and every divisions of mathematics has its extensive applications in many fields. Why many fields? In all fields. And it is brainless to think each and every division as separate entities. Everything is interrelated, the relations is so subtle, peoples fails to notice.

It has became a trend that students dislike mathematics and they do shamelessly accept that. Mathematics is an alien subject to them. Not without proper understanding of mathematical concepts and its applications, i will say they are incompetent. I am one of the incompetent person.

And to teach mathematics in-depth with its all applications and relations between categories is tedious job and no proper tools is found as far I know. But there must be tool for such thing.

And I feel classroom environment for mathematics coaching will prove nothing and useless. Practical environment is necessary. That’s why most of the students feel sleepy especially in mathematics classroom. I am talking about average students here, there are exceptions for sure. Mathematics is so far perceived as memorizing formulas, but it is about understanding formulas.

In this blog i am going to write about my mathematics learning experience as I understood. Feel free to correct me, even to scold me if i m wrong.

Mathematics is the study of Quantity, Structure, Space and Change.

What is Quantity?

What is Structure?

What is Space?

What is Change?

To study mathematics, one should be in a position to answer for the above questions in not less than 100 words. If you got real interest in mathematics, allocate some time and try to get the general idea of these four things. Wikipedia is one best source for that. Not going to provide links here. Because its the job of the pursuer.

Why Symbols and Signs?

tsjeyaganesh — Wed, 02 Dec 2009 17:04:47 +0000

Why symbols and signs? Why not just words?

Here are some of the most commonly used mathematical symbols and signs

Symbol	What Is It?
+	Adding Sign. Often referred to as the ‘plus’ sign.
-	Subtracting Sign. Often referred to as the ‘minus’ sign.
x	Multiplication Sign. Often referred to as the ‘times’ sign.
÷	Division Sign.
=	Equal Sign.
\| \|	Absolute Value
( )	Parenthesis.
[ ]	Square Brackets.
%	Percent Sign – Out of 100.
<	Inequality sign. Less Than.
>	Inequality sign. Greater Than.
!	Factorial.
!	Factorial Sign.

Table 1 : Common Symbols and Signs

I. It reduces space.

(a + b) x c
Add’a’ and ‘b’. multiply the result with ‘c’.

Decide which is better in terms of space??

II. For Better Understanding and simplicity.

(a x b) + (c x d) / e
Multiply ‘a’ and ‘b’, have it as ‘product1′
Multiply ‘c’ and ‘d’, have it as ‘product2′
Add ‘product1′ and ‘product2′, have it as ‘sum1′
Divide ‘sum1′ by ‘e’

Decide which one you better understand? Here if u think u understand it better by words, you are making a big mistake. You will find it difficult when there are many parameters to include and much more operations to perform.

Ok. Can you notice a confusion in above expression in words. You can write the expression also like this

Multiply ‘a’ and ‘b’, have it as ‘product1′
Multiply ‘c’ and ‘d’, have it as ‘product2′
Divide ‘product2′ by ‘e’, have it as ‘factor1′
Add ‘product1′ with ‘factor1′

so which one is correct? these two expressions will gives u different results. here comes the precedence of operators, which is much more difficult when describing the operations with words.

1	() []	Grouping, scope, array/member access
2	* / %	Multiplication, division, modulo
4	+ -	Addition and subtraction

Table 2 : Order of precedence

Order of precedence is nothing but prioritizing the operators. giving privilege to operators. braces get higher priority, followed by multiplication and division symbols and then addition and subtraction symbols. Consider following expression

a + b x c / d

Here you must do highest priority operations first. That is you can multiply ‘b’ with ‘c’ or divide ‘c’ by ‘d’, because multiplication and division gets equal priority, and then only you must perform addition of ‘a’ with the previous result.

Now you may have very well understood why symbols and signs is better than just words. There may be some other reasons for symbols over words. I don’t know that for now. Will update once I come across it. I think this two points got enough advantages.

Nothing but Mathematics

Applications are Essential

Why Symbols and Signs?