## Friday, July 24, 2009

### Engineering Mathematics - Demystified Part 2

Continued from part 1
Is mathematics a science or is science a part of mathematics?
Does anyone remember the advertisement of "Coffee Bite". There is an argument on whether the toffee is a coffee or a toffee and the punch line is that "the argument continues".The same hold good here.
Meaning of science is "field of knowledge". In this sense Mathematics is part of science.
But science deals with only physical world. In that sense mathematics cannot be part of science since there are mathematicians who simply derive certain theorems without any practical application in mind. These theorems may or may not turn into applications at a later stage.
So let the argument continue. Let us don't worry too much about that. Just know the above two facts.

What is the meaning of Mathematics?
Mathematics is derived from a Greek word - mathema, which means learning, study or science.
Is the usage "Maths" correct?Maths is simply a short form of Mathematics.

What is the definition of mathematics, How it evolved?
The standard definition goes like this
"Mathematics is the study of
1. Quantity
2. Space
3. Change
4. Structure"
Now we can try to analyse this defintion in a simple manner.
Quantity - Means study of numbers. Only if number exist we can measure quantity. All the operations done on the numbers are called "Arithmetic".Branch of mathematics which deals with study of quantity is called ARITHMETIC. Study of quantity is the fundamental in mathematics.
Space - Space means study of dimensions. We have one dimension (1D), 2 dimension (2D) and 3 dimension (3D). Dimension means a measurable quantity. 1 dimension means one measurable quantity, 2 dimension means 2 measurable quantities Why dimension is needed? To represent objects. Once we appreciate the concept of quantity, the same is being used to model objects in space. It is in this context we study trigonometry and geometry.Hence mathematics is a study of space.
Change -Some "quantities" change their value with respect to time. When a quantity changes with respect to time, we call it a dynamic system. In real world there are many examples of dynamic system vizwhen we boil water the temperature of the water increasesthe speed of a vehicle etcThe study of such dynamic systems comprises one area of mathematics. Hence mathematics is a study of change.

Structure -It was mentioned that by space we meant the study of objects having different dimensions. Each of these objects have an internal structure. The study of these internal structure is also part of mathematics. A detailed discussion on this will only confuse things. Hence I am limiting this here.
From the above list (ie quantity, space, change and structure), we can easily pick the one which must be evolved initially.
Yes it is quantity.
Now how did this evolve?
Man knew that apples are different from oranges.
But when he saw Three apples and three oranges, he recognized that there is something in common.
The commonality is quantity.
This realisation of quantity was the first step in evolution of mathematics.

Some interesting quotes on mathematics

"Mathematics is the queen of sciences" - Gauss
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality" - Albert Einstein
"Mathematics is the science that draws necessary conclusions"

New Topics to come later about Mathematics
Differentiation - A practical description
Matrix - What is it and why it is needed?