Function

[shahar]

When the Modern History of Math define function, it only deal on quadratic equation and linear equation.
The other equation are have a little notice.
You, can investigate a function and know how it look and then to know detail about how it "look".
But, we need the derivative of the function.
(1) Can I define it by number theory like as:
the usual dictionary definition: "It about numbers, figure, abstract and else" (every dictionary show it)..
And Then NTCM define it as: Use of of the number.
I don't have access to this Encyclopedia part because it one a fee.
So, I can that tell what written there as I remember:
"It first deal with Natural Number, and that Fraction, but also with ... Complex number and the Number itself".
So, the keyword is a Number, first all.
I need the source, the NTCM decide on it and it look to me the exactly definition of Number Theory and not only the Natural Number.
Source to that will be get.
So link to information about it will be great.

(I don't know what the different between the curriculum/syllabus of other Institutes.)

(2) Why this is connected or not connected TO derivative?
Why because of definitions?
I know that We also explore that not only by graph, but also by algebra.
Is the reason it complex Algebra?
O.K. I am done and my keyboard resting. I am waiting for answer.
I hope my English get better.

 

[shahar]

Note:

I don't want to put all the eggs in one basket but I think I have a lot of error.

"We will know, we must know"
(By Hilbert)

 

[Dr.Peterson]

When the Modern History of Math define function, it only deal on quadratic equation and linear equation.
The other equation are have a little notice.
You, can investigate a function and know how it look and then to know detail about how it "look".
But, we need the derivative of the function.
(1) Can I define it by number theory like as:
the usual dictionary definition: "It about numbers, figure, abstract and else" (every dictionary show it)..
And Then NTCM define it as: Use of of the number.
I don't have access to this Encyclopedia part because it one a fee.
So, I can that tell what written there as I remember:
"It first deal with Natural Number, and that Fraction, but also with ... Complex number and the Number itself".
So, the keyword is a Number, first all.
I need the source, the NTCM decide on it and it look to me the exactly definition of Number Theory and not only the Natural Number.
Source to that will be get.
So link to information about it will be great.

(I don't know what the different between the curriculum/syllabus of other Institutes.)

(2) Why this is connected or not connected TO derivative?
Why because of definitions?
I know that We also explore that not only by graph, but also by algebra.
Is the reason it complex Algebra?
O.K. I am done and my keyboard resting. I am waiting for answer.
I hope my English get better.

It's hard to be sure what you are asking, or how these different questions fit together.

I have no idea what you are asking about Modern History of Math and functions. Please give an example. Possibly you are saying that you took a course on history of math, and it only touched on relatively basic functions; but what are you asking for?

You seem to be asking for a definition of the field of math called Number Theory, but only in connection with elementary level math (NCTM). What is called number theory before college would probably include ideas like prime numbers, factoring, and so on. These generally deal only with positive integers. The same is largely true of college-level number theory. What we need to know is the context of your question: Why are you asking, and what will you do with the answer?

I have no idea what any of this has to do with derivatives. Derivatives are only relevant to real numbers (or complex), not to integers.

It will help considerably if you stick to one question at a time, and give examples of what you are asking about.