I think I have a math theory
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this theory is on its first steps so I don't have any Idea about the application of theory.
The theory of curves is a very complicated topic. And if you have no idea about its applications, you will have a hard time solving its problems. I have studied curves in Calculus a few years ago. And when I see a problem now about curves, I feel like I have studied nothing. Are you studying curves in Calculus or in a Differential Geometry course?
Calculus will only teach you the basic idea of curves. If you are really interested in understanding them, you will have to study them in a Differential Geometry course. And if you understood curves pretty good, you would love to extend your knowledge to surfaces.
yeah, but let's discuss my theory, my theory defines an algebraic structure named curves because it's derived from geometric curves
Are you telling me that we are going to discuss a pure theory without writing down a single formula? That's so boring as well as I don't understand mathematics in that way!
no, we have formulas in PDF.
You mean, for example, Closure has this:
[imath]\displaystyle \forall x,y \in \varepsilon, \ \ \ x \oplus y \in \varepsilon[/imath]
Dr.Peterson
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The trouble is that you haven't started with definitions or axioms, so you are not actually talking about anything. As far as I can see, you could replace the word "curve" with, say, "group element"; when you get around to talking about things like curvature, you fail to define it at all. Does an individual curve have a single number called its curvature, or does that vary along the curve? For that matter, does a curve even have parts? You eventually talk about "components", and imply some connection to numbers, and a notation that looks as if a curve is a function of two numbers, or something like that, but you haven't defined what any of that means.
Typically, an abstract theory starts as an extension of a specific concept, so that you initially have some sort of example, at least, to communicate what sort of object and operation you envision. Are you picturing combining two curves by concatenating them, or something else?
You will find as you study further that there is in fact a theory of curves; in fact, there are several concepts that could be described that way. What you have at this point is not a theory, just an ad for something you claim is coming, but whose actual existence is questionable. I'm not investing in it (yet)! But when you learn more math, you will see some real things you will want to "invest in", because their value, and reality, will be clear. And you will have a better idea of what it makes to earn buy-in on a theory (for example, it should be interesting, or useful, or both).
Oh, I'm sorry I sent the Incomplete PDF I will edit it
Steven G
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I didn't open the pdf. I wonder how many here would say that an example is needed in theoretical math?
I recall when I was studying math at the graduate level that most of the lectures were of the form Theorem-Proof, Theorem-Proof, ....
It was pure theory. It could have been I took courses that typically go that way and stayed away from applied math courses.
you are right, but there is a catch I have given some examples of usage of this theory but still, there is room for finding examples for this theory.
Professor Steven. You will have to open the PDF file if we want to have a discussion.
I can see that you have extended your theory in the PDF file. So, it is your theory, not ours, right? I suppose that you understand it all. Therefore, could you please explain to me what does 2.1 Algebraic Curve mean with an example?
Dr.Peterson
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Needed? Perhaps not. But it is important in introducing a new idea, and especially in convincing others that it is worth pursuing. To show why we bother defining fields, for example, we show that the real numbers and the rational numbers are fields. Anything that there are two of seems worth naming and studying ...
I still see a lot missing. What does it mean to add two curves? And why do you vary between f(x, y), f(x), and [imath]\gamma(t)[/imath]?
Then you indicate that you are aware that there is already a specific theory of algebraic curves, to which you don't seem to be adding anything. Why do you claim to be discussing "curves", but only define algebraic curves?
I feel as if I were looking at AI-generated material, since AI is much better at looking meaningful than at actually being valid.
an algebraic curve is a set of points that satisfies a polynomial function in [imath]\mathbb{R}^2[/imath] space, for example, we have curve C as a curve with three points on it A, B, and C that these points are paired x and y if we give these pairs to a function f defined as [imath]f(x, y) = x^3 -yx + y[/imath][math][/math] and f get zero then these points structure a algebraic curve.
Does this mean any function with two variables represent a curve?
if by this you mean a curve of kind of my theory, yeah pretty much.