this theory is on its first steps so I don't have any Idea about the application of theory.Reading is boring. Examples make theory meaningful. Therefore, why not throw at us an example or a problem to discuss instead of reading a story without a single picture.
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?this theory is on its first steps so I don't have any Idea about the application of theory.
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.I am studying them in calculus, but I am talking about an algebraic structure derived from geometric curves.
yeah, but let's discuss my theory, my theory defines an algebraic structure named curves because it's derived from geometric curvesCalculus 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.
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!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
You mean, for example, Closure has this:no, we have formulas in PDF.
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.OK guys, I think I have a math theory, A theory about mathematical structures or Algebraical structures named curves, I attach a PDF to this post to see my theory.
Oh, I'm sorry I sent the Incomplete PDF I will edit itThe 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).
I didn't open the pdf. I wonder how many here would say that an example is needed in theoretical math?Reading is boring. Examples make theory meaningful. Therefore, why not throw at us an example or a problem to discuss instead of reading a story without a single picture.
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.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.
Professor Steven. You will have to open the PDF file if we want to have a discussion.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.
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?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.
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 wonder how many here would say that an example is needed in theoretical math?
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]?this is the better pdf and complete pdf
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.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?
Does this mean any function with two variables represent a curve?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.
if by this you mean a curve of kind of my theory, yeah pretty much.Does this mean any function with two variables represent a curve?