Discuss & Learn How To Make Money Online
Would you like to react to this message? Create an account in a few clicks or log in to continue.

Go down
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:04 pm
Algebraic curves are the curves considered in algebraic geometry. A plane algebraic curve is the set of the points of coordinates x, y such that f(x, y) = 0, where f is a polynomial in two variables defined over some field F.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:04 pm
If the teacher wants to add points for missed questions to everyone's grade, but the highest grade is a 98 percent, then she can't add more than two points because it would give that kid a number above 100%. Unless the teacher is willing to give extra credit for the test, then she can't adjust the scores enough to count very much.
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:04 pm
Algebraic geometry normally looks not only on points with coordinates in F but on all the points with coordinates in an algebraically closed field K. If C is a curve defined by a polynomial f with coefficients in F, the curve is said to be defined over F.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:04 pm
If the teacher wants to bump a grade to 100 percent, everyone will again only get 2 points added to their grade, which isn't a significant jump.
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
The points of the curve C with coordinates in a field G are said to be rational over G and can be denoted C(G)). When G is the field of the rational numbers, one simply talks of rational points.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
If the teacher wants to use the square root, it isn't fair to that student with the 98 percent because the grade would only go up one point.
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
Algebraic curves can also be space curves, or curves in a space of higher dimension, say n. They are defined as algebraic varieties of dimension one. They may be obtained as the common solutions of at least nā€“1 polynomial equations in n variables.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
Grading on a curve has long been disputed in the academic world, just as weighting scores have. The main benefit to using the curve is that it fights grade inflation:
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
If nā€“1 polynomials are sufficient to define a curve in a space of dimension n, the curve is said to be a complete intersection. By eliminating variables (by any tool of elimination theory), an algebraic curve may be projected onto a plane algebraic curve, which however may introduce new singularities such as cusps or double points.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
if a teacher doesn't grade on a curve, forty percent of her class could get an "A," which means that the "A" doesn't mean very much.
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
A plane curve may also be completed in a curve in the projective plane: if a curve is defined by a polynomial f of total degree d, then wdf(u/w, v/w) simplifies to a homogeneous polynomial g(u, v, w) of degree d.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:05 pm
An "A" grade should mean "excellent" if it means anything, and theoretically, 40 percent of any given group of students are not "excellent."
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
The values of u, v, w such that g(u, v, w) = 0 are the homogeneous coordinates of the points of the completion of the curve in the projective plane and the points of the initial curve are those such w is not zero. An example is the Fermat curve un + vn = wn, which has an affine form xn + yn = 1. A similar process of homogenization may be defined for curves in higher dimensional spaces
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
However, if a teacher strictly bases the grades on the curve, then it restricts the number of students who can excel.
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
Important examples of algebraic curves are the conics, which are nonsingular curves of degree two and genus zero, and elliptic curves, which are nonsingular curves of genus one studied in number theory and which have important applications to cryptography.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
Thus, a forced grade is a disincentive to study: students will think "no point in studying too hard, Susan and Ted will get the only As available on the curve."
avatar
Dhruv singhaniya
Posts : 12549
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
Because algebraic curves in fields of characteristic zero are most often studied over the complex numbers, algebraic curves in algebraic geometry may be considered as real surfaces. In particular, the nonsingular complex projective algebraic curves are called Riemann surfaces.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
And they create an atmosphere that's toxic. Who wants a class full of finger-pointing students blaming the one or two stars?
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
Teacher Adam Grant suggests using the curve only to increase scores and building a collaborative atmosphere, so students help each other to get better scores.
avatar
Abhishek
Posts : 12935
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:06 pm
The point of a test is not the score, he argues but to teach your students how to learn new things.
avatar
Aditya992000
Posts : 9257
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:35 pm
The yield curve is gaining attention these days. When the two-year Treasury bond yield creeps above the 10-year yield ā€” which it's threatening to do ā€” market watchers say a recession follows.
avatar
Aditya992000
Posts : 9257
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:36 pm
On Tuesday, the yield curve showed flatness in the midyear range, and wire services reported a slight inversion of 2 basis points between the benchmark 2-year and 5-year notes. That is, the 2-year bond at one point showed a yield of 2.82% vs. 2.80% for the 5-year note.
avatar
Aditya992000
Posts : 9257
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:36 pm
Meanwhile, Bloomberg data showed that the spread between the benchmark 2-year and 10-year bonds got squeezed to 52 basis points. On Jan. 1 this year, the spread was 102 basis points, or more than a full percentage point.
avatar
Aditya992000
Posts : 9257
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:37 pm
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that its curvature need not be zero
avatar
Aditya992000
Posts : 9257
Join date : 2019-01-07

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Wed Jan 16, 2019 12:37 pm
Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context
Sponsored content

What is a Curve ? - Page 3 Empty Re: What is a Curve ?

Back to top
Permissions in this forum:
You cannot reply to topics in this forum