sykh

21 ms·

181.
by sykh 9y ago
x+3 is an element of the polynomial ring Q[x]. More precisely it is syntactic sugar for the infinite tuple (3, 1, 0, 0, ....) A polynomial ring in one variable is an infinite direct sum of the base ring with addition component wise and mult
182.
by sykh 9y ago
Polynomials in multiple variables always have the variables ordered. Sometimes the ordering is not important or explicitly stated but in reality they are supposed to be ordered. If we start with x y + 2 = 0 we can apply the function f(x)
183.
by sykh 9y ago
That may be a consequence of such laws but do you have evidence that this is the consequence that the people making this law want? What evidence do you have for the motivations for the people making this law.
184.
by sykh 9y ago
Let me be more precise. Assume x+3 is an element of R[x] with x an indeterminate and R a ring with characteristic not equal to 3. Then x+3 defines a natural map from R to R. The equation x+3=1 is just a shorthand way of asking for the pr
185.
by sykh 9y ago
There is a solution. An equation is really a question. x+3 = 1 is asking the question, “what value for x makes x+3 the number 1?” The polynomial x+3 is defined for all values in R, the base ring you are working in. We are trying to find t
186.
by sykh 9y ago
Solutions to equations in multiple variables are ordered tuples. For instance, x y + 2 = 0 has infinitely many solutions. One of them is (1, -2).
187.
by sykh 9y ago
Let’s assume we are talking about Q, the rationals. x+3 is an element of Q[x]. This element of Q[x] defines a natural map from Q to Q. The equation x+3 = -2 is equivalent to finding the pre-image of -2 of this natural map. x is actually
188.
by sykh 9y ago
With this proposal they want to impede freedom of information while at the same time get some of that sweet tax money in the pockets of their allies. This sounds plausible but do you have evidence that it is actually true? An equally plau
189.
by sykh 9y ago
Think about the equation x + 3 = 1 Typically we write that the solution is "x = –2". This to me is the most abusive form of usage for "=" in mathematics. The solution to the equation is –2. The solution to the equatio
190.
by sykh 9y ago
To me you ignore too much students' responsibilities when it comes to their education. I suppose to you I seem to ignore too much teachers' responsibilities when it come to education. I don’t think that I do. I invest as much t
191.
by sykh 9y ago
Yes, there has been a change in the purpose of higher education in the U.S. As you say the credential is the goal and not knowledge. This is especially so at urban community colleges. All I can do as a teacher at a community college is t
192.
by sykh 9y ago
The number of inspiring people is much less than the number of teaching positions. And the number of inspiring mathematically talented people with enough knowledge to teach mathematics is much less than the number of math teaching position
193.
by sykh 9y ago
I’m not saying a standardized test would be a great way to measure learning, just that it is better than looking at passing rates. Passing rates are easy to make higher. When talking about student success in my experience it’s always abou
194.
by sykh 9y ago
It's an interesting hypothetical. Here's how I run the course. I have lectures for each topic (the lectures I've created). Accompanying the lectures are problem sets along with solutions. Students are expected to watch the
195.
by sykh 9y ago
The statements you quoted are about apathetic students. Do you have a cure for apathy in learning? I don't. Teachers come in a variety of talents and have a variety of teaching styles. One thing that colleges do poorly is align a st
196.
by sykh 9y ago
Well passing rate is a very bad meaurement. It’s so easy to fudge. In math a standardized final exam written by a third party would be a much better measurement of learning in my opinion.
197.
by sykh 9y ago
The passing rate has improved a bit but dropout rates are essentially unchanged. What has mostly changed is that the students can’t fake the fact they didn’t do the work. My dean has been supportive. I don’t do student opinion surveys so
198.
by sykh 9y ago
I’ve been doing flipped classrooms for nine years now. I teach mathematics at a community college. What I’ve found so that students drop out much sooner in my flipped classroom style versus traditional lecture style class. But the overal
199.
by sykh 9y ago
I think the change in the publics’ perception on the harm of plastic will happen in stages. This will just be a first step. In the U.S. I don’t think people are ready for major changes due to the politicization of environmental issues.
200.
by sykh 9y ago
In comparing Facebook to newspapers and others scale matters. When you have an addicting service at the scale of Facebook that also has the ability to sway elections or public opinion at the scale they do then it becomes a problem. Requir
201.
by sykh 9y ago
We’ll certainly don’t not accept my clarifications. At some point it is just being pig headed to do otherwise. I don’t need to reread my original comment because I know what I intended b6 it. I’ve since clarified. An expert claims inequa
202.
by sykh 9y ago
I misread “fund” as “food”. I’m on a mobile device without my glasses. Sorry for the error. The mistake was mine. It is bad for you to ignore the rest of what I wrote in my previous comment. I think I did make it clear what I was talking
203.
by sykh 9y ago
You added a phrase that I did not write. as just jealous I did not write this or imply this. People who struggle with food or housing are not merely jealous. They have real concerns and need. The discussion I referred was not about suc
204.
by sykh 9y ago
I haven't read Pinker's book and he is certainly more knowledgeable than I am on the topic. What does he say about attitudes like "keeping up with the Joneses", jealousy, and similar emotions? It seems to me that most
205.
by sykh 9y ago
Don't ISPs like Comcast have access to orders of magnitude fewer users? I think it has to do with scale and the fact the Cambridge Analytica used Facebook data and not, it seems, Comcast data. Overall Facebook is just the focal point
206.
by sykh 9y ago
...will ever go up against the power of the Chinese state. There are lots of examples of religious fervor going up against a state and winning. If a movement gains sufficient mindshare and it’s adherents are sufficiently galvanized then
207.
by sykh 9y ago
I don't know the particulars in this case but is Nestlé going to pay proper amount for this water? If the public doesn't want the plant then shouldn't their desires carry some weight? Especially since it doesn't appear
208.
by sykh 9y ago
My parents were citizens. They were born in Minnesota and later in life moved to Panama for work.
209.
by sykh 9y ago
We did have a governor appointed by the President. I believe it was considered a territory of the United States. We were part of a federal court circuit. I don’t think it was a lease. My understanding is that the Bunau-Varilla treaty ga
210.
by sykh 9y ago
I was born in the Canal Zone when it was a U.S. territory. Both parents were American. By an act of Congress I am a natural born citizen. I’ve always been under the impression that it was well established that it is a power of the governm

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