What does this mean?

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Mark

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Message 1069 - Posted: 13 Jun 2014, 3:43:54 UTC

I am just wondering what does this project lead to? What can solving these problems lead to?
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Profile Eric Driver
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Message 1070 - Posted: 13 Jun 2014, 7:18:39 UTC - in response to Message 1069.  

I am just wondering what does this project lead to? What can solving these problems lead to?


Here is a link to the project description:
http://numberfields.asu.edu/NumberFields/ProjectDescription.html

I'd be interested in some feedback on the description, especially if there are parts that are hard to understand. I've been doing this stuff so long, I can't tell which parts need more explaining.

Also, the main page has a link to a table of the results.

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Message 1071 - Posted: 14 Jun 2014, 19:27:07 UTC - in response to Message 1070.  

I am just wondering what does this project lead to? What can solving these problems lead to?


Here is a link to the project description:
http://numberfields.asu.edu/NumberFields/ProjectDescription.html

I'd be interested in some feedback on the description, especially if there are parts that are hard to understand. I've been doing this stuff so long, I can't tell which parts need more explaining.

Also, the main page has a link to a table of the results.




Hi Mark,

as Eric says you can find the informations on the project description.

Mostly this project is active on basic search, but nobody was charted it before NF@Home.

This project can help by solving modern problems, like mandelbrot theorem. [Now we are in the chaostheorem, and if we go a little bit deeper at DNA-Science and the the science of Wind waves [quantum physics, because liniaer wave theorem is wrong]]

We see that this project is realy complex, and hard to understand. I´m sure that we can´t understand it...


@Eric The Low GRD fields are computed?

Some links:

http://en.wikipedia.org/wiki/Fractal
http://en.wikipedia.org/wiki/Wind_wave
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SandJ

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Message 1780 - Posted: 24 Oct 2016, 18:55:00 UTC - in response to Message 1071.  

I've also read the project description and I am no wiser. For once, Wikipedia is no help either, even with the most basic term field :

In mathematics, a field is one of the fundamental algebraic structures used in abstract algebra. It is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.

This isn't a problem of number field theory, it is a problem of explanation. For example, the person who wrote this:

Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication (the latter excluding zero), with "compatible" being formalized by distributivity, and the caveat that the additive and the multiplicative identities are distinct (0 ≠ 1).

was giggling to themselves when they put in the word "intuitively".
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Profile Eric Driver
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Message 1781 - Posted: 25 Oct 2016, 0:16:04 UTC - in response to Message 1780.  

I've also read the project description and I am no wiser. For once, Wikipedia is no help either, even with the most basic term field :

In mathematics, a field is one of the fundamental algebraic structures used in abstract algebra. It is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.

This isn't a problem of number field theory, it is a problem of explanation. For example, the person who wrote this:

Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication (the latter excluding zero), with "compatible" being formalized by distributivity, and the caveat that the additive and the multiplicative identities are distinct (0 ≠ 1).

was giggling to themselves when they put in the word "intuitively".


Is there 1 part in particular that gives you trouble. Commutative (also called Abelian) means a+b=b+a and a*b=b*a. Or is it the mathematical definition of "group" that gives you a problem?

Maybe it's easier to think of it in terms of examples such as the field of rational numbers. For any two rational numbers a and b; a+b, a*b, and a/b are also rational numbers (provided b is nonzero). As a counter-example, the integers are not a field since a/b is not necessarily an integer. This project deals with fields that are finite extensions of the rationals.
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Message 2460 - Posted: 9 Jun 2019, 16:28:59 UTC

I want to understand what this means someday.

When I read the words "basic research" and "uncharted territory" within the project description, I got excited. So excited, I signed up.

Right now, it looks like a very long bridge from understanding MATH265 concepts (Calculus I for Engineers to those of you not fortunate enough to be a Sundevil) to understanding number fields.

I have faith in reason. What I lack is faith in my own capacity to reason.

If I ever complete ASU's online BSEE program, is it remotely possible to pursue mathematics at the graduate level?

Best Regards.
The Creator has not answered. The carbon-units infestation is to be removed from the Creator's planet.
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Profile Eric Driver
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Message 2461 - Posted: 9 Jun 2019, 20:44:46 UTC - in response to Message 2460.  

I want to understand what this means someday.

When I read the words "basic research" and "uncharted territory" within the project description, I got excited. So excited, I signed up.

Right now, it looks like a very long bridge from understanding MATH265 concepts (Calculus I for Engineers to those of you not fortunate enough to be a Sundevil) to understanding number fields.

I have faith in reason. What I lack is faith in my own capacity to reason.

If I ever complete ASU's online BSEE program, is it remotely possible to pursue mathematics at the graduate level?

Best Regards.


As it turns out, I got my BSEE from ASU and then went back for my PhD in Math. So yes, it can be done, but you really need to enjoy math. I would suggest taking some math courses for your electives. Linear algebra should be part of the standard curriculum which will introduce you to the concept of vector spaces (vector spaces are defined over fields, so naturally you will also get exposed to fields). I would also suggest taking "Abstract Algebra" - not only will it give you a good overview of groups, rings, fields, etc; but the knowledge will come in handy if you decide to take algebraic coding theory from the EE department.
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