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It's kinda like limits in calculus, only with a lot of the assumptions removed.

m and n are families of maps, with pairs of indices so that m(a, b) is a particular map that moves from the object with index a to the object with index b; if our indexing set is the real numbers, then it's like moving to the right along the number line.
Suppose you have the positive integers numbers as your indexing set, and at each integer you attach a copy of the integers labeled Z(n). The copies are all isomorphic, but they are different copies.
You also have maps from the various copies to other copies, so that for a ≤ b, there is a map m(a, b) taking the element 1 in Z(a) to some element l in Z, i.e. m(a, b)(1) = l in Z(b), and m(a, b)(k) = k*l. This would be a right mapping family, since the maps go from lower index to higher index, and the right limit has the arrow pointing to the right.
A left limit would have maps from Z(b) to Z(a).

This is part of what is called category theory, which grew out of of abstract algebra and topology so a lot of the examples are in those particular branches. Since category theory is basically an attempt to strip away the semantics from various results in mathematics, there are interpretations of categorical notions in a lot of different branches of mathematics; the categorical limits can become limits in analysis (calculus), geometry, combinatorics, number theory, etc, just by specifying what kind of objects and what kind of maps you can have.
So in algebra you want the objects to be groups or rings, and the maps to be group- or ring-homomorphisms, and possibly more structure than that. In topology you want the objects to be topological spaces and the maps to be continuous. In geometry you want the objects to be smooth manifolds and the maps to be smooth, or isometries, or somesuch.

That is pretty cool Layra!

Also I am taking a course on advanced Euclidean Geometry next semester for tits and shits. (Hooray vulgarity!)


I wonder if it would be a good idea to start a "Cranks" thread in the Science section of the ED or somewhere in this guild. I think that if we chose the cranks right, we could illustrate many common scientific and mathematical misconceptions and edumacate quite a few people.

I've bounced around a lot when it comes to interests (Though I've never ventured into pure mathematics). First it was solid state physics, then it was chaos theory, then it was high energy quantum field theory, then it was biology(!), then it was molecular electronics. I've settled on molecular electronics (Lots of QM and EM), and am doing a PhD in it; I'm hoping my interests have stopped undergoing these perennial seizures.

Yeah, I was generally thinking of the stuff that is OBVIOUSLY crank. Things that defy important, known, results. Because the things that are obviously crank are some of the ones that are going to be the best at educating people. Like perpetual motion machines, the horrible video, etc.

Also, I have succesfully found some books on fractal geometry!

biggrin

It's the Kenneth book. It is a book that makes me happy.

EDIT: WTF@ Posting order




It's certainly good to know that I'm not the only one who is dealing with/has dealt with this. I've recently started relearning chemistry because my interest in that seems to be spiking lately.


I seem to have forgotten EVERYTHING.

And I'm also finally buckling down and actually learning proper physics. (Not the horrible stuff in high school without any calculus.)

My interests generally pinball between EE, Chemistry, and what could be called applied and pure math. Physics seems to take a backseat for me. I have no idea why.

Should I learn Tensor Calculus? Y/N? I mean, if I ever want to learn GR or SR it's gonna be important right?

For those who haven't heard, guilds are currently suffering from a rather severe bug. As you may have noticed, posts are not being placed in the proper spots.

More worringly, it is possible for topics to get deleted because of this bug. There is no news on the cause of this bug, or when it may get fixed. The best thing to do for the moment is to simply not use guilds.

What's EE (Electronic Engineering?). There are a lot of Chemists working with me. Chemists and Engineers converge somewhat at the mesoscopic level. It's all Wigner transforms, Density Functional Theory, and Non Equilibrium Green's functions.

I've never formally learned tensor calculus, and simply learned what I needed to when I came across it. But then, my level of physics with QED is such that I can understand the formalism and read papers on it, but I would be terrible at doing actual theoretical research on it, and tensors really show their stuff in GR, the field I have completely neglected. My two cents would be to only learn TC if you are interested in it, or after you have decided to dive into QFT or GR. If you are serious about getting into those fields at a theoretical level, then TC is definitely necessary.

OO!!!! THE PHYSICS TEACHER AT MY SCHOOL CALLED MY DUMB AMD MEAN CLASSMATE STUPID!!! It was like payback because she is always calling people stupid, even though she is failing and they are passing. Although it was more of an implication than a direct statement, but it still was awesome. I can't wait to get into his class. But I am even more excited for CHEMISTRY next year. The teacher is super awesome, he is helping the robotics team, so i know him already. he is really cool, and likes to have fun. apparently he does a lot of semi-dangerous experiments in his class. plus, my dad and grandfather blew up their chemistry lab in highschool, so im gonna continue the tradition. yay!!! ok, maybe not, but it would be awesome.

The entire global warming topic bothers me. All the drama and news is over unimportant aspects of the subject, and nobody seems to care about the meaningful parts.

I really have to wonder just how science can get so twisted around.