## Search found 61 matches

Tue Sep 07, 2010 10:35 pm UTC
Forum: Mathematics
Topic: "Maximum" and "Maximal"
Replies: 19
Views: 6026

### Re: "Maximum" and "Maximal"

To say what Tirian said in a slightly more colloquial manner, an element is maximal if you can't add anything to it to make it bigger. For example, in a disconnected graph, an edge might be a maximal tree, but there might be some other tree in another component that's bigger. An element is a maximu...
Sat Jul 31, 2010 12:53 am UTC
Forum: Mathematics
Topic: Transitive group actions on the sphere
Replies: 54
Views: 5936

### Re: Transitive group actions on the sphere

OT, but http://www.amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/0821847813/ref=sr_1_1?ie=UTF8&s=books&qid=1280534259&sr=8-1 :-) Thanks for that. I'm taking some proper algebra courses this year including group theory, and rings and modules. I'm getting tired of being wrong...
Sat Jul 31, 2010 12:37 am UTC
Forum: Mathematics
Topic: Transitive group actions on the sphere
Replies: 54
Views: 5936

### Re: Transitive group actions on the sphere

I suspect the same is true for all n>3, but have no proof at the moment. I'm also not sure whether there are natural examples of such subgroups for any/all such n other than 4. I suspect that its true for even n>3, but not odd. The even case has -I in SO(n), but for the odd, you force a lot of unsa...
Fri Jul 30, 2010 11:36 pm UTC
Forum: Mathematics
Topic: Transitive group actions on the sphere
Replies: 54
Views: 5936

### Re: Transitive group actions on the sphere

Thanks guys, I see the complications now. I'll see if I can scheme up something else. This is what happens when you learn math from the internet I'm afraid. :lol: OT, but http://www.amazon.com/Algebra-Chapter-Graduate-Studies-Mathematics/dp/0821847813/ref=sr_1_1?ie=UTF8&s=books&qid=12805342...
Fri Jul 30, 2010 6:46 pm UTC
Forum: Mathematics
Topic: Transitive group actions on the sphere
Replies: 54
Views: 5936

### Re: Transitive group actions on the sphere

Isn't it natural to think the smallest group acting transitively on the sphere should be homeomorphic to a sphere? Perhaps it is natural to think that, but it would be incorrect, since there is no Lie group homeomorphic to S n when n is not 0, 1, or 3. Good point. Then I have nothing to contribute ...
Fri Jul 30, 2010 6:35 pm UTC
Forum: Mathematics
Topic: Transitive group actions on the sphere
Replies: 54
Views: 5936

### Re: Transitive group actions on the sphere

Isn't it natural to think the smallest group acting transitively on the sphere should be homeomorphic to a sphere?
Fri Jul 30, 2010 5:31 pm UTC
Forum: Mathematics
Topic: Transitive group actions on the sphere
Replies: 54
Views: 5936

### Re: Transitive group actions on the sphere

Just a thought (this is not my ballpark at all yet :-)), hopefully this makes sense, and if it doesn't feel free to ignore it: Let's write S=(R/2\pi)^{\oplus n-1} . Can we establish a group isomorphism S\cong SO(n) ? We have some obvious duplicates in S if we map \phi:S\to S^{n-1}\su...
Sat Jul 24, 2010 8:23 pm UTC
Forum: Mathematics
Topic: Killing infinites and using computables instead of reals
Replies: 31
Views: 7523

### Re: Killing infinites and using computables instead of reals

I'm not sure if I understand you correctly, but I think you just killed the natural numbers.
Sat Jul 24, 2010 11:51 am UTC
Forum: Mathematics
Topic: Intersection of Line Segments in a Circle
Replies: 32
Views: 4328

### Re: Intersection of Line Segments in a Circle

@antonfire: I know no statistics at all, but I figured it was natural to assume a 'linear' distribution. A what? As far as I can tell (you're not being very clear), the two ways you gave of choosing line segments randomly give you different distributions. See the Bertrand Paradox . Meant 'uniform'....
Fri Jul 23, 2010 10:41 pm UTC
Forum: Mathematics
Topic: Intersection of Line Segments in a Circle
Replies: 32
Views: 4328

### Re: Intersection of Line Segments in a Circle

For which values of s_j,t_j,a_j, b_j does f_j=f_i have a solution for all i,j\in J , and what is the probability you'll get it right if you pick values at random? I'm a bit confused by your phrasing here, so I'm not sure what you intended. I meant this: Given s_j,t_j,a_j, b_j , what is the probabil...
Fri Jul 23, 2010 9:50 pm UTC
Forum: Mathematics
Topic: Intersection of Line Segments in a Circle
Replies: 32
Views: 4328

### Re: Intersection of Line Segments in a Circle

What is being asked is basically this: Given I=[0,1], and affine linear maps f,g:I\to D^2\subset R^2 , what is the probability that there exists a point in p \in I such that f(p)=g(p) ? To ease the notation, let's consider a family of maps indexed by J . Let r=1 (the radius of the ci...
Fri Jul 23, 2010 9:03 pm UTC
Forum: Mathematics
Topic: Intersection of Line Segments in a Circle
Replies: 32
Views: 4328

### Re: Intersection of Line Segments in a Circle

If the circle har radius r, let's try to assume the average length would be r. If you're lucky (I don't know probability), assuming the lines don't intersect the origin won't affect the result. Because then you can slice the circle in half, with one of the halves containing the first line., and if t...
Fri Jul 23, 2010 7:53 pm UTC
Forum: Mathematics
Topic: How do we know i is well defined?
Replies: 16
Views: 2866

### Re: How do we know i is well defined?

@Cleverbeans: Let k,K be fields. If there exists a homomorphism k \rightarrow K , we say that K extends k and write K/k . This is just notation in the case of extension, and we read K over k. In fact, a better notation is K:k , or something completely different. Do not let that bug you though, every...
Thu Jul 22, 2010 12:19 pm UTC
Forum: Mathematics
Topic: How do we know i is well defined?
Replies: 16
Views: 2866

### Re: How do we know i is well defined?

Check out: http://en.wikipedia.org/wiki/Quotient_ring . In particular, look at the example of how to construct the complex plane rigorously from the real numbers. Assuming you believe that the reals exist and that polynomial rings exist, the complex plane pops right out of it, no strings attached. ...
Wed Jul 21, 2010 11:57 pm UTC
Forum: Mathematics
Topic: Math discovered or invented?
Replies: 110
Views: 18272

### Re: Math discovered or invented?

I don't find this argument very convincing because Euclidean Space is fundamentally a human invention. It may model reality fairly well at certain points, but Euclidean space can't really be said to physically "exist." Sure it can. At some point here, space has positive curvature. At some...
Wed Jun 30, 2010 11:02 am UTC
Forum: Mathematics
Topic: Modular law for ideals
Replies: 9
Views: 2082

### Re: Modular law for ideals

@DavCrav: The reason I wanted a more conceptual proof is that I often find the more enlightening. I find it to be the case with operations on sets in general that the proofs are nice and easy, yet unremarkable and unmemorable. The problem may well be unmendable. Your rundown is still very interestin...
Mon Jun 28, 2010 7:19 am UTC
Forum: Mathematics
Topic: Modular law for ideals
Replies: 9
Views: 2082

### Re: Modular law for ideals

Yakk wrote:So, I'm guessing you want some kind of category-theoretic proof, or something that uses the common properties of both vector spaces and ideals?

Yes, thanks for extracting this from my garble.
Sun Jun 27, 2010 9:47 am UTC
Forum: Mathematics
Topic: Modular law for ideals
Replies: 9
Views: 2082

### Re: Modular law for ideals

Yeah, they do when you mention it, nevermind then. I think a 'pretty proof' would be a better thing to ask.
Sat Jun 26, 2010 12:33 pm UTC
Forum: Mathematics
Topic: Modular law for ideals
Replies: 9
Views: 2082

### Modular law for ideals

Hello, I'm reading Atiyah-MacDonald. It's trodding along slowly but surely. On page 6 we are presented with the modular law: I\cap (J+K)=I\cap J+I\cap K if I\supseteq J or I\supseteq K . I know I can prove this by chasing elements, but I suspect there's a beautiful linear algebra-esque proof...
Thu Jun 24, 2010 1:09 pm UTC
Forum: Mathematics
Topic: Hating on the statisticians
Replies: 72
Views: 10329

### Re: Hating on the statisticians

Define 'World'.
Wed Jun 23, 2010 10:56 am UTC
Forum: Mathematics
Topic: Hating on the statisticians
Replies: 72
Views: 10329

### Re: Hating on the statisticians

Black wrote:Everyone makes fun of everyone else. It is the healthiest form of respect.

Except philosophers. I'm serious when I make fun of them.

I might print this out and hang it on my wall.
Sun Jun 20, 2010 3:50 pm UTC
Forum: Mathematics
Topic: The inverse image of prime ideals.
Replies: 5
Views: 1869

### Re: The inverse image of prime ideals.

Thanks for the good replies! Tokens edit 'I should mention that this is just an explicit way of saying "apply the first isomorphism theorem to the composite [imath]A \overset{f}\to B \to B/q[/imath]"' nailed it for me.
Sat Jun 19, 2010 12:35 am UTC
Forum: Mathematics
Topic: The inverse image of prime ideals.
Replies: 5
Views: 1869

### The inverse image of prime ideals.

Hi, I'm trying to read 'Introduction to Commutative Algebra' by Atiyah and MacDonald. It's quite terse, but I take it as good practice. Anyway, I quite quickly came across the following statement (an early stumbling block): "If f:A\to B is a ring homomorphism and q is a prime ideal in B , then ...
Sun Apr 18, 2010 8:52 pm UTC
Forum: Mathematics
Topic: Dot Product Applications
Replies: 19
Views: 7222

### Re: Dot Product Applications

Have a look at the geometric interpretation of the dot product. Given two vectors V,W , V\cdot W can be thought of as the length of the projection of V unto W , multiplied by the magnitude of W . The order with which you do this tends to commute (that is, if the matrix of your vectors have real numb...
Fri Apr 16, 2010 11:46 pm UTC
Forum: Mathematics
Replies: 367
Views: 85478

You can compactify R with infinity, but at best you'll get a metric space. That is, you'll lose a lot of the well behaved algebraic structure of the real numbers (that which makes it into a field). k/0=infty if you define it to be, but don't expect it to have beautiful properties.
Sat Mar 27, 2010 11:35 am UTC
Forum: Mathematics
Topic: amsthm
Replies: 2
Views: 1051

### Re: amsthm

Yeah exactly it, thanks.
Thu Mar 25, 2010 10:32 pm UTC
Forum: Mathematics
Topic: amsthm
Replies: 2
Views: 1051

### amsthm

Hi,
I want to make a nice setup for amsthm to incorporate in my standard LaTeX-template.

Anyone got a standard setup that they've made to look nice? I'd appreciate a copy-pasta, and maybe there are others that would as well.
thanks,
ed
Wed Mar 24, 2010 6:36 pm UTC
Forum: Mathematics
Topic: Can you get better at math?
Replies: 28
Views: 3820

### Re: Can you get better at math?

OP: crush pill is of course completely off the charts wrong. I won't hold that against him, but don't let it get to you. Nothing wrong in learning scheme or something like that though. I ask, what do you consider as mathematical intuition really? What is mathematical intuition? Mathematical intuitio...
Tue Mar 23, 2010 1:39 pm UTC
Forum: Mathematics
Topic: Can you get better at math?
Replies: 28
Views: 3820

### Re: Can you get better at math?

Another good and hard exercise is reading up on something like point-set topology way before your time. This is a good way to get used to manipulations of systems of symbols without any real way of "getting it" So true. I loved my topology class though. Yeah, you revisit the topic at a la...
Tue Mar 23, 2010 12:03 pm UTC
Forum: Mathematics
Topic: Can you get better at math?
Replies: 28
Views: 3820

### Re: Can you get better at math?

There are plenty of (not disjoint) approaches to mathematics. One is working with calculations and equations, and another is working with theories and understanding. I find that when working with theories, calculations and equations often follow, but that the converse is not always true. That is, un...
Sat Mar 20, 2010 10:33 pm UTC
Forum: Mathematics
Topic: The crux of abstract algebra, I need help
Replies: 4
Views: 1475

### Re: The crux of abstract algebra, I need help

Thanks! These are exactly the kinds of answers I'm looking for. @Suffusion: I'm doing "the whole book". That is, group theory, ring theory, ..., galois theory. It's a first course thing. It seems to me that in the end, all the stuff I'm learning this semester is stuff I absolutely HAVE to ...
Thu Mar 18, 2010 3:22 pm UTC
Forum: Mathematics
Topic: The crux of abstract algebra, I need help
Replies: 4
Views: 1475

### The crux of abstract algebra, I need help

Hello I'm currently taking a course on abstract algebra using Fraleigh's wonderful book on the subject. Now, for reasons other than laziness I haven't been able to attend classes very much. I still want to finish class and I intend on working hard to get there, but I need to catch up on the big pict...
Tue Jan 26, 2010 4:30 pm UTC
Forum: Mathematics
Topic: A subring of the reals???
Replies: 20
Views: 1733

### Re: A subring of the reals???

You show that something is a field by verifying the field axioms. Anyway, I never understood this x - y condition. It's usually just as hard to verify as showing closure under addition and additive inverse, and either way it doesn't take much time. What I meant by my comment is that there are reall...
Tue Jan 26, 2010 8:17 am UTC
Forum: Mathematics
Topic: A subring of the reals???
Replies: 20
Views: 1733

### Re: A subring of the reals???

I think the slickest way of checking if the subset E of a ring R is a subring is the following: For all x, y in E, x-y is in E, and xy is in E. If you want a ring with identity, substitute the last check with xy^(-1) edit: multiplication isn't necessarily a group. You should verify that this...
Tue Jan 19, 2010 3:58 pm UTC
Forum: Mathematics
Topic: Epsilon-Delta proof
Replies: 10
Views: 4559

### Re: Epsilon-Delta proof

Also, read the definition again and again and again. Every time you read it, you make another copy, so just read it 'til it sticks. Think about it, try to visualize it. You'll lay in your bed one night and go "ah!". From there, it's a matter of practice. Talking to your class mates about i...
Tue Jan 19, 2010 8:22 am UTC
Forum: Mathematics
Topic: I'm bad at maths. Any ideas why?
Replies: 36
Views: 4638

### Re: I'm bad at maths. Any ideas why?

I must admit however, matrices are pretty tedious. Until, I guess, you get to the point where its properties are what is interesting, and not the actual multiplication of them. Because matrices has some decent properties.
Fri Jan 15, 2010 7:51 pm UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9646

### Re: Mathematics and intellect

"A Scheme is a collection of points along with a collection T of collections of those points containing the collection of no points and the collection of all points, with the properties that for any collections of points U, V in the collection T, the collection of all points contained in both ...
Thu Jan 14, 2010 1:36 pm UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9646

### Re: Mathematics and intellect

Sorry, I wasn't clear. I meant translate the formulae (specialized mathematical notation, whatever) into English. The text, if it was in English, stays in English. I believe that mathematics is clearer without notation. I have seen this explicitly given as advice for mathematical writing from at le...
Thu Jan 14, 2010 11:29 am UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9646

### Re: Mathematics and intellect

Contrary to some of the first replies, in a sense I think you can say we actually are more intelligent. Not in the usual sense, but in our knowledge that the brain as a muscle which can be trained. Most people don't consider that, and thus understanding is a tautology from the outset: If they get it...
Tue Nov 24, 2009 10:28 pm UTC
Forum: Mathematics
Topic: The mathematics of CTRL-C CTRL-V
Replies: 28
Views: 4213

### Re: The mathematics of CTRL-C CTRL-V

Regarding this, I've reached the conclusion after a bunch of coding, that errors are invariant under copy-paste transformations.