Search found 248 matches

by DavCrav
Fri Mar 25, 2011 9:35 am UTC
Forum: Mathematics
Topic: Finite group extensions
Replies: 37
Views: 3859

Re: Finite group extensions

Important point, everyone: In group theory, if "G is an extension of K by H" then K is a normal subgroup of G and H is the quotient. Often in other areas of algebra, Ext(A,B) means B is the kernel and A is the quotient. This is probably the source of confusion. Almost certainly, a finite ...
by DavCrav
Wed Mar 23, 2011 10:58 am UTC
Forum: Mathematics
Topic: Finite group extensions
Replies: 37
Views: 3859

Re: Finite group extensions

Important point, everyone: In group theory, if "G is an extension of K by H" then K is a normal subgroup of G and H is the quotient. Often in other areas of algebra, Ext(A,B) means B is the kernel and A is the quotient. This is probably the source of confusion. Almost certainly, a finite e...
by DavCrav
Fri Feb 25, 2011 10:49 am UTC
Forum: Mathematics
Topic: Primitive roots mod p
Replies: 7
Views: 1857

Re: Primitive roots mod p

eta oin shrdlu wrote:
DavCrav wrote:I have a great solution for the second part [...]
Is this a proof that the smallest primitive root grows without bound (which is how I interpret the question), or that the number of primitive roots grows without bound?


No, you are right. Whoops. Well, I answered a different question...
by DavCrav
Wed Feb 23, 2011 10:05 am UTC
Forum: Mathematics
Topic: Primitive roots mod p
Replies: 7
Views: 1857

Re: Primitive roots mod p

I have a great solution for the second part, and I can tell it in full because I don't think you will be able to use it for your homework. :D We will prove that, for all n, there exists a prime p such that there are at least 2^{n-1} primitive roots mod p. To see this, note that the number of primiti...
by DavCrav
Fri Feb 11, 2011 11:57 am UTC
Forum: Mathematics
Topic: The Tau Manifesto
Replies: 165
Views: 43782

Re: The Tau Manifesto

Kurushimi wrote:
the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.

That doesn't make sense. You mean to tell me if I piled together everything in the universe, it would amount to 1/16th of something? Of what exactly, huh?


Sixteen Universes?
by DavCrav
Fri Jan 21, 2011 12:33 pm UTC
Forum: Mathematics
Topic: History of Complex Analysis and Topology
Replies: 5
Views: 2395

Re: History of Complex Analysis and Topology

I'm not sure how much of this stuff it has in it, but there's a book simply called History of Topology, edited by Ioan James, from North-Holland. This has lots and lots of information. I had a look at the table of contents of my copy, and it seems to be considering Poincaré on, but you can try it.
by DavCrav
Wed Jan 05, 2011 11:58 am UTC
Forum: Mathematics
Topic: Sets of measure zero
Replies: 20
Views: 2581

Re: Sets of measure zero

Well, think about it this way. A person claims to have a true random number generator, which produces a random number in the interval [0,1] by spitting out its bits one at a time, which it obtains by measuring the spin of an electron alternately in the x and y directions. The many-universes interpr...
by DavCrav
Tue Dec 21, 2010 1:09 pm UTC
Forum: Mathematics
Topic: Undergrad project on the classification of FSGs
Replies: 8
Views: 1157

Re: Undergrad project on the classification of FSGs

OK, I'm sorry to have to break this to you, but after three years of group theory, you haven't the slightest chance of understanding any of CFSG. I have ten years of group theory behind me, and I broadly have a rough idea of what's going on. If you want something like CFSG, there are various miniatu...
by DavCrav
Thu Nov 04, 2010 10:51 am UTC
Forum: Mathematics
Topic: My idea on why math is hard...
Replies: 28
Views: 3863

Re: My idea on why math is hard...

Quote in my math course: "A mathematician is a device for turning coffee into theorems." Your quote is from Paul Erdos, and actually "coffee" in that case was a euphemism for amphetamines, to which he was addicted. Not as cute now, I imagine. Erm, citation needed. I thought it w...
by DavCrav
Wed Oct 27, 2010 9:00 am UTC
Forum: Mathematics
Topic: I need some kind of help (Proof on Equivalence Relation)
Replies: 26
Views: 2381

Re: I need some kind of help (Proof on Equivalence Relation)

remember that an equivalence relation R on A is a subset of AxA... (My point was that this is not how I, or most people, think of an equivalence relation: we think of it as a partition of A...) Do you really think this is true? It's not how I think of an equivalence relation. For me, an equivalence...
by DavCrav
Mon Oct 25, 2010 8:25 am UTC
Forum: Mathematics
Topic: I need some kind of help (Proof on Equivalence Relation)
Replies: 26
Views: 2381

Re: I need some kind of help (Proof on Equivalence Relation)

Tinyboss wrote:remember that an equivalence relation R on A is a subset of AxA...


(My point was that this is not how I, or most people, think of an equivalence relation: we think of it as a partition of A...)
by DavCrav
Sun Oct 24, 2010 9:24 pm UTC
Forum: Mathematics
Topic: I need some kind of help (Proof on Equivalence Relation)
Replies: 26
Views: 2381

Re: I need some kind of help (Proof on Equivalence Relation)

Erm... In order to make sense of this problem I need to know what the phrase "cardinality of an equivalence relation" means. It certainly isn't the number of equivalences classes, as then this statement is blatantly false.
by DavCrav
Fri Oct 15, 2010 10:30 am UTC
Forum: Mathematics
Topic: I don't want a flu shot.
Replies: 33
Views: 4861

Re: I don't want a flu shot.

[blah blah blah] I think the rest of the forum here is a bit too unprofessional and [blah blah blah] (You see what I did there? :twisted: ) I was under the impression that this wasn't the official forum of the Royal Statistical Society. The point is, that when people come on here wanting ammunition...
by DavCrav
Mon Oct 04, 2010 9:56 am UTC
Forum: Mathematics
Topic: Finding an English translation of a math paper...
Replies: 7
Views: 1693

Re: Finding an English translation of a math paper...

I want to read it because it proves that a graph is planar if and only if it does not contain K(3,3) (bipartite graph) or a 5-clique, which I would like to understand in a thorough way before trying to learn more advanced results in this area of graph theory. If you didn't know, this is just called...
by DavCrav
Fri Oct 01, 2010 10:02 am UTC
Forum: Mathematics
Topic: A rectangle with rounded edges is not an oval
Replies: 22
Views: 19100

Re: A rectangle with rounded edges is not an oval

I've seen the word "stadium" to refer to a rectangle with corners replaced by quarter-circles. e.g., the Bunimovitch stadium.
by DavCrav
Fri Sep 10, 2010 7:36 am UTC
Forum: Mathematics
Topic: multiplicity of totient function
Replies: 17
Views: 2978

Re: multiplicity of totient function

Sorry to drag this thing up, but I came up with an easy proof of this (obviously already known, I guess), using cyclic groups. Firstly, if d and e are coprime, then it is well known that C_{de}=C_d\times C_e , where C_n is the cyclic group of order n . Notice that a generator for the cyclic group C_...
by DavCrav
Wed Sep 01, 2010 12:50 am UTC
Forum: Mathematics
Topic: Finished my book
Replies: 6
Views: 974

Re: Finished my book

Yakk wrote:Congratulations! Now for the important question:
what colour is the cover?


I don't know. I rather hope they let me pick the colour of the stripe. (It's grey, with a stripe on the bottom-right of the cover.)
by DavCrav
Sat Aug 28, 2010 5:48 pm UTC
Forum: Mathematics
Topic: That d used for partial derivatives
Replies: 21
Views: 4659

Re: That d used for partial derivatives

`Del' is definitely the [imath]\nabla[/imath] operator, in particular the Laplacian being called `del-squared'. `Dee' I know, `curly dee' I can imagine, all others no way. But i'm a purey, so I can be ignored, I guess!
by DavCrav
Sat Aug 28, 2010 5:42 pm UTC
Forum: Mathematics
Topic: Finished my book
Replies: 6
Views: 974

Re: Finished my book

It's a graduate/expert text (i.e., reference work or can be used as a textbook) on a new subject called fusion systems. These things are categories that attempt to model fusion (how conjugacy classes of subgroups combine in the whole group) in a p-group. It includes bits of group theory, representat...
by DavCrav
Sat Aug 28, 2010 5:39 pm UTC
Forum: Mathematics
Topic: New poll shows that correlation is causation
Replies: 14
Views: 3709

Re: New poll shows that correlation is causation

Talith wrote:
Tirian wrote:I used to think correlation implied causation. Then I took a statistics class. Now I don't.

I'm certain the class caused you to change your mind.


Well, maybe.
by DavCrav
Sat Aug 28, 2010 5:32 pm UTC
Forum: Mathematics
Topic: Finished my book
Replies: 6
Views: 974

Finished my book

I'm not around here very often (well, I am, but mostly lurk), but post occasionally. I just thought (because there's nobody around at the moment to shout at) that I have just finished writing my book, and have sent it to the publishers! Go me! Edit: I should point out that my book isn't titled "...
by DavCrav
Sat Aug 14, 2010 9:54 am UTC
Forum: Mathematics
Topic: You can solve any rubik's cube in 20 moves.
Replies: 27
Views: 4978

Re: You can solve any rubik's cube in 20 moves.

I'm more interested in the advances (if any) in computational group theory behind this. Working out 'God's number' for the Rubik's cube is just one instance of the following: Suppose you have a group presentation, and you are told the group is finite (let's say you even know its order, exponent, wh...
by DavCrav
Fri Aug 13, 2010 12:43 pm UTC
Forum: Mathematics
Topic: Pairing off points: More surprising trickiness
Replies: 18
Views: 2478

Re: Pairing off points: More surprising trickiness

This question was asked, with a few extra stages, as part of an interview question for 17-year olds at St John's Oxford. With some prodding, the idea is you can solve this in about ten-fifteen minutes. :)
by DavCrav
Fri Aug 13, 2010 11:44 am UTC
Forum: Mathematics
Topic: Revised Simple Proof of Beal's Conjecture
Replies: 29
Views: 4160

Re: Revised Simple Proof of Beal's Conjecture

Just thought I'd say, in before the lock! :twisted: Also, this: It's only wrong in one direction. If a+b=c, then the left side can always be factored into the form P(Q+R). This is true. The problem comes from the fact that if the factorization is P=1, Q=a, and R=b, then this gets you nothing, becaus...
by DavCrav
Wed Aug 11, 2010 10:46 am UTC
Forum: Mathematics
Topic: Thank you for #435
Replies: 42
Views: 5300

Re: Thank you for #435

Purity was a hilarious comic but I want to particularly thank you for making the mathematician a girl. I am a woman with a math degree and far too often hear other women respond to my degree with "Woooow, I could never do that." It's time to break through stereotypes in this area of study...
by DavCrav
Mon Jul 05, 2010 9:14 am UTC
Forum: Mathematics
Topic: Is it just me, or does the average guy really suck at math?
Replies: 57
Views: 8062

Re: Is it just me, or does the average guy really suck at ma

(x-10)^2-100+51=0 (x-10)^2=49 (x-10)=+/-7 x=17 or 3 certainly possible in your head! Admittedly if the root wasn't calculable that'd be harder. I don't know any root finding algorithms off the top of my head. Hmm. My standard way is: 51 = 3 * 17. Note that 3+17 is 20, which is what we want. Check t...
by DavCrav
Wed Jun 30, 2010 5:13 pm UTC
Forum: Mathematics
Topic: Modular law for ideals
Replies: 9
Views: 1999

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 interesti...
by DavCrav
Wed Jun 30, 2010 8:42 am UTC
Forum: Mathematics
Topic: Modular law for ideals
Replies: 9
Views: 1999

Re: Modular law for ideals

OK, stop. What you are trying to prove here is the following: 1) The intersection is the largest ideal contained in both 2) The sum is the smallest ideal containing both 3) The poset of ideals of a ring is a modular lattice. The first two are obvious, and indeed are sometimes the definition of inter...
by DavCrav
Sun Jun 27, 2010 9:54 am UTC
Forum: Mathematics
Topic: The inverse image of prime ideals.
Replies: 5
Views: 1844

Re: The inverse image of prime ideals.

I think I may be being very slow here - what are you taking A, B and C to be? C=f^{-1}(q). Also, I want to cut B down so that I just have the image of f as B, and replace q with the intersection of B and q, which is still prime in B. This doesn't change C, and so (A/B)/(C/B) is simply B/q, and A/C ...
by DavCrav
Sun Jun 20, 2010 9:14 am UTC
Forum: Mathematics
Topic: The inverse image of prime ideals.
Replies: 5
Views: 1844

Re: The inverse image of prime ideals.

I'd very much like a proof, or suggestions on how to construct one! This is "standard" in algebra, and is basically the third isomorphism theorem. This says that if A is an object, and B and C are subobjects with B contained in C, then (A/B)/(C/B)=A/C as long as these quotients make sense...
by DavCrav
Fri Jun 04, 2010 9:31 am UTC
Forum: Mathematics
Topic: NUMB3RS Parody
Replies: 25
Views: 5394

Re: NUMB3RS Parody

Hey guys, I don't know if there are any NUMB3RS fans about, but in honor of its sixth and final season, we did a parody of it in our webcomic. http://www.cuttingroomcomic.com/CuttingRoom/Comic/Entries/2010/6/1_NUMB3RS.html You don't need to parody this show. It is already a parody...
by DavCrav
Wed Jun 02, 2010 8:53 am UTC
Forum: Mathematics
Topic: Most interesting mathematician?
Replies: 35
Views: 5147

Re: Most interesting mathematician?

John Conway. is an interesting guy, yes. He has boxes in the attic labelled with each month, where all the random things he's drawn on during that month are kept. This is the best filing system as far as he's concerned. At least that's what his wife told me. :) He was still playing a friend of mine...
by DavCrav
Sun May 30, 2010 9:51 pm UTC
Forum: Mathematics
Topic: Most interesting mathematician?
Replies: 35
Views: 5147

Re: Most interesting mathematician?

dissonant wrote:My vote is for GROTHENDIECK.


This.
by DavCrav
Sat May 29, 2010 11:03 am UTC
Forum: Mathematics
Topic: Wish I had seen/understood this comic sooner...
Replies: 36
Views: 4651

Re: Wish I had seen/understood this comic sooner...

May I be the first to say that's a rubbish comic/joke.

That is all.
by DavCrav
Sun May 02, 2010 10:21 pm UTC
Forum: Mathematics
Topic: Top Colleges for Undergraduate Mathematics
Replies: 30
Views: 9130

Re: Top Colleges for Undergraduate Mathematics

Generally, as far as in know in England it ranks more like this: Cambridge Imperial Warwick Oxford though, I'm not sure about Warwick and Oxford, I AM sure that Imperial is way better than Oxford for maths. Hmm. No. Sorry. You can be sure of things, but I'd like to see evidence. Once you get to the...
by DavCrav
Wed Apr 28, 2010 7:43 am UTC
Forum: Mathematics
Topic: First Math Paper
Replies: 6
Views: 1322

Re: First Math Paper

Are you sure it's not simply that they want an anonymised version of your paper that they can use for the peer review process? I believe this is correct. I've submitted and refereeed a fair few maths papers though, and this has never been suggested. It sounds at least slightly dodgy. Edit: a list o...
by DavCrav
Tue Apr 20, 2010 6:21 pm UTC
Forum: Mathematics
Topic: What is the twelve-fold way?
Replies: 3
Views: 949

Re: What is the twelve-fold way?

Damn. There was me hoping it was some Zen/Jedi stuff...
by DavCrav
Mon Apr 19, 2010 5:38 pm UTC
Forum: Mathematics
Topic: the invasion process
Replies: 1
Views: 749

Re: the invasion process

My percolation theory is very rusty, but I remember there being a result that says that if it is probability 1 that there is an infinite cluster, there is probability 1 that there is exactly one infinite cluster. But it's been a while...
by DavCrav
Mon Apr 12, 2010 11:42 pm UTC
Forum: Mathematics
Topic: PhD Woooooooooo
Replies: 23
Views: 3774

Re: PhD Woooooooooo

Gee, majikthise, how ever did you guess? I do geometric group theory, which is sort of the offspring of geometric topology and combinatorial group theory. There's a lot of group presentations, Cayley graphs, and other things that let you deal with groups as though they're metric spaces. "Phase...
by DavCrav
Sun Apr 11, 2010 5:42 pm UTC
Forum: Mathematics
Topic: New value of pi?
Replies: 45
Views: 6738

Re: New value of pi?

Wow, that website is awful. I can't believe he says the golden ratio is transcendental in the second sentence. I know I shouldn't bite about this website, but at one point he says that pi is transcendental, and then later he says it's (14-sqrt(2))/4. Come on, be consistent in being a blithering idi...

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