Search found 248 matches

by DavCrav
Tue Jan 19, 2010 10:31 am UTC
Forum: Mathematics
Topic: I'm bad at maths. Any ideas why?
Replies: 36
Views: 4494

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

Not liking maths because you find matrices boring is like not liking carpentry because you think hammers are boring. Hammers are fairly boring, it's what you can do with hammers that is interesting. And even then, to build interesting things, you need a lot more complicated tools than hammers.
by DavCrav
Mon Jan 18, 2010 9:19 pm UTC
Forum: Mathematics
Topic: The ideal number.
Replies: 70
Views: 7883

Re: The ideal number.

Syrin wrote:I'm rather fond of 808017424794512875886459904961710757005754368000000000, myself.


I was ninja'd, but as soon as I saw this I wanted to say 'that's a monstrous number'. I thank you.
by DavCrav
Mon Jan 18, 2010 9:43 am UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9388

Re: Mathematics and intellect

In the arts, logic and reason in your work are just gravy, as I see it. Whereas with maths and science, it's essentially required. If you're talking to "artsy folk" who call themselves "artsy" simply because they've exposed themselves to a lot of art, please punch them in the fa...
by DavCrav
Sun Jan 17, 2010 1:18 pm UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9388

Re: Mathematics and intellect

1. What is the second law of thermodynamics? 2. Why does wood burn? 3. Why does a fan cool you down? 4. What is natural selection? 5. What effects do banks have on the economy? 6. Why does iron rust? Bonus: Why doesn't aluminum (seem to) rust? 7. What is calculus? 8. Describe the digestive system. ...
by DavCrav
Sat Jan 16, 2010 9:27 am UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9388

Re: Mathematics and intellect

@Everyone: The point of those questions was to prove a few things: 1) Firstly, they weren't aimed at people who have just finished their degree. They are aimed at those people at the top of their profession (in pretty much any profession) who have been around for a long time and claim to have lots o...
by DavCrav
Fri Jan 15, 2010 12:24 pm UTC
Forum: Mathematics
Topic: Shuffling Cards
Replies: 17
Views: 2602

Re: Shuffling Cards

I should just note that there is an entire theory of this, which goes under several names, one of which is harmonic analysis on finite groups. The group you are looking at here is the symmetric group on 52 letters. A perfect riffle shuffle is a permutation of order 8 in this group, but an imperfect ...
by DavCrav
Fri Jan 15, 2010 11:52 am UTC
Forum: Mathematics
Topic: Mathematics and intellect
Replies: 85
Views: 9388

Re: Mathematics and intellect

Surely in the argument of mathematician versus say literary critic, we need to clarify the mathematician bit. There's mathematicians of the calibre of Fermat, who produce new and ground-breaking work during their lifetime. And then there's your average maths post-grad. Who makes a tiny incremental ...
by DavCrav
Wed Jan 13, 2010 12:40 pm UTC
Forum: Mathematics
Topic: Group theory: do some sets have implied operations?
Replies: 10
Views: 1609

Re: Group theory: do some sets have implied operations?

2) The reverse addition and multiplication operations, where 1 is the additive identity. Notice these groups are isomorphic of course but not the same when you consider the actual sets. 1*1=1.1*0=1, 0*0=0 I should just point out that this isn't a group, since both elements are idempotents (i.e., sq...
by DavCrav
Wed Dec 23, 2009 12:26 pm UTC
Forum: Mathematics
Topic: Can't remember what it's called
Replies: 6
Views: 1187

Re: Can't remember what it's called

There's also a sigmoid function.
by DavCrav
Sat Dec 05, 2009 12:29 am UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 65926

Re: Wrong on the Internet: John Gabriel

Is there any way to get these 'knols' removed from the intertubes? If Google want someone with a good-sounding e-mail address to send an expert opinion that they're junk, I can provide this...
by DavCrav
Fri Nov 27, 2009 10:57 pm UTC
Forum: Mathematics
Topic: I think I proved Fermat's Last Theorem
Replies: 44
Views: 7083

Re: Has Fermats Last Theorem been solved?

Talith wrote:Iirc it took several months for his proof to be peer reviewed...


If it only took several months it is quite quick by most journal standards...
by DavCrav
Tue Nov 10, 2009 11:51 am UTC
Forum: Mathematics
Topic: Distance between (0,0) and (1,1) = 1 for some path?
Replies: 44
Views: 5657

Re: Distance between (0,0) and (1,1) = 1 for some path?

jestingrabbit wrote:
edahl wrote:I'm no expert, but this metric might help: [imath]d(p,q)=\frac {|p_1-p_2|+|q_1-q_2| }{2}[/imath].


FTFY. Its the manhattan norm. For stupid reasons.


Although anyone calling it the Manhattan norm rather than the [imath]L_1[/imath]-norm gets an Americans-think-they-invented-everything slap from Minkowski. :twisted:
by DavCrav
Sun Nov 08, 2009 11:50 am UTC
Forum: Mathematics
Topic: Primes
Replies: 4
Views: 784

Re: Primes

As far as I know, it is conjectured (but not proved) that there is always a prime between [imath]n^2[/imath] and [imath](n+1)^2[/imath], which is a lot stronger than the bound given in Bertrand's Postulate.
by DavCrav
Wed Oct 28, 2009 9:03 am UTC
Forum: Mathematics
Topic: Second Ace Paradox
Replies: 66
Views: 8245

Re: Second Ace Paradox

I was discussing this with a friend, and we decided that one can make the situation by considering just three cards: Ace, King and Queen. I take a card, and you keep two. What is the probability that I have the Queen? 1/3. If you tell me that you have the Ace, then my probability is 1/2, just like i...
by DavCrav
Mon Oct 19, 2009 8:55 am UTC
Forum: Mathematics
Topic: Second Ace Paradox
Replies: 66
Views: 8245

Re: Second Ace Paradox

maybe I have to think about this more, but I don't buy this. My point is that we didn't fix the ace of spades beforehand. If the bridge player (or indeed anyone) said that they had an ace, then it has to be an ace of something, and you gain no more information when they indeed tell you it's the ace ...
by DavCrav
Tue Sep 29, 2009 9:06 am UTC
Forum: Mathematics
Topic: Truncated Conic
Replies: 7
Views: 918

Re: Truncated Conic

By the way, the word you are looking for is frustum.
by DavCrav
Sun Sep 27, 2009 7:03 pm UTC
Forum: Mathematics
Topic: Quintic equations
Replies: 14
Views: 1532

Re: Quintic equations

Yakk wrote:Some teenager came up with Galois theory (well, the basis of it, and the proof) before dieing at the age of 20.


One of the rare cases of a teenager knowing a lot, rather than merely thinking he does...
by DavCrav
Fri Aug 28, 2009 10:26 am UTC
Forum: Mathematics
Topic: Simple Sequences and Series
Replies: 6
Views: 961

Re: Simple Sequences and Series

The one for the sum of cubes is quite fun, because it is the square of the sum of integers. That is,
[math]\sum_{i=1}^n i^3=\left(\sum_{i=1}^n i\right)^2.[/math]
by DavCrav
Wed Aug 19, 2009 8:16 am UTC
Forum: Mathematics
Topic: Sudoku algebra
Replies: 11
Views: 2081

Re: Sudoku algebra

This is why I gave my recommendation as to the definition of the Sudoku group. It has to be a group, so should only consist of invertible transformations, and it should be nice if it follows the same pattern as the classical groups, so being a set of matrices that stabilize (in this case) a collecti...
by DavCrav
Tue Aug 18, 2009 10:45 pm UTC
Forum: Mathematics
Topic: Sudoku algebra
Replies: 11
Views: 2081

Re: Sudoku algebra

The construction you are trying to make is that of a wreath product. (See the O'Nan--Scott theorem for this.) The permutations of the rows is a direct product H of three copies of the symmetric group on three letters, and the permutations on the columns is the saying. You can also flip diagonally to...
by DavCrav
Sun Aug 09, 2009 1:36 pm UTC
Forum: Mathematics
Topic: Magnets and polyhedra
Replies: 15
Views: 6300

Re: Magnets and polyhedra

Two words: Lobel frames.
by DavCrav
Sun Jul 19, 2009 4:28 pm UTC
Forum: Mathematics
Topic: Graphing X^X
Replies: 13
Views: 2264

Re: Graphing X^X

t0rajir0u wrote:In any case, what all this means at the end of the day is that [imath]x^x[/imath] is a horribly unnatural function that nobody ever thinks about, ever.


Hmm.
by DavCrav
Wed Jul 15, 2009 5:57 pm UTC
Forum: Mathematics
Topic: Graph Theory (Bollobás) Discussion
Replies: 21
Views: 2301

Re: Graph Theory (Bollobás) Discussion

I don't know if I have the time to guarantee that I can read this, given that I have a book of my own to write, but I had a flick through the book, and Chapter 1 is all standard, Chapters 2 and 3 seem a bit off the beaten track to me, but Chapter 4,6, and 7 look very interesting.
by DavCrav
Sun Jul 12, 2009 8:07 pm UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4420

Re: math book club

Bollobas's book is the main graph theory reference that I have in my bookcase; it generally has most things I've needed in it, until you need more specialized results on graph theory, like excluded minor theorems, etc.
by DavCrav
Sun Jul 12, 2009 6:26 pm UTC
Forum: Mathematics
Topic: math book club
Replies: 62
Views: 4420

Re: math book club

I just purchased the Dover graph theory book via allbookstores - should be 1-2 weeks before it arrives at my house, but then I'll be good to go. I have another wee volume on graph theory that I've played around with before; judging on that basis, I'd think high school alg sounds about right as a pr...
by DavCrav
Sat Jul 11, 2009 11:27 am UTC
Forum: Mathematics
Topic: pythagoras triplet
Replies: 23
Views: 3271

Re: pythagoras triplet

I do apologise for the miscommunication, however, given the fact there exists other possibilities, you should know what I meant, not that I was wrong - which is the problem with communication over the internet. Yes, of course! What you said was wrong but, if you change some of the words so that the...
by DavCrav
Sat Jun 13, 2009 9:44 am UTC
Forum: Mathematics
Topic: Constructing Abstract Groups of a Given Order
Replies: 17
Views: 1793

Re: Constructing Abstract Groups of a Given Order

I'm taking issue with the statement that there aren't good algorithms as well. Methods using the associated Lie ring can be used to construct all groups of order at most p^7 for example, and groups of composite order are much easier to understand given the possible Sylow structures. They aren't algo...
by DavCrav
Fri Jun 12, 2009 8:50 am UTC
Forum: Mathematics
Topic: Constructing Abstract Groups of a Given Order
Replies: 17
Views: 1793

Re: Constructing Abstract Groups of a Given Order

Yes, but an algorithm that needs to check more cases than the number of atoms in the universe for even moderate values of n is not, by any reasonable standard, an algorithm. For groups of small order, it's much more effective to start from the Sylow theorems, which eliminates many more cases, and p...
by DavCrav
Tue Jun 09, 2009 6:57 pm UTC
Forum: Mathematics
Topic: Constructing Abstract Groups of a Given Order
Replies: 17
Views: 1793

Re: Constructing Abstract Groups of a Given Order

The main problem is constructing the groups of order p^n ; so far this is known up to n=7 for all primes, and for p=2 it's either 1024 or 2048 (I can't remember which). Even the fact that the number of groups of order p^n is a polynomial in p is still unknown, and opnion is divided on whether it's ...
by DavCrav
Mon Jun 08, 2009 12:01 am UTC
Forum: Mathematics
Topic: Constructing Abstract Groups of a Given Order
Replies: 17
Views: 1793

Re: Constructing Abstract Groups of a Given Order

The quaternion group of order 8 for example is not a non-trivial semi-direct product. Or the cyclic group of order 4... The main problem is constructing the groups of order p^n ; so far this is known up to n=7 for all primes, and for p=2 it's either 1024 or 2048 (I can't remember which). Even the f...
by DavCrav
Wed Jun 03, 2009 1:06 pm UTC
Forum: Mathematics
Topic: how do I pronounce the cartesian product
Replies: 14
Views: 2193

Re: how do I pronounce the cartesian product

The only way I have ever heard it called is 'cross', as it generally doesn't lead to confusion with vector cross products. (Indeed, these are often denoted by \wedge anyway...) Having a unique name for each concept sounds appealing but runs into problems, swith words like regular, normal, etc. being...
by DavCrav
Mon May 25, 2009 9:59 am UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 2943

Re: A question about random walks

Am I right in remembering that the probability that you return infinitely often to the origin is 1 for p=0.5 and 0 otherwise, and an application of the above and Kolmogorv's zero-one law? This illustrates the dichotomy very nicely.
by DavCrav
Fri May 22, 2009 8:35 am UTC
Forum: Mathematics
Topic: ITT: Why Math Is Awesome.
Replies: 51
Views: 6274

Re: ITT: Why Math Is Awesome.

And it's completely independent of money and technology, in the sense that you don't need either to do math. I do have to disagree with this: apart from most of applied mathematics, there's also what's occasionally my field of computation representation theory, and this generally works on the margi...
by DavCrav
Thu May 21, 2009 9:43 pm UTC
Forum: Mathematics
Topic: New Mathematical Operation: Swagger
Replies: 19
Views: 2708

Re: New Mathematical Operation: Swagger

You would swagger even if it were a small third-world country? Obviously we have different standards...
by DavCrav
Thu May 21, 2009 7:44 pm UTC
Forum: Mathematics
Topic: New Mathematical Operation: Swagger
Replies: 19
Views: 2708

Re: New Mathematical Operation: Swagger

quintopia wrote:So I take it you define the swagger of a one digit number to be zero?


If I were under ten I would find it difficult to have reason to have swagger, wouldn't you?
by DavCrav
Tue May 19, 2009 7:23 pm UTC
Forum: Mathematics
Topic: ITT: Why Math Is Awesome.
Replies: 51
Views: 6274

Re: ITT: Why Math Is Awesome.

For example, I hope someday that it is possible to simultaneously talk about every object to which we can associate something that could reasonably be called a "zeta function." The examples I know of: - Varieties / schemes / function fields - Graphs - Recognizable languages - Posets - Cat...
by DavCrav
Mon May 18, 2009 12:24 am UTC
Forum: Mathematics
Topic: ITT: Why Math Is Awesome.
Replies: 51
Views: 6274

Re: ITT: Why Math Is Awesome.

I like how abstract and precise it is. It's consistency is kind of reassuring, while all the same it's fun trying to find holes in that consistency. *Shushes Gödel, who sits in the corner rocking backwards and forwards...* Completeness and consistency are not the same thing. Indeed, and Gödel has a...
by DavCrav
Sun May 17, 2009 11:45 pm UTC
Forum: Mathematics
Topic: ITT: Why Math Is Awesome.
Replies: 51
Views: 6274

Re: ITT: Why Math Is Awesome.

I like how abstract and precise it is. It's consistency is kind of reassuring, while all the same it's fun trying to find holes in that consistency. *Shushes Gödel, who sits in the corner rocking backwards and forwards...* Edit: Why do I like mathematics? I don't know any more. I'm not sure I do, a...
by DavCrav
Fri May 15, 2009 5:36 pm UTC
Forum: Mathematics
Topic: Courses, Abridged
Replies: 19
Views: 2402

Re: Courses, Abridged

I'll try to list the single most important thing from each subject (imho) as requested. Just be mindful that presented in this way they probably won't make much sense nor will this list replace a REAL course on the subject. Linear algebra: For any n-dimensional vector space, V, one can always find ...
by DavCrav
Fri May 15, 2009 5:25 pm UTC
Forum: Mathematics
Topic: Submitting a paper
Replies: 14
Views: 1668

Re: Submitting a paper

quintopia wrote:
DavCrav wrote:I've had professors ask me where I think a certain paper should be submitted.


Which is what I said I would do in the professor's place. What's the problem here?


Well, I'm not a student (was until recently though). I was talking about them asking me for advice on where to put their papers...

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