## Search found 248 matches

- 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.

- 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.

- 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...

- 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. ...

- 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...

- 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 ...

- 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 ...

- 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...

- 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.

- 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...

- 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...

- 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.

- 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.

- 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...

- 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 ...

- 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.

- 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...

- 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]

[math]\sum_{i=1}^n i^3=\left(\sum_{i=1}^n i\right)^2.[/math]

- 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...

- 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...

- 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.

- 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.

- 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.

- 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.

- 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...

- 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...

- 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...

- 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...

- 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 ...

- 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...

- 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...

- 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.

- 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...

- 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...

- 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?

- 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...

- 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...

- 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...

- 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 ...

- 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...