## Search found 251 matches

- Sun May 17, 2009 11:45 pm UTC
- Forum: Mathematics
- Topic: ITT: Why Math Is Awesome.
- Replies:
**51** - Views:
**6327**

### 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:
**2427**

### 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:
**1683**

### 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...

- Thu May 14, 2009 9:40 am UTC
- Forum: Mathematics
- Topic: Submitting a paper
- Replies:
**14** - Views:
**1683**

### Re: Submitting a paper

I don't understand some people on here. If this person is an undergraduate, there is no way they could pick their way through the ridiculous waltz of journals. That's not easy for grad students and even postdocs, and advice is sought from other people whatever the level of the academic. I've had pro...

- Sun May 10, 2009 10:53 pm UTC
- Forum: Mathematics
- Topic: Semisimple Lie algebras
- Replies:
**5** - Views:
**852**

### Re: Semisimple Lie algebras

Since L is a subalgebra of sl, it inherits a natural action on the n-dimensional ambient space. This is apparently a simple application of weight spaces, but since I don't have the lecture notes for the course, I cannot work out how it applies. (The guy who set the exam question tells me that it is ...

- Sun May 10, 2009 11:05 am UTC
- Forum: Mathematics
- Topic: Semisimple Lie algebras
- Replies:
**5** - Views:
**852**

### Re: Semisimple Lie algebras

mike-l wrote:Isn't the subalgebra of diagonal matrices abelian and hence solvable?

Ah yes. This is what happens when I miss a word out of the question. Let's try again.

Let [imath]L[/imath] be a subalgebra of [imath]\mathrm{sl}_n(\mathbb{C})[/imath], where [imath]n\geq 2[/imath], and [imath]L[/imath] acts irreducibly. Show that [imath]L[/imath] is semisimple.

- Fri May 08, 2009 12:48 am UTC
- Forum: Mathematics
- Topic: Semisimple Lie algebras
- Replies:
**5** - Views:
**852**

### Semisimple Lie algebras

I'm quite embarrassed to have to ask this question, but this is a backup in case the person who is meant to give me the answer fails to do so. Let L be a subalgebra of \mathrm{sl}_n(\mathbb{C}) , where n\geq 2 . Show that L is semisimple. This should be done with basic Lie algebra theory (wh...

- Fri Apr 24, 2009 4:51 pm UTC
- Forum: Forum Games
- Topic: Name a smaller (closer to zero) number.
- Replies:
**52** - Views:
**4845**

### Re: Name a smaller (closer to zero) number.

headprogrammingczar wrote:[imath]\frac{1}{\aleph_0}[/imath]

It technically isn't infinity...

Erm?

- Fri Apr 24, 2009 9:30 am UTC
- Forum: Mathematics
- Topic: Dimension of magic square vector spaces
- Replies:
**26** - Views:
**4971**

### Re: Dimension of magic square vector spaces

If one does not require that the diagonals add up to the magic constant, one actually has that the product of two magic squares is a magic square, and so if the coefficients come from a ring R, then all magic squares form an R-algebra. In http://people.maths.ox.ac.uk/~craven/oldweb/magicalgebras.pdf...

- Thu Apr 23, 2009 9:46 pm UTC
- Forum: Mathematics
- Topic: Famous professors thread
- Replies:
**10** - Views:
**2066**

### Re: Famous professors thread

the anecdotes are interesting and all, but i see no one has decided to follow my convention of linking to an important result and instead opted for the generic bio and home pages. I probably have an unfair advantage, because I'm coming from Oxford... In no particular order, I've been lectured to by...

- Thu Apr 23, 2009 6:36 pm UTC
- Forum: Mathematics
- Topic: Famous professors thread
- Replies:
**10** - Views:
**2066**

### Re: Famous professors thread

I probably have an unfair advantage, because I'm coming from Oxford... In no particular order, I've been lectured to by John Thompson, Jon Alperin, jon Carlson, Dave Benson, Efim Zelmanov, Michael Aschbacher, Gus Lehrer, Boris Zil'ber, Dominic Joyce, Raphael Rouquier, Peter Neumann, Dan Segal, Marcu...

- Wed Apr 22, 2009 7:36 pm UTC
- Forum: Mathematics
- Topic: A Toughie
- Replies:
**24** - Views:
**2050**

### Re: A Toughie

The problem with statements about determining whether a number is rational or not is that the numbers you start off with, the computable numbers (those for which there is some algorithm to work out their decimal expansion, essentially) form a countable subset of the reals, and so the question doesn'...

- Wed Apr 22, 2009 7:30 pm UTC
- Forum: Mathematics
- Topic: question that I have no Idea how to go about
- Replies:
**10** - Views:
**1199**

### Re: question that I have no Idea how to go about

Well, this hitting thing is confusing, as in it's not adequately explained, but it must seriously affect the probabilities, because otherwise the probability is 1/1296 = 0.77%...

- Sun Mar 29, 2009 10:19 pm UTC
- Forum: Mathematics
- Topic: Singularics - Claims to prove RH by dividing by 0
- Replies:
**21** - Views:
**3497**

### Re: Singularics - Claims to prove RH by dividing by 0

Any set of random (or seemingly random) periodic values ρx can be infinitely defined (meaning that there are an infinite number of solutions for the order of the values) in reverse with a simple function Ν (m), the Neutronic Function. I'm not even sure what that means. Obviously a PhD in mathematic...

- Tue Mar 17, 2009 6:38 pm UTC
- Forum: Mathematics
- Topic: How can (0,1) exist?
- Replies:
**11** - Views:
**1810**

### Re: How can (0,1) exist?

Is it incorrect to say that there exists no n such that \sum_1^n{\frac{9}{10^n}} is not in the interval (0,1)? To be nitpicky, yes. What you meant to say is that there exists no natural number n such that \sum_{k=1}^n{\frac{9}{10^k}} is not in the interval (0,1). Actually, assuming that n is at lea...

- Mon Mar 09, 2009 10:38 am UTC
- Forum: Mathematics
- Topic: Find if a number has a root
- Replies:
**8** - Views:
**1245**

### Re: Find if a number has a root

FWIW, a year or so ago, I was looking for perfect powers that are close neighbours. Such pairs (& triplets) are reasonably common in the small numbers (eg, 121, 125, 128) but they start to thin out fairly quickly. Such groupings tend to occur with perfect squares or powers of 2 (which I suppose...

- Sun Mar 08, 2009 2:58 pm UTC
- Forum: Mathematics
- Topic: dexa- rotation of mathematical proportion/equations
- Replies:
**7** - Views:
**1281**

### Re: dexa- rotation of mathematical proportion/equations

I seriously hope that at some point I don't jump off the deep end like this guy...

- Sun Mar 08, 2009 10:52 am UTC
- Forum: Mathematics
- Topic: Representation theory help
- Replies:
**23** - Views:
**2112**

### Re: Representation theory help

For instance, in abelian groups all subgroups are kernels of homomorphisms. In general groups, if we want to 'quotient out' a non-normal subgroup, the best we can do (AFAIK) is map to the set of right cosets. But in what sense could this map be considered as if it's a homomorphism, and the resultin...

- Sun Mar 08, 2009 1:22 am UTC
- Forum: Mathematics
- Topic: Real life arguments solved with math
- Replies:
**12** - Views:
**1459**

### Re: Real life arguments solved with math

Right: please contrast What it means at its most basic level with Huh?? The geodesic flow on a compact surface of constant negative curvature is plenty continuous, and the distance between any two unit vectors is bounded above (certainly, it is less than the diameter of a fundamental region of the a...

- Sun Mar 08, 2009 1:11 am UTC
- Forum: Mathematics
- Topic: group theory question
- Replies:
**14** - Views:
**2108**

### Re: group theory question

I think I need to know what `wreath product problems' are first, before directing you anywhere... The wreath product is a nice construction, and interacts well with representations.

- Sun Mar 08, 2009 1:10 am UTC
- Forum: Mathematics
- Topic: Representation theory help
- Replies:
**23** - Views:
**2112**

### Re: Representation theory help

There's a book in our college library called 'Cohomologie non-abelienne'. It was too difficult for me to get much out of out, but from what I have read elsewhere, non-abelian cohomology gives rather little reward for a huge amount of work, compared to all the wonderful structure that exists for abe...

- Sat Mar 07, 2009 8:59 pm UTC
- Forum: Mathematics
- Topic: Real life arguments solved with math
- Replies:
**12** - Views:
**1459**

### Re: Real life arguments solved with math

Once I was arguing with a friend about controlled chaos. My friend (who debated in high school) stated that there is no such thing, and was convinced that there was no logical argument that could prove him wrong. I am reminded of a quotation of Charles Babbage: "I am not able rightly to appreh...

- Sat Mar 07, 2009 8:53 pm UTC
- Forum: Mathematics
- Topic: Proof that the sqrt of 2 is irrational?
- Replies:
**28** - Views:
**3989**

### Re: Proof that the sqrt of 2 is irrational?

@Everyone arguing about this stuff. Seriously, you're doing it wrong. It is easy to define an even number to be one of the form 2n, and an odd number to be one of the form 2n+1. Then using well-ordering, you can prove that every number is either even or odd, and cannot be both. Then algebraic manipu...

- Sat Mar 07, 2009 4:24 pm UTC
- Forum: Mathematics
- Topic: Representation theory help
- Replies:
**23** - Views:
**2112**

### Re: Representation theory help

Time to split responses, I suppose To DavCrav: Thanks for the suggestion - I know the Diaconis notes, but was unaware of the book... though on checking it is in a part of the library I pass through frequently. If you know of any applications of modular representation theory, you would be a hero. Er...

- Sat Mar 07, 2009 2:32 pm UTC
- Forum: Mathematics
- Topic: Representation theory help
- Replies:
**23** - Views:
**2112**

### Re: Representation theory help

So the overall concept was explained to me on a particularly long plane flight, but there's still a lot I don't understand. What confuses me the most is the process of finding and using a representation. Given a specific group, how does one go about deciding upon a representation. And then, what is...

- Sat Mar 07, 2009 2:26 pm UTC
- Forum: Mathematics
- Topic: dexa- rotation of mathematical proportion/equations
- Replies:
**7** - Views:
**1281**

### Re: dexa- rotation of mathematical proportion/equations

cameronv wrote:I would like help from mathematicians in ths forum that we know each other...

I would like to help, but... no I cannot think of anything suitable. I'm wondering if English is perhaps not your first language. And it appears that mathematics is not one of your languages at all...

- Sat Mar 07, 2009 2:17 pm UTC
- Forum: Mathematics
- Topic: Representation theory help
- Replies:
**23** - Views:
**2112**

### Re: Representation theory help

I'm not familiar with Fourier analysis, but I'd have thought that the special thing about the integers, the torus and the reals is that they're all abelian, and in this case you have Pontryagin duality and whatnot. I don't know if the methods of classical Fourier analysis carry over all that well t...

- Wed Mar 04, 2009 12:32 am UTC
- Forum: Mathematics
- Topic: Favourite Erroneous "Proofs"
- Replies:
**194** - Views:
**43432**

### Re: Favourite Erroneous "Proofs"

Yes, that sort of thing. I don't know whether the diagonal fallacy is called that everywhere, but that is what I know of it as. It comes from the assumption that every subobject of the product of two objects is a product itself; the name comes from this fallacy applied to 2-dimensional vector spaces...

- Tue Mar 03, 2009 11:44 pm UTC
- Forum: Mathematics
- Topic: Favourite Erroneous "Proofs"
- Replies:
**194** - Views:
**43432**

### Re: Favourite Erroneous "Proofs"

I can't believe I've read through four-and-a-half pages of erroneous proofs with all to show for it some divide-by-zero problems. How about the diagonal fallacy? Broadly speaking, this comes from the assumption (for example) that in the direct product of two groups, G and H , every subgroup is of th...

- Tue Mar 03, 2009 11:55 am UTC
- Forum: Mathematics
- Topic: Working on Gilbreath's Conjecture
- Replies:
**9** - Views:
**1921**

### Re: Working on Gilbreath's Conjecture

I'm afraid I can't see how your method can be easily rescued. Your statement on the first half of the second page (If f(j) is changed but a_{i,j} still does not exceed 2^{j-i} , level i = 1 starts with a 2 and then is all odd numbers, then a_{j,j} still must be equal to 1, when j > 1 ) appea...

- Wed Feb 25, 2009 2:16 pm UTC
- Forum: Mathematics
- Topic: Strong Induction and Recursive Functions
- Replies:
**4** - Views:
**1093**

### Re: Strong Induction and Recursive Functions

Another method is to notice that f(0) and f(1) are correct, and to prove that for the f given, it satisfies the equation given. Then appeal to the fact that the function so defined in the question is unique.

- Sun Feb 01, 2009 1:59 pm UTC
- Forum: Mathematics
- Topic: Two somewhat difficult questions (not-homework related)
- Replies:
**21** - Views:
**2104**

### Re: Two somewhat difficult questions (not-homework related)

In general, this problem of finding the black islands in the situation is the idea of so-called percolation theory. To give a demonstration that this area is hard, if you had chosen 60% rather than 50% chance, you would have exactly one, infinite component (as n\to \infty ) with probability 1. (That...

- Mon Jan 19, 2009 11:39 am UTC
- Forum: Mathematics
- Topic: Bourbaki
- Replies:
**2** - Views:
**546**

### Re: Bourbaki

They are very useful as reference material, but they aren't textbooks by any real measure. If you want to learn a topic, read another book. If you already know a topic, and want to refresh your memory or glance at things, they are very useful. I have three of them myself, and whenever Springer do on...

- Mon Jan 19, 2009 11:34 am UTC
- Forum: Mathematics
- Topic: Where to publish
- Replies:
**10** - Views:
**1458**

### Re: Where to publish

In my spare time I wrote a short mathematical paper deriving an expression for what seems to be a mathematical coincidence, thus showing that it isn't one. First I submitted it to the Canadian Mathematical Bulletin (I'm Canadian), but they rejected it in three minutes and told me to try the America...

- Mon Jan 19, 2009 11:24 am UTC
- Forum: Mathematics
- Topic: MATH PUZZLE!
- Replies:
**25** - Views:
**2468**

### Re: MATH PUZZLE!

After a math lecture in Harvard the students went to the cafeteria and each one of them took a cup of tea and cheese sandwich. They all paid $18.94. How many students where they? THANKS!! As many as you want. You simply said that each of them paid $18.94, which tells you nothing. However, I'd menti...

- Sun Dec 28, 2008 9:59 am UTC
- Forum: Mathematics
- Topic: group theory question
- Replies:
**14** - Views:
**2108**

### Re: group theory question

I asked a Scandinavian person, and she said that it's pronounced something like 'Zee-loff'. And while were at it, Lie (as in Lie groups and Lie algebras) is pronounced 'Lee-uh'. Anyway...

- Mon Dec 22, 2008 12:27 am UTC
- Forum: Mathematics
- Topic: question about permutation cycles
- Replies:
**3** - Views:
**1379**

### Re: question about permutation cycles

In general, conjugation of one permutation by another is very easy to do. (This is why computation in symmetric groups is much easier than in other groups.) If you are conjugating x by g, then write out x as cycles. Now, apply g to each of the numbers in the cycle, but don't alter the cycle . This i...

- Mon Dec 22, 2008 12:13 am UTC
- Forum: Mathematics
- Topic: Looking for a Group
- Replies:
**11** - Views:
**2335**

### Re: Looking for a Group

OK, this is getting quite complicated, so let's try to distill what's happened here: The OP was looking for an infinite, finitely generated, amenable group, whose abelianization is finite, and is residually finite. More generally, he was looking for one of those groups such that all subgroups of fin...

- Thu Dec 11, 2008 9:33 pm UTC
- Forum: Mathematics
- Topic: group theory question
- Replies:
**14** - Views:
**2108**

### Re: group theory question

OK, let's go step by step: Let x be the generator for the infinite cyclic subgroup of index 2. Let y be an element outside x. By considering G/<x>, one easily sees that y 2 is in G, since (<x>y) 2 =<x>, (as G/<x> is cyclic of order 2). The map g-> g y (i.e., conjugation by y) is a homomorphism (in f...

- Thu Dec 11, 2008 12:16 pm UTC
- Forum: Mathematics
- Topic: group theory question
- Replies:
**14** - Views:
**2108**

### Re: group theory question

Let the infinite cyclic group be generated by x, and let y be an element of G not in <x>. Consider the element x^y: where can that be sent, given that y^2 is in <x>, and so must act trivially on x. If y acts trivially on x, then G is abelian, and you should be able to do it. So y acts non-trivially ...