## Search found 248 matches

- Fri Sep 06, 2013 9:25 pm UTC
- Forum: Mathematics
- Topic: basic doubt about groups
- Replies:
**19** - Views:
**4960**

### Re: basic doubt about groups

The integers under addition are finitely generated and are not a product of cyclic groups. I'm genuinely curious what definition of cyclic you use that excludes Z, because it can't be "a group other than Z which is generated by one element". E.g., a group G is cyclic if there exists x in ...

- Sun Aug 25, 2013 12:36 pm UTC
- Forum: Mathematics
- Topic: When will $1 be the smallest denomination?
- Replies:
**51** - Views:
**10347**

### Re: When will $1 be the smallest denomination?

gmalivuk wrote:It is a fake boxing stance.

Aha. I still prefer the mid fist pump explanation...

- Sun Aug 25, 2013 12:45 am UTC
- Forum: Mathematics
- Topic: When will $1 be the smallest denomination?
- Replies:
**51** - Views:
**10347**

### Re: When will $1 be the smallest denomination?

This is just a general question gmalivuk, but your photo looks like one of the following three things are happening: 1) You are dancing. 2) You are mid fist pump. 3) You are attempting (badly) a boxing stance. I was just interested as to which. I have nothing of value (ha!) to add to this thread, by...

- Sun Aug 25, 2013 12:42 am UTC
- Forum: Mathematics
- Topic: S subset N, exists an r in N such that if r in S then S=N
- Replies:
**14** - Views:
**3943**

### Re: S subset N, exists an r in N such that if r in S then S=

Anyway I do think that we often fail to give due respect to the awesome power of the universal quantifier. It lets us quantify over uncountable sets, most of whose members we could never name. That's a lot of power ... use it wisely! :-) Luckily I rarely have to invoke uncountable anything in my re...

- Sat Aug 24, 2013 4:24 pm UTC
- Forum: Mathematics
- Topic: S subset N, exists an r in N such that if r in S then S=N
- Replies:
**14** - Views:
**3943**

### Re: S subset N, exists an r in N such that if r in S then S=

This sort of thing is OK in a nice set like the natural numbers, but suppose we replace N by R. Now this sentence becomes a bit more interesting. Let S be the subset of all definable numbers. This can mean definable in *any way*: by computer programs, by algorithms, using words, anything reasonable...

- Fri Aug 23, 2013 10:09 pm UTC
- Forum: Mathematics
- Topic: S subset N, exists an r in N such that if r in S then S=N
- Replies:
**14** - Views:
**3943**

### Re: S subset N, exists an r in N such that if r in S then S=

This sort of thing is OK in a nice set like the natural numbers, but suppose we replace N by R. Now this sentence becomes a bit more interesting. Let S be the subset of all definable numbers. This can mean definable in *any way*: by computer programs, by algorithms, using words, anything reasonable....

- Fri Aug 23, 2013 8:49 pm UTC
- Forum: Mathematics
- Topic: S subset N, exists an r in N such that if r in S then S=N
- Replies:
**14** - Views:
**3943**

### Re: S subset N, exists an r in N such that if r in S then S=

The first line says: let S be a subset of N, so you have a fixed subset before you start. It's the difference between the two sentences: 1) For any number x, there is a number y such that y is larger than x. 2) There is a number y such that, for any number x, y is larger than x. Since S is chosen to...

- Thu Aug 22, 2013 6:41 pm UTC
- Forum: Mathematics
- Topic: Group theory II
- Replies:
**46** - Views:
**13633**

### Re: Group theory II

Cool. Can you check whether the group <a,b|a 2 , b 3 , (ab) 7 , [a,b] 10 , ([a,b] 4 b) 7 > is infinite? I just found out that when I ask for the order, and magma says 0, it does not mean infinite, it means it does not know. Therefore the online magma calculator is of no use to this problem. Also, i...

- Thu Aug 22, 2013 3:58 pm UTC
- Forum: Mathematics
- Topic: Group theory II
- Replies:
**46** - Views:
**13633**

### Re: Group theory II

Wait, so do you have magma (the real version not the online calculator)? Yes. I am a professional mathematician, so I have this sort of access, along with my own server to run this stuff on. Also, for 1) Thanks for proving that the Janko group J 1 is in fact a quotient of the group <a,b|a 2 , b 3 ,...

- Wed Aug 21, 2013 11:43 am UTC
- Forum: Mathematics
- Topic: Group theory II
- Replies:
**46** - Views:
**13633**

### Re: Group theory II

In an infinite group? Not that I know of. It seems to me that even in a finitely presented group, there could be infinitely many normal subgroups of bounded order... (Don't quote me on this.) This is false. In any finitely generated group, there are only finitely many subgroups of a given index. Ed...

- Thu Mar 14, 2013 9:25 am UTC
- Forum: Mathematics
- Topic: Groups & Their Presentations
- Replies:
**10** - Views:
**2529**

### Re: Groups & Their Presentations

While what letterX and stewbasic are saying is technically true, in reality your problem is much more tractable, since you don't want to change the generators. In this case it is a case of applying Tietze transformations to see whether one may reduce the word, and Magma has done that for you in the ...

- Wed Mar 13, 2013 6:46 pm UTC
- Forum: Mathematics
- Topic: Groups & Their Presentations
- Replies:
**10** - Views:
**2529**

### Re: Groups & Their Presentations

I typed the group into Magma and applied ReduceGenerators to it, and it came up with two relations for your group, namely b^-2aba^-1b^-1a^-1b^2a and b^-1ab^-1a^-1baba^-1b^-1aba^-1, so that G=<a,b|b^-2aba^-1b^-1a^-1b^2a,b^-1ab^-1a^-1baba^-1b^-1aba^-1>, with the same generators as before. Magma refuse...

- Sat Feb 02, 2013 2:58 pm UTC
- Forum: Mathematics
- Topic: Next great mathematical invention
- Replies:
**17** - Views:
**4321**

### Re: Next great mathematical invention

Yeah, the Laplace example is great. Nothing that was discovered in relativity and quantum theory could be said to have been "hiding in" the work he was familiar with. It was all quite novel. I cannot find such a quote by Laplace. On the contrary: What we know is not much. What we do not k...

- Sat Feb 02, 2013 2:31 pm UTC
- Forum: Mathematics
- Topic: Next great mathematical invention
- Replies:
**17** - Views:
**4321**

### Re: Next great mathematical invention

Carrying on the thought of fishfry, since calculus we had analysis, set theory (ZFC, GB, etc.), then category theory, and from what I can gather, although I'm not an expert on this, intensional dependent type theory. And that's just in foundations of mathematics.Entirely new fields of mathematics ha...

- Mon Oct 29, 2012 10:31 am UTC
- Forum: Mathematics
- Topic: group theory
- Replies:
**64** - Views:
**24908**

### Re: group theory

There's an online Magma calculator here: http://magma.maths.usyd.edu.au/calc/ I doubt if the SmallGroup database goes that far though. The paper that constructs all such groups is by A.E. Western, called Groups of Order p3q, which appeared in Proc. LMS back in 1898. The description is pretty complic...

- Thu Oct 25, 2012 9:50 am UTC
- Forum: Mathematics
- Topic: group theory
- Replies:
**64** - Views:
**24908**

### Re: group theory

The problem of finding all the non-isomorphic groups of order n is a fundamental question in group theory, so I think that what I am doing is group theory, even though it is not using very advanced techniques. With all due respect, no it isn't a fundamental question. The number of groups of order p...

- Mon Oct 22, 2012 10:21 am UTC
- Forum: Mathematics
- Topic: group theory
- Replies:
**64** - Views:
**24908**

### Re: group theory

A couple of things from earlier in the thread that I cannot find answers/responses to, so I'll post them here. Sorry if this is re-supplying information. 1) The automorphism group of (C_p)^n is GL_n(p), and in general if Z is a cyclic group, Aut(Z^n)=GL_n(Z). The easiest way to see this is that the ...

- Sun Oct 21, 2012 10:12 am UTC
- Forum: Mathematics
- Topic: The projective Weil representation of SL_2(Z/nZ)
- Replies:
**1** - Views:
**617**

### Re: The projective Weil representation of SL_2(Z/nZ)

The problem lies because you are misinterpreting Schur's Lemma. It says that *endomorphisms* of an irreducible representation are scalars, but not maps between isomorphic representations. For example, take the representations of a cyclic group of order 2 given by diag(1,-1) and diag(-1,1). These are...

- Wed Aug 01, 2012 6:34 pm UTC
- Forum: Mathematics
- Topic: Prime Ideals in C[x,y]
- Replies:
**3** - Views:
**3898**

### Re: Prime Ideals in C[x,y]

I'm concerned: you seem to imply that you think that every prime ideal of C[x,y] is maximal. However, there are plenty of ideals whose quotient is C[x] (e.g., (y)), which is an integral domain, so (y-a) is a prime ideal, for example.

- Wed Aug 01, 2012 6:27 pm UTC
- Forum: Mathematics
- Topic: group theory
- Replies:
**64** - Views:
**24908**

### Re: group theory

Just to let you know, inside GL_2(q) there are elements of order q+1, q-1 and q. This follows from the cyclotomic Sylow theory of groups of Lie type (but in the GL_2 case, much more easily) which says that, whenever \Phi_d(q)^a divides the order of GL_n(q) as a polynomial in q, there exists...

- Wed Aug 01, 2012 6:20 pm UTC
- Forum: Mathematics
- Topic: Investing in different countries
- Replies:
**9** - Views:
**3440**

### Re: Investing in different countries

What you are talking about is the carry trade.

http://en.wikipedia.org/wiki/Carry_%28investment%29

The reason that the Yen was so strong throughout the 90s and much of the 00s is because people borrowed in Yen and converted to other currencies.

http://en.wikipedia.org/wiki/Carry_%28investment%29

The reason that the Yen was so strong throughout the 90s and much of the 00s is because people borrowed in Yen and converted to other currencies.

- Wed Aug 01, 2012 6:17 pm UTC
- Forum: Mathematics
- Topic: Proof by Exhaustion - Is this sufficient?
- Replies:
**4** - Views:
**2385**

### Re: Proof by Exhaustion - Is this sufficient?

Alternatively, notice that the operation of taking remainders when dividing by 4 "commutes" with multiplication, in the sense that if I take the remainder of xy, it is equal to the remainder of x times the remainder of y (possibly after you take remainders again, as 3*3=9, which should be ...

- Sun Jul 22, 2012 9:37 pm UTC
- Forum: Mathematics
- Topic: group theory
- Replies:
**64** - Views:
**24908**

### Re: group theory

Just to let you know, inside GL_2(q) there are elements of order q+1, q-1 and q. This follows from the cyclotomic Sylow theory of groups of Lie type (but in the GL_2 case, much more easily) which says that, whenever \Phi_d(q)^a divides the order of GL_n(q) as a polynomial in q, there exists ...

- Wed Jul 06, 2011 10:36 am UTC
- Forum: Mathematics
- Topic: Research adviser question.
- Replies:
**17** - Views:
**2549**

### Re: Research adviser question.

As this is a maths forum, I'm thinking maths journals here: Ann of Math: 2-4 years is standard from submission to print. Invent Math: has an 18-month backlog, from appearing online to print. Math Z: 15 month backlog (my paper appeared in print last month, online in March 2010). Advances in Math: not...

- Tue May 10, 2011 11:39 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0896: "ZOmbeis"
- Replies:
**125** - Views:
**32299**

### Re: 0896: "Marie Curie"

(being a bit of a feminist, but in a good way) Just so you all know, this is the most abhorrent statement I have seen today. Don't get caught in the idea that being a feminist is bad, lest your brain get devoured by utahraptors. Or, just continue being a complete fuckhead, and have a nice fucking d...

- Tue May 10, 2011 9:19 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0896: "ZOmbeis"
- Replies:
**125** - Views:
**32299**

### Re: 0896: "Marie Curie"

On the subject of Emmy Noether, her appointment at Göttingen was only blocked by a bunch of historians, not the scientists. So don't blame science, blame the historians... However, this is all rubbish. Emmy Noether is as well remembered in mathematical history now as she deserves. If anybody here co...

- Mon Apr 25, 2011 9:53 am UTC
- Forum: Mathematics
- Topic: Jordan Normal Form
- Replies:
**7** - Views:
**1914**

### Re: Jordan Normal Form

jestingrabbit wrote:Also, I wouldn't call that matrix idempotent.

I guess he meant nilpotent...

- Mon Apr 18, 2011 5:43 pm UTC
- Forum: Mathematics
- Topic: Getting my undergrad in math. How about you?
- Replies:
**51** - Views:
**8191**

### Re: Getting my undergrad in math. How about you?

I hope they are sparse! Nope. That's why I gave it to a big computer. But the entries are from F_3, which helps. Strassen? Big-iron, or GPU based? I only meant a big computer, not a supercomputer. It's only multiplying some matrices together: they aren't even over 100,000 dimensions! I ...

- Mon Apr 18, 2011 12:20 pm UTC
- Forum: Mathematics
- Topic: If you learned statistics would you never buy insurance?
- Replies:
**92** - Views:
**10640**

### Re: If you learned statistics would you never buy insurance?

Well through the normal curve I honestly can't imagine a kind of insurance where claims are normally distributed, though. (Well, the totals are for the insurers, because of the previously mentioned central limit theorem. But individual claims are never normally distributed.) Honestly, this looks mo...

- Mon Apr 18, 2011 8:12 am UTC
- Forum: Mathematics
- Topic: If you learned statistics would you never buy insurance?
- Replies:
**92** - Views:
**10640**

### Re: If you learned statistics would you never buy insurance?

I think the point is that you (and indeed I) have insurance only for things that I am required to (car) and things for which the cost of it going wrong is too high (house). I don't insure my phone, as I can replace it, and I don't have extended warranties, since these are essentially insurance for t...

- Mon Apr 18, 2011 12:10 am UTC
- Forum: Mathematics
- Topic: Getting my undergrad in math. How about you?
- Replies:
**51** - Views:
**8191**

### Re: Getting my undergrad in math. How about you?

It's a representation of a finite group, in particular the Suzuki sporadic simple group. I want to understand how certain group elements act under this representation, so I have to multiply the matrices together to get the action of that element. That's the easy bit really. The hard bit is finding t...

- Sun Apr 17, 2011 7:26 pm UTC
- Forum: Mathematics
- Topic: Basic sin(x)cos(x)dx integral question
- Replies:
**4** - Views:
**2800**

### Re: Basic sin(x)cos(x)dx integral question

Why don't you start with [imath]2\cos x\sin x=\sin 2x[/imath]?

- Sun Apr 17, 2011 5:28 pm UTC
- Forum: Mathematics
- Topic: Getting my undergrad in math. How about you?
- Replies:
**51** - Views:
**8191**

### Re: Getting my undergrad in math. How about you?

Yakk wrote:I hope they are sparse!

Nope. That's why I gave it to a big computer. But the entries are from F_3, which helps.

- Sun Apr 17, 2011 3:33 pm UTC
- Forum: Mathematics
- Topic: Getting my undergrad in math. How about you?
- Replies:
**51** - Views:
**8191**

### Re: Getting my undergrad in math. How about you?

Age: 29

Education level: Ph.D. in group representation theory.

What I'm doing: postdoc at Oxford.

What I'm doing right now: waiting for a computer program to finish multiplying together 33000-dimensional matrices...

Education level: Ph.D. in group representation theory.

What I'm doing: postdoc at Oxford.

What I'm doing right now: waiting for a computer program to finish multiplying together 33000-dimensional matrices...

- Sun Apr 17, 2011 3:30 pm UTC
- Forum: Mathematics
- Topic: Free Will & Reimann Hypothesis?
- Replies:
**11** - Views:
**1735**

### Re: Free Will & Reimann Hypothesis?

...Also, humans are by nature finite creatures, so our set of beliefs at any given moment (or over the course of our lives) is finite. Just thought I'd have a wonder about this: I believe "n+1 is greater than n" with any integer in place of n. This means that I have an unbounded set of be...

- Wed Apr 13, 2011 9:27 am UTC
- Forum: Mathematics
- Topic: Writing a Calculus Textbook
- Replies:
**6** - Views:
**2188**

### Re: Writing a Calculus Textbook

Do any of you think this is feasible? Quite honestly, no. I have written a book, and you should expect, for a day's work, to have at most 3-5 pages of decent work, which will then have to be rewritten again. In addition, by this time I had had years of practice writing mathematics, so in three week...

- Wed Apr 13, 2011 9:17 am UTC
- Forum: Mathematics
- Topic: Random Integer
- Replies:
**18** - Views:
**2734**

### Re: Random Integer

... I think the second could will have labeled the planet with life on it with some infinite number and somewhere in the universe there is a first and last planet... even if there are an infinite number of them. It's similar to, say, how there are an infinite number of reals between 0 and 1 and yet...

- Wed Mar 30, 2011 9:38 am UTC
- Forum: Mathematics
- Topic: Finite group extensions
- Replies:
**37** - Views:
**3859**

### Re: infinite group extensions

I obviously accept your word on this. I recall being surprised by the language, because it feels more natural to me that the object being extended is a subobject of the extended object. I don't know why in homological algebra texts a different usage has been adopted, and I was rather looking for an...

- Sun Mar 27, 2011 6:38 pm UTC
- Forum: Mathematics
- Topic: Finite group extensions
- Replies:
**37** - Views:
**3859**

### Re: Finite group extensions

mike-l wrote:And on the off chance the person you're talking to isn't a group theorist, if it isn't clear from context, it's probably best to ask.

I also said that this term doesn't exist in group theory (I mean a finite group extension), so it's good to ask in any case!

- Sat Mar 26, 2011 12:03 pm UTC
- Forum: Mathematics
- Topic: Finite group extensions
- Replies:
**37** - Views:
**3859**

### Re: Finite group extensions

Explanation: Wikipedia is wrong. E.g., Robinson's A Course in the Theory of Groups, p310, Segal's Polycyclic Groups, p38. I trust Derek and Dan over Wikipedia. Oh, and other source: I'm a professional group theorist. PlanetMath has it your way, Wolfram has it my way. Jyrki quoted a text that has it...