Search found 19 matches

by jimbob_barnes
Tue Aug 21, 2012 1:37 am UTC
Forum: Mathematics
Topic: Problems for Freshpeople
Replies: 9
Views: 2117

Re: Problems for Freshpeople

He is in France :(
by jimbob_barnes
Tue Aug 21, 2012 1:10 am UTC
Forum: Mathematics
Topic: Problems for Freshpeople
Replies: 9
Views: 2117

Problems for Freshpeople

Hey there everyone. I'm TAing a course for first-year undergrads on calculus, I have my first ever session on Thursday so I want to make a good start. The problem is that the students will only have had one lecture prior to seeing me, and I am not supposed to teach the lecture content before the pro...
by jimbob_barnes
Thu Mar 22, 2012 10:54 pm UTC
Forum: Mathematics
Topic: Kleene's Second Recursion Theorem and more general advice
Replies: 3
Views: 2799

Kleene's Second Recursion Theorem and more general advice

Ok so here is a little context, this academic year I've been applying to graduate schools for a PhD in mathematics, particularly in logic. So far I have places in Cornell, CUNY and Illinois at Chicago and the deadline for picking places is coming up quickly. Now my tutor informs me that Cornell is v...
by jimbob_barnes
Thu Dec 01, 2011 3:53 pm UTC
Forum: Mathematics
Topic: Again with the measure theory.
Replies: 11
Views: 2070

Re: Again with the measure theory.

Yes! That works, it took almost a page of TeX to work it all through but yes I got it working.
Thank you all for your help and a special mention goes to jestingrabbit.
by jimbob_barnes
Tue Nov 29, 2011 9:19 pm UTC
Forum: Mathematics
Topic: Again with the measure theory.
Replies: 11
Views: 2070

Re: Again with the measure theory.

Yakk - I don't really understand what you are trying to say wrt 3), as you saying that f_k ---->f in metric does imply f_k---->f yet the converse doesn't hold, or the other way round? I also don't see how part 3 connects to part 4 as one is about metrics and the second is about linear maps. Rabbit -...
by jimbob_barnes
Mon Nov 28, 2011 9:23 pm UTC
Forum: Mathematics
Topic: Again with the measure theory.
Replies: 11
Views: 2070

Again with the measure theory.

Edit: All done. Ok, so I'm back again with more measure theory. It may be that I am just very tired because I have been trying to get applications to graduate school all weekend. However when I look at these problems I really have no idea what to do, here we go: 1) Find the Radon-Nikodym derivative ...
by jimbob_barnes
Fri Oct 21, 2011 7:10 am UTC
Forum: Mathematics
Topic: Measure Theory and Cantor Sets.
Replies: 9
Views: 1598

Re: Measure Theory and Cantor Sets.

Thanks for the "general homework doing advise" I really didn't know that doing maths takes time. The fact that the lecturer handed out the assignment sheet on last Friday, that I had to travel to a different country to do the GRE on the weekend and that I had a backlog of work from using m...
by jimbob_barnes
Thu Oct 20, 2011 9:51 pm UTC
Forum: Mathematics
Topic: Measure Theory and Cantor Sets.
Replies: 9
Views: 1598

Re: Measure Theory and Cantor Sets.

Ok, are you trying to hint that I use the slight extension of the geometric sum \Sigma^{\infty} a(k^i)=\frac{a}{1-k} . I suppose you have to mean that because as I gathered from my first analysis course, evaluating the limit of a series is generally hard . So do I instead try a_0=k and a_i=(...
by jimbob_barnes
Thu Oct 20, 2011 9:10 pm UTC
Forum: Mathematics
Topic: Measure Theory and Cantor Sets.
Replies: 9
Views: 1598

Re: Measure Theory and Cantor Sets.

In my reply to you I did indicate that any sequence A_n=c with c in (0,1) has 0 measure, so yes it is easy to calculate, but I had already calculated it. Explicitly: L=1-\Sigma_{k=0}^{\infty}a_k(1-a_{k-1})\ldots(1-a_0)=1-\Sigma_{k=0}^{\infty}c(1-c)...(1-c) (with K (1-...
by jimbob_barnes
Thu Oct 20, 2011 5:49 pm UTC
Forum: Mathematics
Topic: Measure Theory and Cantor Sets.
Replies: 9
Views: 1598

Re: Measure Theory and Cantor Sets.

Well in the lecture we went through the famous case, i.e. (a_n)=1/3 for all n and we found that it has length 0. I used a quick argument about geometric progressions to show that any constant sequence leads with a cantor set with 0 length. Another example given in lecture was a_n=\frac{1}{(n+2&#...
by jimbob_barnes
Thu Oct 20, 2011 5:12 pm UTC
Forum: Mathematics
Topic: Measure Theory and Cantor Sets.
Replies: 9
Views: 1598

Measure Theory and Cantor Sets.

Okey dokey, so I've been going over my first Measure Theory assignment sheet and I am stuck on a few questions. Any pointers would be fantastic, there are 3 in total: 1) Given any 0 < l < 1 find a sequence (a_n) of elements of (0,1) so that the symmetric Cantor set obtained with the starting interva...
by jimbob_barnes
Wed May 12, 2010 11:00 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0739: "Malamanteau"
Replies: 165
Views: 44047

Re: "Malamanteau" discussion

sourmìlk wrote:I think the actual joke is that the word "malamanteau" is itself a malamanteau.

The word is recursive


You mean autological, it expresses a property which (supposedly) it has itself.

The question is, is "autological" an autological word?
by jimbob_barnes
Fri Feb 19, 2010 12:39 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0704: "Principle of Explosion"
Replies: 104
Views: 32578

Re: "Principle of Explosion" Discussion

You assure me you'll wear a raincoat tomorrow if it rains. If it rains and you wear a raincoat, your statement was true. If it rains and you don't wear a raincoat, your statement has been proven false. If it doesn't rain, I have no idea whether you would have worn a raincoat or not. I'll happily ad...
by jimbob_barnes
Mon Feb 01, 2010 7:43 pm UTC
Forum: Mathematics
Topic: Formal Logic - Capturing a property
Replies: 2
Views: 702

Re: Formal Logic - Capturing a property

In the interest of brevity I shortened to sigma1 complete hoping people would realise, the part I need help with is proving that if for a given property P which is written as a wff in sigma1, and all numbers n P(n) is false then Q proves ~P(n). In the book it proves that, say 3 is not lesser than 2 ...
by jimbob_barnes
Mon Feb 01, 2010 4:45 pm UTC
Forum: Mathematics
Topic: Formal Logic - Capturing a property
Replies: 2
Views: 702

Formal Logic - Capturing a property

Hey all, I am currently taking a logic course which will culminate in Godel's incompleteness theorems, although at this point we are somewhat far off. Anyway at the moment we are talking about Robinson arithmetic (Q) and in particular what properties it expresses. I.e. Q expresses a property of the ...
by jimbob_barnes
Sat Jan 23, 2010 12:43 am UTC
Forum: Mathematics
Topic: Basic group theory question at which I fail
Replies: 4
Views: 1035

Re: Basic group theory question at which I fail

god I'm such a Failure, I know its past midnight where I am but I should have been able to see that

I don't think I am going to get on well with this course as a friend had to tell me which function to use to show <R,+> is isomorphic to <R>0,x>

sigh
by jimbob_barnes
Sat Jan 23, 2010 12:23 am UTC
Forum: Mathematics
Topic: Basic group theory question at which I fail
Replies: 4
Views: 1035

Basic group theory question at which I fail

Ok guys, here is the question. Let S be a finite set with a binary operation * : S x S -> S satisfying associativity (for all a,b,c in S (a*b)*c = a*(b*c)) and closure (a,b in S implies a*b is in S). In addition let * follow the cancellation laws for a,b,c in S a*b = a*c => b=c and b*a = c*a => b=c....
by jimbob_barnes
Fri Jan 15, 2010 1:28 pm UTC
Forum: Mathematics
Topic: Shuffling Cards
Replies: 17
Views: 2687

Re: Shuffling Cards

A program (it might be difficult to do this manually) could weed all permutations which are sufficiently unfavorable (energy-floods/droughts) and distribute the probability to the remaining options. I don't think this is cheating because it does not favor any particular player. (An example conditio...
by jimbob_barnes
Wed Jan 13, 2010 1:50 pm UTC
Forum: Mathematics
Topic: Shuffling Cards
Replies: 17
Views: 2687

Re: Shuffling Cards

Thanks for responding guys! 2) How could I approach shuffling a pokemon deck in a manner that would almost consistently result in a fair distribution of energy. Any shuffle which properly randomises the cards will sometimes always throw up an unfriendly distribution. Formally if you have a deck of ...

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