User talk:J D Bowen

DISCUSSION MOVED TO Talk:Main Page BECAUSE IT IS A SITE-WIDE STYLE QUESTION. --Cynic (talk) 18:56, 11 January 2009 (UTC)

Since in places we're plainly covering (or intending to cover) the same or very similar ground, no doubt we'll be hacking each other's work to shreds somewhat! I will try to ensure that anything I change is kept in, commented out inside so you'll be able to restore what you think I've taken too many liberties with. --Matt Westwood 23:07, 20 January 2009 (UTC)

Group Examples
Yep, I think I like that ...

So you define, say, Definition:Quaternion Group and have a sentence in it that says "For proof that it is a group, see Quaternion Group" which will redirect to Dicyclic Group. (Better done like that than to go straight to Dicyclic Group in case we decide to make Quaternion Group its own special page, and better to jump straight to the proof of Dicyclic Group than to go the roundabout way of via Definition:Dicyclic Group.

Yep, same with Definition:Alternating Group which goes to "For proof that it is a group, see Alternating Group".

Okay, let's do this. Thanks for taking this one on, as I say I was getting bogged down on groups, which is why I changed to something I'm more comfortable with (analysis), which is dead boring but straightforward and undeniably essential to get right. --Matt Westwood 22:34, 22 January 2009 (UTC)

Equivalency
Oh fair enough (although I'm not sure I have any respect for the authorities you quote, my bible is the Oxford English Dictionary) ... but it means equivalence, right?

Since "equivalence" is what's been used throughout till now (e.g. see Material Equivalence), and "equivalency" is ugly and wasteful (it requires more syllables to say) and its use is AFAIK limited to American English, whereas "equivalence" usage is more worldwide, I'd recommend "equivalence". Your call though, you wrote the page whose name I changed. Feel free to change it back. --Matt Westwood 17:54, 10 April 2009 (UTC)

About the sandbox
Good idea if you're writing to the sandbox not to delete the top three lines. I've just put them back. --Matt Westwood 21:58, 29 April 2009 (UTC)

Might be worth setting up your own sandbox. You can do that by setting up a page User:J D Bowen/Sandbox.

Oh and another BTW: please use my "User Talk" page, not my main page, when writing a message - I edit my own page on a sporadic basis and there are going to be inevitable edit conflicts. --Matt Westwood 22:25, 29 April 2009 (UTC)

Congratulations!
Best wishes for the PhD!

Apologies
... on behalf of the troll who corrupted your user page. I have reverted it and prevented the user doing it again.

Contacting You
I would like to discuss another wiki with you, but I have been blocked on that wiki and cannot edit there. Can I email you, or simply discuss with you here? Chris3145 20:37, 23 October 2009 (UTC)

I've pinched something
... off your sandbox. Hope you don't mind:


 * Product of Row Sum Unity Matrices

Feel free to delete it and resubmit it if you feel I've misappropriated. --Matt Westwood 08:06, 27 June 2010 (UTC)
 * Haha, no problem at all. I'm doing a course in finite fourier analysis and using this site to tec my homework, so feel free to go through the history or anything i put up for proofs. J D Bowen 21:36, 27 June 2010 (UTC)

I'm following your homework ...
... and I'm hoping you aren't going to be in too much of a hurry to delete any of it. There's stuff there which is crying out to be plundered! Trouble is, I'm not in a position to do much about it at the moment, I'm too busy Tidying Up.

Also, notice there's others here who seem to be treading the same ground as you. Gather you've been spreading the word. Good stuff. --prime mover 17:58, 8 September 2010 (UTC)
 * I'm certainly not planning on deleting any of it! And yeah, somebody commented on how convenient it must be to be able to access and work on our HW anywhere without constantly emailing ourselves tex documents, so I told them about this site.  Hopefully it leads to some new contributors.  J D Bowen 18:42, 8 September 2010 (UTC)


 * I suggested to one of the new correspondents that h/w ought to go in a subpage of their own home page / sandbox etc, and moved the work into that page. I've heard nothing from them since. Please feel free to reassure them that this is what has happened and their work did not get deleted out of hand. --prime mover 20:50, 8 September 2010 (UTC)
 * For sure. I've gone over my HWs and while I'm too busy grading/doing more homework to formalize these for inclusion here, things which I think might have a place here:
 * 1.3.16 and 1.4.7 here detail the number of m-cycles in the symmetric group, and the order of the general linear group over a finite field. The latter could be expanded to apply to any size matrices fairly easily.
 * 1, 2, and 3 might belong here as proofs of statements re. supremum and such, but they are probably already on here somewhere.
 * 2 and 3 are some basic results about vector spaces and spanning sets, could be good to have if we don't have this already.
 * Only number 7, I think, would belong on a page here.
 * Like I said, I might get around to doing this or I might not. But for whoever bothers to do this, there's the handy reference on what might belong (and the rest probably doesn't).J D Bowen 03:27, 9 September 2010 (UTC)

Basis Expansion Theorem
I gave it a raking over to display it better and also to link with other results and definitions.

Note that I think you might have conflated the concepts of series and sequence.

The sequence $$\left \langle {a_n}\right \rangle$$ is, for example:
 * $$3, 1, 4, 1, 5, 9, \ldots$$

whereas the series $$\left \langle {s_n}\right \rangle$$ is defined as:
 * $$s_n = \sum_{i=0}^n a_i 10^{-i}$$

which works out as:
 * $$3, 3.1, 3.14, 3.141, 3.1415, 3.14159, \ldots$$

Thus a series is a sequence - it's a sequence of partial sums.

Sorry to labour the point if it's all obvious, I'm really trying to convince myself more than anyone else, I'm actually an amateur.

Anyway, I changed a couple of cases where you referred to $$\left \langle {a_n}\right \rangle$$ as a series, and called it a sequence. Hope you concur. --prime mover 21:41, 9 September 2010 (UTC)
 * Next time, correct my homework for me BEFORE I turn it in =P J D Bowen 23:55, 9 September 2010 (UTC)
 * Although I have to say I'm not a fan of $$\langle a_n \rangle \ $$ for a sequence instead of the brackets $$\left\{{a_n }\right\} \ $$. The bracket notation illustrates clearly that the sequence is a set indexed by the natural numbers, and if we feel the need to be explicit about the "ordering" we can write $$\left\{{a_n}\right\}_{n=1, \dots, \infty} \ $$ or something.  For me, at least, the notation $$\langle a_n \rangle \ $$ instantly makes me think of the group/subgroup generated by $$a_n \ $$.  It's a notational choice, not really important, but yeah.  That's my take. J D Bowen 00:01, 10 September 2010 (UTC)
 * Oops! tee-hee ... maybe I ought to consider that career change to teaching after all ...
 * About the notation for sequences: I understand the confusion with the "group generator" notation, but IMO the set notation version is flawed because it implicitly carries the intellectual baggage that "order does not matter". The alternative notation of $$(a_n)$$ is beginning to look attractive for precisely that reason - "things in round brackets make you think of ordering".
 * Wonder if there's a PhD thesis on the psychology of mathematical symbols?--prime mover 05:43, 10 September 2010 (UTC)

LaTeX and education
Purely as a matter of interest ...

What's the status vis-a-vis LaTeX being used in the education community for general communication of ideas? When I was last in ed (on the receiving end) back in 2002-05, it wasn't talked about, and not even the materials were stamped "written in LaTeX". No encouragement was made to use s/w for writing the assignments, it was all longhand except for those modules based around s/w tools (we generally used Mathcad, which was a reasonable application). I did try an add-on extension for Equation Editor for Word which I paid for, but it was never good enough or reliable enough (or come to that quick enough) for it to be usable in anger. The assignment I turned in using it wasn't commented on in any way, and I got the distinct idea that electronic presentation of material was discouraged.

Very few people seemed to have heard of LaTeX and no encouragement was made to pick it up. It was only after I'd finished my degree and wanted a serious means of writing a large body of mathematical text that my need for such a tool became important.

And now I don't know how I could have possibly lived without it.

What's your experience? --prime mover 05:33, 11 September 2010 (UTC)
 * Well it's pretty different now, or at least in my program - two of my professors demand homeworks be texed up. Basically everything I get digitally from the department is in tex, which kind of frustrates me because I'm used to documents in mathematica, that's what we did when I was undergrad.
 * Somehow it seems like it became the industry standard overnight. Or at least, that's the sense I get.  *shrug* J D Bowen 05:52, 11 September 2010 (UTC)
 * I can't imagine life without tex or mathematica. Reading handwritten math?  Ugh! J D Bowen 05:53, 11 September 2010 (UTC)
 * I've steered clear of Mathematica (I sadly don't need it in my current career, best I can do is attempt to persuade the mgmt that I have a better and more versatile way of implementing our process control without actually scaring them off that I'll be implementing a directed acyclic graph structure and hence recycle the customer network hierarchy algorithms, yadayada) as I gather it's expensive. Not sure if it still is. Must investigate. --prime mover 07:02, 11 September 2010 (UTC)
 * Found this, by the way: Will it rot my students' brains if they use Mathematica? - fascinating piece which I endorse. --prime mover 07:02, 11 September 2010 (UTC)