class in session, part 2: third down, incomplete pass .. (also: #1200)

so i punted.

today was already lecture 3 of 4 and i planned sufficiently poorly so that the $\LaTeX$/PDF notes for lecture 2 were still only half-complete.  despite this, they remain self-contained, readable, and just-barely-suitable for public consumption [1].

this pains me nontrivially [2].

if these lectures were part of a "real" course .. that is, where one would solve problem sets and get actual credit .. then the students would be lost.

this is not an exaggeration.  i can tell something isn't quite clear, if only because my collaborator was part of the audience, and she had a great many questions about some points i made.

so if she, an established researcher, could not catch everything then what chances would a ph.d. student have to be able to catch something .. especially if this is not their field of interest?

[sighs]
so yes, i gave up.

between a final push of research collaboration this week and writing up my own notes [3] for lecture 4, i see little-to-no time available for catching up with the $\LaTeX$ for lecture 2 and proceeding with lecture 3 from this afternoon.  so if is infeasible to do so, then why bother?

instead i posted onto my webpage some PDF scans of some notes from previous talks.  it's not a perfect solution, but it's better than nothing.  more than that, it's important to make something available for those students who may actually want to look at the details [4].

yes, probably none of the students will actually do this .. but if there is a nonzero probability that one might, then it is worth doing.

i also have other reasons for disappointment.  for example, i really wanted to have the lecture notes in wiki format.  my reasons involve symmetry:

i thought about what i wish other researchers would do in expositional formats, how very interesting (but technical) topics could be made more accessible, and how great it would be if a proof were actually "clickable" ..!

here i mean more than just having the information publicly available.  yes, the arXiv is a great thing .. but the mathematics opens only in PS or PDF or even DVI.  though there have been many strides in progress and in improvement for the user interface, none of these are really that clickable.

take, for example, a theorem in the text where the citation is hyperlinked.  if you click on the link, then you are teleported to the end of the PDF file, where one finds the references.

[this is an example of what i mean, regarding hyperlinks]

if the PDF opened in a web browser, then pressing [Back] can exit the PDF and lead you back to the previous webpage.  pressing [Forward] then re-opens the PDF back to the damned beginning!

argh ..!
it's a small matter, but i still get annoyed by it. \-:

in contrast, a wiki fits seamlessly into the medium that is the internet.  these days, mathjax, asciimath and other $\LaTeX$-rendering tools for the web are sufficiently robust, so that publishing maths on the web needn't ruin one's sense of aesthetics [5].  moreover, any sufficiently important definition usually has its own wiki, and one can link directly to it [6].

smooth and sweet, no fuss; wouldn't that be great? (-:

.. right: as for this talk of symmetry, i have this crazy idea that if i do this and convince others that it's a good idea and not hard to do, then maybe those others will do the same .. \-:

on a completely unrelated note:

according to the count from blogger this is post #1200.  it still amazes me that i still have mathematical things to write about, even after these seven (7..!) years of blogging.  the best explanation is that i'm moving along in my academic career; with the changes comes a different perspective and new things to write about.

on the other hand, i think i'm starting to get repetitive with the themes in this blog post.  i can't conveniently count the number of times that i've written about my neuroses about giving talks, rants about teaching, and the frustrations of research.

i don't know.  maybe i should end this blog once and for all, but there's no sense in making a hasty decision now.

i'll make a final decision by post #1300. (-:



[1] you can find the notes on my new homepage; just google me and click on "talks and lectures" ..

[2] this seems to me a sentence that could only have been written by an academic.

[3] to clarify, there are at least two kinds of notes: (A) those intended to be shared publicly, and (B) those intended to be like a script for delivering the lecture.  in that sense, giving a good lecture is like acting a very specific role.

[4] one could make the argument that if a student is really interested, then (s)he will go to your paper and read it carefully.  i don't disagree with that .. but that assumes that a student is paying attention to only one thing.  student or not, when was the last time that anyone had only one thing for which to be responsible?

[5] part of the appeal of $\LaTeX$, admittedly, is how fluidly and aesthetically the typography appears.  that can really matter, if for example one uses a cumbersome notation, like $\tilde{f}_{i_j}$ to indicate convex combinations of a sub-subsequence $f_{i_j}$ of an initial sequence $f_i$.

[6] not to get too "meta" on you readers .. but those of you who clicked on the mathjax link (or were thinking about it) must know exactly what i mean!