Comments for Mathematics and Computation

Comment on The hydra game by Why Is There Something? | Gödel's Lost Letter and P=NP

Why Is There Something? | Gödel's Lost Letter and P=NP — Sat, 01 Jun 2013 03:58:01 +0000

[...] objects of the world so that the subtraction always stops, but that this is hard to prove. See this note by Andrej Bauer on “The hydra game” for a discussion of such [...]

Comment on Video lectures as screencasts by Andrej Bauer

Andrej Bauer — Thu, 30 May 2013 23:13:44 +0000

@Scott: thanks for the info! In my experience students prefer longer lectures than many short ones (this is actually the result of a poll), something around 30 to 45 minutes seems optimal. (I suspect they just don’t know how to use the “couch mode” on Vimeo.) So I keep my video lectures in one piece, sometimes 90 minutes long, but I equip them with tables of contents that allow students to jump directly to a particular part of the lecture. The one thing I still miss is a decent program for writing on screen with my Wacom Tablet. Quill for Android seems good, but that is for Android.

Comment on Video lectures as screencasts by Scott D. Reid

Scott D. Reid — Thu, 30 May 2013 23:02:19 +0000

I have been video recording my lectures for about 3 years now. I do everything myself. I have a Kodak Z5 video camera to recorder me as I deliver the lecture. I also use ScreenFlow on my MacBook Pro laptop. Depending on the room, I either use the built-n mic or in one case, I have an audio line in from the amplifier from the lapel mic the imports into my laptop (evens out my voice if I move away from the lectern). I tend to annotate my slides with OnmiDazzle because the laser pointer doesn’t show up on the video. I would use the Kodak to also record and white board work that I do. I would use the editor in ScreenFlow to zoom in or out of the video from the Kodak that I import into ScreenFlow. ScreenFlow files are large, but they include my lecture slides that were projected with the LCD projector, the audio and my external video from the Kodak.

I recently purchased a Wacom Bamboo that I plan on using this fall to annotate my slide rather than with my mouse; hoping I can do a better job of writing and drawing with it and OmniDazzle. I use Keynote and my plan is to use the Keynote black screen rather than the lecture theatre whiteboards. I select black screen while lecturing, and using coloured pens, doodle or write away, then back to the lecture slides. This way the “whiteboard” work I do is sharp, clean and recorded off of my laptop (rather than recorded on the Kodak from the other end of the lecture theatre, digitally zoomed and cropped and enhanced…….). My lectures are 90 minutes and I am looking into trying to break them up. Despite this, I export them to a file format that plays in QuickTime (Mac/Windows), on students smartphones and on their MP3 players (eg. iPod Touch).

Students love it.

Hope these ideas help.

Scott

Comment on Substitution is pullback by Andrej Bauer

Andrej Bauer — Sun, 26 May 2013 11:39:09 +0000

@Udday: pullbacks can be generalized, for example in fibered categories. What sort of generalization are you talking about?

Comment on Substitution is pullback by Uday Reddy

Uday Reddy — Sun, 26 May 2013 10:37:40 +0000

Intuitively, composition is also a pullback. $f;g$ is the “pullback” of a morphism $g : B \to C$ along $f : A \to B$ to obtain a morphism of type $A \to C$.

One way of formalizing the intuition is to work in subsumptive reflexive graph categories (Dunphy & Reddy, Parametric Limits, LICS 2004), where we have “logical relations” in addition to morphisms. Perhaps there are other ways as well.