Do you find it a good idea to take lecture notes (even detailed lecture notes) in mathematical lectures?
Related question: Digital Pen for Math: Your Experiences?
[Math] Taking lecture notes in lectures
soft-question
Related Solutions
Some material from the undergrad rep theory course in Cambridge: Example sheets, A recent set of notes (by Martin), and a less recent (but very nice) set of notes (by Teleman).
I have some experience with both the situation posed by the question and Matt Noonan's modification in the comments.
Note taking in seminars: At a recent conference, I took notes directly on to my computer using a graphics tablet in conjunction with the program xournal. I have gotten a little frustrated in the past at having stacks of notes from seminars that are virtually useless to me because I'm rubbish at organising them and finding them again. The main benefit of writing them directly on to my computer was that I could then add the files to my reference database (refbase) where I could store the meta-data in searchable form. To emphasise that point, it is the meta-data that is searchable, not the information from the original talk.
I found a few other side-benefits from this method. I was slightly faster in writing on a graphics tablet than on paper; I think that that is to do with a different posture and the fact that to go from looking at the computer screen to looking at the board is quicker than going from hunched over paper to looking at a board. This might not be the same for something like a digital pen, though. I think I was also faster because I was less bothered about what my notes looked like - when writing on real paper, I try not to waste paper so if the lecture is getting near the end, I'll cram the last bit on the small bit left of the current page rather than start a new one; on the computer, I just make the page bigger. It's also easier to correct things, and to add more space in the middle of something already written (when the lecturer goes back and adds yet more symbols to the diagram!).
The only drawback at that conference was when my computer ran out of battery power 5 minutes before the end of the seminar and I lost the whole lot because the program didn't have an auto-save feature! (I wrote one that evening - isn't open source wonderful! - but I see now that the latest version of xournal as auto-save anyway).
Another drawback is simply the amount of desk space that this system takes up. I couldn't do this at another recent conference because it was in one of those auditoria where there is a tiny side desk which forces you to write on postage stamps.
I did think of trying to combine LaTeXing seminar notes with a graphics tablet: the idea being to have a LaTeX document in to which you type the majority of the notes, but then overlay diagrams (or other annotations) with the pen. While I think that this would be feasible, the software needs a little tweaking for all of this to work seamlessly.
Incidentally, decent graphics tablets are extremely cheap (I got mine for about 35 quid), and it doesn't take much to get used to writing on a different place to where the text appears, so if you're not sure but think it's something you'd like to try, I'd recommend a simple graphics tablet over getting something more expensive in the first instance. Also, a graphics tablet is great if you want to put fancy animations in your talks.
Giving Seminars/Lectures Using a Beamer+Pen: I'm now in the course of my second course doing this. I prepare the lectures using LaTeX+beamer but when I give them then I have a graphics tablet to hand to make annotations as necessary. Sometimes I leave whole problems to be "done live" - by the students, that is. The first time through, I used my graphics tablet and xournal. This time, the lecture hall that I'm in has a PC with a "write-on screen". Unfortunately, it runs Windows but fortunately, there's jarnal. There is a "new page" facility which brings up a blank slide on which you can write whatsoever you like. After the lecture, I put the annotations on the web page for the students.
I should say that there are several reasons that I've switched from chalk to presentations for lecturing.
I give better lectures/seminars when I use a computer than when I use chalk. This is (I think) because it forces me to prepare the whole seminar/lecture properly in advance and not think "I know how to do that" without carefully checking that I really do.
Chalk dust irritates my skin.
I teach in English but my students listen in Norwegian. If I gave the traditional "copy down everything I write on the board" lecture then the lag time while I waited for them to copy stuff down would be too great (I mean that the time that I assign for the students to catch up with copying down and be ready to listen to me again is significantly longer because they are reading, writing, and hearing in a non-native language). So I make the notes available in advance so that they have a baseline of what I'm going to say and can add to it as they feel the need.
I can actually look at the students and see their reactions while I'm lecturing instead of spending half the time looking at the board. That means that I can be far more reactive in what I'm actually saying.
The main drawback is the increased preparation time. But, due to 1, I'm not sure how much of that is because it forces me to prepare properly and how much is due to the nature of the preparation. An additional benefit will be that I have much less preparation to do next time I teach those courses (I say "will" because I've yet to repeat one of these courses. Perhaps I should say "hope").
You can see what it all looks like by looking at the course webpages for these two courses, they are here for the completed course and here for the current course.
Note: I have lots of macros that interact nicely with beamer and make life considerably easier for myself. I also ended up hacking xournal a little to make it better for note-taking. Same again for refbase to make it suitable for mathematicians (it was written by geologists). I'm happy to share any of these modifications, of course.
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Best Answer
I usually bring a pad of paper with me to talks, but don't take notes. I do write down things I want to revisit later, and sometimes it turns into full blown note-taking. Taking notes reduces my ability to concentrate on the lecture, so if it's a really difficult lecture or if the material is totally new to me, taking notes is a sure way to not get much out of the lecture (unless I commit a large chunk of time to reviewing the notes afterwards).
If I know I'm going to review the material carefully (e.g. if I'm taking a class and I'm putting a lot of effort into it), then I live-TeX notes, which has a number of advantages:
If you're considering live-TeXing, try it! It's a lot easier than you might think. Also, look at this page of advice I wrote up when I found myself repeating it to many people.
Edit: By the way, I post all my source, and you're welcome to look at it if you want to see how I set up my headers or manage my files. If I have an svn repository for the notes, you can get them with the command
svn checkout svn://sheafy.net/courses/halg_sp2008(to get my homological algebra notes from Peter Teichner's course for example). If there's no svn repository, you can download the tgz (tar+gzip) file and uncompress it.