New game, everyone! Work have bought me an iPad. I have so far discovered this is basically a touch screen interface through which I can write email, read Twitter and play pinball, but I’ve heard a rumour that it can do even more than that. I’d like you to suggest what else I might do with it.

Work, in this case, is being a lecturer of mathematics at Nottingham Trent University, which I will be doing for the next academic year. Last year I taught using a tablet PC. I was involved a little with such technology in my work under the National HE STEM Programme, and edited a booklet of contributions on that sort of thing. Basically, last year I made an outline PDF in LaTeX and wrote on this during lectures, publishing the annotated PDF for the students. I liked this because it meant that I could write and project large enough for everyone to see in quite a large lecture theatre, face the audience while writing and provide a copy for students after the event. I might do much the same next year, but I would like to explore the possibilities using my new kit as well or instead, principally for delivering lectures and perhaps recording short worked examples.

I now have an iPad and a LiveScribe Pen, with which to carry on my explorations in that area. It is fairly clear what to do with the pen – I can write out worked examples and solutions and record myself doing so. The iPad has rather more possibilities. I have a stylus which is apparently good for writing (rather than, say, pointing or drawing) and a connector to plug the iPad into the standard lecture theatre projector system, so I can lecture from the iPad provided I have the right app. I also have a £50 Apple App Store gift card so apps can happily be free or cost money (up to a point!). I have the Wolfram Alpha app, but basically assume I have nothing else.

Questions:

1. What is a good PDF annotator app for the iPad? I would like to load a PDF I made on my computer in LaTeX, write on it in class and export the result back to PDF. I have enough money to try a few different ones and compare, if necessary.
2. Can I record what I am writing/doing as a video? How would this work? (I expect not.)
3. What other useful apps should I try?
4. Is there anything else I should be thinking about with the iPad or the LiveScribe pen?

I am teaching university mathematics so apps and uses need to be relevant to that. Either apps I could use with my students in class or ones that would help me with my job. I will be running the first year calculus and linear algebra module, also teaching (though not in charge of what happens) on some computational and numerical methods stuff around Matlab etc. I will be doing some basic maths for forensic science. I also run the Maths Arcade, which means puzzles and games are in. I give talks at conferences which are usually a PDF made by LibreOffice Impress. Please make your suggestions in the comments below. Thank you!

EDIT (28/08/2013):  I wrote a follow-up round-up post here: Your suggestions of iPad apps for university mathematics teaching.