Last year (yes, I'm really slow with writing things up "lately") I did a presentation about convex analysis as part of a seminar about inverse problems in imaging.
I want to write about it today.
The seminar was based on the book 'Handbook of Mathematical Methods in Imaging (Springer Reference)'. It's very expensive and, in my opinion, pretty useless to learn about any details. At least the chapter about duality and convex programming was very dense and you could not learn anything from it without consulting other book.
The presentation was supposed to give an overview over duality and convex analysis and serve as introduction. Summarzing 42 very concise pages in 45 minutes is impossible, so I had to choose a few topics that give an overview over the important concepts and go into detail there.
The book itself does not really contain many proofs which makes it hard to follow. As a mathematician I like proofs. They help clear things up usually and they can give valuable insight into the methods of a theory when they're good.
But proofs suck when you see them on powerpoint slides. They also suck when you're the presenter.
So I gave a blackboard presentation---using a few slides only to show some pictures and sketches which I could not draw well enough on a blackboard.
To prepare the presentation I used OneNote and my Bamboo tablet. I scribbled all down over a weekend in one OneNote notebook and later extracted some sketches into another notebook that I used instead of a PowerPoint presentation. I exported the original notes as PDF and used this as handout after the presentation.
The presentation was alright. I had fun writing everything down on the blackboard and developing the subset of the theory I wanted to present, and the audience was content with it, too, because it was just at the right speed and like a lecture everybody was used, too.
In retrospect I can say that using OneNote and a tablet to create a blackboard presentation was the best decision. I don't want to think of the time I would have lost if I had created everything with LaTeX or PowerPoint.
Long story short: here are my notes :)