New year, new research, same problems

The research ground of my PhD is now behind, summed up in the thesis. It may come up again in the future, I may have to offer some presentation on or help code real applications that make use of those ideas and results, but that's something for some more or less distant future.

This new year I'll be coping with a new research topic, whose iceberg tip is given by systems of linear interval equations. Too bad I have to (quickly) rack up a lot of background topics before I can fully understand the implications and difficulties of the research: coming from a fully theoretical math past means I have no knowledge of finite elements, matrix manipulation or interval analysis. These are three distinct topics I have to prepare myself with, knowing I will face totally different challenges when they'll come together.

It's time like this that I wish more material was available online. It's easy to find course notes on very classical subjects. It's also not too hard to find very recent research material (be it with generic search engines like Google or more specific sites like Citeseer), but don't keep your hopes on finding in-depth texts on modern math subjects: if your university library doesn't carry the relative textbooks, tough (and expensive) luck.

My immediate needs involve getting enough background on the topics and the recent advancements to see if things like affine arithmetic would help in the process. Of course, I need to get steeled enough in the matter to present it. Luckily, online material to (affirmatively) answer the question can be found. Now it's just a matter of studying the subject more in depth, rather than just relying on some trivial example.

It's hard but nice to have some serious work to do.