In lecture 6 at June 8 we will start with chapter 4 of the lecture note. I think that we will be able to cover section 4.1 completely.

In the next we will finish section 3.1 and probably already start with the singular value decomposition. Please also prepare questions while you work through the material!

For lecture four on May 11, I will cover the intro of chapter 3 and section 3.1 on generalized inverses. If time permits we will also start with the singular value decomposition (section 3.2).

We use the next lecture to finish chapter 2 and additionally I will spend some time to cover some motivating examples of inverse problems. So you just need to prepare for the remaining part of chapter 2 and the rest of the lecture will be additional material not in the lecture notes.

I forgot to mention in the beginning: You may hand in your exercise sheet in groups of at most two people!

As StudIP had some problems around 10 and 11 today, I opened a different meeting room. In case you missed the lecture: We covered the first chapter on linear operators, but unfortunately, recording of the meeting is not yet avaible.

For the lecture next week we will meet in the "Lecture hall" under the meetings tab. In case, StudIP will have problems again, we will resort to the other room, but I will send a note via email in this case.

Next week we will cover chapter 2 on compact operators in Hilbert space.

In addition to the more formal syllabus below, here is a little bit more information on how I plan to run this lecture. It will be my first online-only lecture (probably for you too?), and so we will have to figure a few things out while we go. Here is my plan:

• I will give lectures with a conference tool (most probably the BigBlueButton instance hostet by TU Braunschweig which will be accessible through the "Meetings" tab above). I plan to use a kind of document camera to record me writing on paper and also the webcam on my laptop to record me. So you should be able to see and hear me talking and also see my handwriting in parallel. To attend the lecture you need some device with a few specifications: The screen should not be too small and you need a speaker, headphones or headset. A mircophone will be helpful if you want to ask questions during the lecture (but not strictly necessary, since the will be a chat in parallel). You don't need a camera but you can join the meeting with your camera too, if you prefer. The lectures will be held at the time which is annouced and start on Monday 20.04.2020. I will also record the lecture so that you can re-watch the lectures later.
• Since the space on a sheet of paper is much smaller than the space on a blackboard, we will slightly change the way the lecture goes: After the first lecture I will announce which part of the lecture notes by Christian Clason (see syllabus) I will treat in the next lecture and you should go through these pages to get a grip on definitions and also an impression of the results. In the lecture I will cover the things you already read more briefly - but please interrupt me if I should cover anything in more detail and also ask questions at any time.
• I will open the "Blubber channel" for the lecture, which is a chat you can find in the tabs above. If you have any questions or suggestions outside lecture time, just put them there.
• The homework assignment will be uploaded as pdf as usual and you can submit scans of your homework via an upload folder in Stud.IP. If you don't have a scanner available, you should download some app which can do document scans (I used Notebloc and Mircosoft Office Lens so far - both are ok, but I guess that there are better apps available - if you have any suggestions, please let me know!. Please scan your work into one single file - preferrably a pdf.

Since this is my first online-only lecture, I rely on you feedback! If you any complaints or suggestions on how the lecture should be run differently, or if you have any problems with the lecture please let me know! You can use the Blubber channel on email me. You can even leave comments below this posts (I think - at least I activated this feature…).

Lecture format

The lecture "Inverse Problems" consists of 2SWS of lecture and 1SWS exercise class and both will be held in English (although you can ask questions in both English and German and please always ask if there is any word you could not understand).

The lectures and the exercise class will be held online. The tool for the online classes is to be decided and depends on the possibilities that are offered within Stud.IP when the lecture is about to start on Monday, April 20. Up to now, the choices are BigBlueButton and Zoom.

To attend the online lectures and exercise classes you need a device with camera (not strictly necessary), a stable internet connection and a headset (a simple one should be enough) would be preferable.
 

Homework, Studien- and Prüfungsleistungen

There will be bi-weekly homework and the exercise classes will also be held every other week. The schedule and the deadlines for the homework assignments will be announced when the exercises are ready.

For the "Studienleistung Hausaufgaben" you need to have 50% of the points on the homework assignments.

For the "Prüfungsleistung" there will be oral exams in the summer (anything else will be decided later on, depending how the situation develops).
 

Prerequisitivies

For this lecture you need basic analysis (calculus) and linear algebra, i.e. theory of functions of one and several real variables, and vector spaces. Moreover, basic knowledge about Hilbert spaces is assumed (e.g. inner products, orthonormal bases). Also basic topological notions such as metric spaces, compactness and continuity will be needed.
 

Literature

The lectures are based on the lecture notes "Regularization of inverse problems" by Christian Clason which can be obtained on the preprint server arxiv.org at https://arxiv.org/abs/2001.00617.

Further reading about regularization of inverse problems:

• - Kein Probleme mit Inversen Problemen, Andreas Rieder, Vieweg, 2003.  https://link.springer.com/book/10.1007/978-3-322-80234-7
• Regularization of inverse problems, Heinz Engl, Martin Hanke and Andreas Neubauer, Kluwer Academic Publishing, 1996