Discussion of Course "Advanced Numerical Methods for CSE"
The course Advanced Numerical Methods for CSE was first taught in Autumn Term 2017 as a "beta-version" with substantial need for improvement. Therefore the participants of the course are requested to state their opinions and make suggestions about possible improvements of the course.- Was the selection of topics and their balance appropriate? Please take into account that scores of topics would fit the title of the course, but, of course, only a few can be treated in 14 weeks. You may also suggest topics that you consider eligible and interesting.
- Was the balance of theory and algorithms reasonable?
- Was too much prior knowledge required?
- What do you think about the homework problems and projects? (Please take into account that the topics were largely new to the assistants, as well, and that they stuggled as much as you when writing codes for the master solution).
- How could be lecture material be improved?
I found the course quite good overall, but sometimes I was lost in the details. A periodical overview of what we're currently doing and how it fits into the big picture would be nice. A concrete example in BEM would be repeating the relationships between H-spaces, the boundary integral operators, and the pde we're trying to solve.
Congratulations to teacher and assistants alike on developing such an interesting class with a modern selection of topics, fully deserving the "Advanced" in the title. The errors in some of the solutions are further confirmation that the topic is not easy even for the teaching assistants and require a deep understanding which prof. Hiptmair clearly has. Sometimes however, the teacher seemed unable to understand my difficulties: to his merit, he has spent enough time during and after class with me.
- Script and bibliography: The script is rather dry and not of easy reading: it is dense with formulas and contains no intuitive explanation. To a student lost in the formulas (me), the bibliobiography is of no help either, as it is aimed to math graduate students whereas the class was given to CS/CSE students. The videotaping of the lecture is useful, but since the videos cannot easily be searched, I turned to the script very often. I seem to be the only one who has perused it judging by the amount of reports in Moodle. If the teacher decides that this is the level the script should have, the bibliography should contain a gentler introduction.
- Teaching: Especially for the section on harmonic functions, the lectures were a series of theorem-proofs with little intuition given as to why the statement in the theorem must be correct. The main result was often preceeded by a full lecture of seemingly unrelated minor results, making me loose sight of their purpose. Moreover, after attending the lectures, I still have little intuition of what an harmonic function is, even though I can follow the proofs. In my daily job, in industry, giving a clear intuitive idea of the subject is as important as getting the math right: I assume not all students will pursue an academic career.
- Exercises: I found them extremely useful; publishing the solution along with the problem was an excellent choice Some of the problems are missing the reason why one is led in one particular direction and some of the solutions are minimal: I would have found a bit of text explaining what the result mean would have helped.
- C++, algorithm development, 14 week course: Pick two. C++ does not seem well suited for quickly trying out algorithmic ideas: there is boilerplate to write, which places an inertial barrier to throwing the code away and restarting. Since the course aims at presenting algorithms with low operation count, not fast execution, can the choice of the programming language be reconsidered?