Background. I teach math at a German university (both undergraduate courses and courses for Master programmes), mostly for students who major in mathematics or very similar programmes. Students typically choose their major before starting their studies. Courses aimed at students who major in mathematics are proof-based from the very beginning and proofs are an essential part of both homework and exam problems.
Context. I regularly find myself in discussions about whether every course should be designed around measurable learning objectives. When I point out that I don't know how I should do this for any but the most elemantary math courses that I teach, this usually leads to one of the following two points:
The very generic comment that it's of course possible, if one just commits enough to doing it.
Some examples to show how it should be done, but which are extremely elementary (along the lines of "How to prove a formula by induction").
Both answers don't help me to see how this could be done in my courses in practice.
Empirically, when I look at descriptions of math courses (in Germany, those are collected in so-called "module descriptions" which are supposed to have a section that lists the learning objectives) I always see one of two patterns: Either the objectives are formulated extremely vaguely (which contradicts the goal to make them measurable) or they are essentially a rewording of the table of contents (sometimes enriched by a few verbs to make it sound more like objectives rather than contents).
Question. I'm looking for concrete examples of somewhat advanced math courses that are based on explicitly stated measurable learning objectives.
Criteria for a good answer:
It should be a proof-based course which requires a certain level of abstraction. I'm thinking, for instance, of an introduction to point set topology or measure theory or group theory or functional analysis, or anything of a similar level.
I am not interested in "Introduction to proofs" like courses, because for such courses I can see myself how this approach can work.
The description of the learning objectives should be sufficiently concrete to make it clear that and how they can be measured. Moreover, they should not merely be a slight rephrasing of the course contents (because if they were, I wouldn't see the point of it).
It's not so important for me to have access to all the courses materials. I'd mainly like to see the description of the learning objectives and a (maybe brief) description of the course contents.
Bonus points if the course is even part of an entire math programme that is designed around measurable learning objectives (but that's not a requirement).
I'd be happy with sources in English or German (or, if there's no help otherwise, in French).
Note. This question is not about the following things:
I'm not asking about opinions on whether basing courses on measurable learning oucomes is a good or bad idea. I'm only asking for concrete examples where it has been done.
I'm not looking for advice on how I could create such a list of measurable learning objectives myself for a course. This would also be an interesting question, but it is not part of this question.
