In recent years I have seen several courses in pure math in the undergrad level (year 2, 3, 4) such as real analysis and topology where the entire course consists of:
- notes written during the lecture (with several recommended textbooks that the prof does not follow in detail), and
- a long list of exercises questions drawn from various sources with no solution provided to the students
The questions for the exams are directly drawn from the list of exercises questions with modifications. There is absolutely no homework, no grades aside from grades of several exams and solution to exercises are never given aside from hints you can obtain by talking to the professors.
From talking to the professors, I get the sense that they are mainly concerned about:
- cheating, using homework solution from online of standard texts thus hindering mathematical development
- encouraging students to think more about problems
- providing ways to incentize students to do exercises by putting modified exercise problems on exams
- weeding out students who are not committed to learning about math
Has anyone ever went through or conducted such a course? Is this an effective way to deliver a proof based math course? Are there any potential pitfalls and flaws using this approach?