By the nature of a Massive Open Online Course (MOOC) a student is given permission to read the course materiel, and to copy or summarize it into notes for personal use. The instructor should not use any content doe which such permission is not available unless it is a quote, clearly indicated as such.
Even if the instructor does use a brief quote, there should be an educational exception to copyright which will apply.
The ideas in the course are not protected by copyright. The student is expected to learn them and use them.
The specific words of the instructor, or of others that the instructor quotes will normally be protected. Except in personal notes, the student should not reuse the exact words except as clearly identified and properly attributed brief quotations. Names, specific technical terms and formal definitions may normally be reused, they are not protected by copyright or have been made available for general use.
Formal definitions are usually facts with no other exact way to express them, and so are not protected.
Rewriting the ideas taught in the course into the student's own words is not copyright infringement, it is allowed and indeed encouraged.