Aggregation vs Ternary relationship – When to use

I'm going to share some terminology with you that may help in your research.

The relationship you pictured is what is called a "ternary" relationship. It involves three entities. The simple relationships we usually deal with involve only two entities, and could be called "binary". There are "quaternary" relatinships, and so on. The general term is "n-ary".

You may also want to look up the following: Star schema, Ralph Kimball, Data warehousing, and multidimensional data model. A star schema is basically the intersection of relational tables and multidimensional modeling. There's too much here for me to do the subject justice. Happy hunting!

Somewhat unintuitively you should drop the reference to course and just leave the references to user and topic in the Undergoing table. To answer directly your question: there should be only two participating entities so it is not a ternary relationship.

This is one of those interesting cases in normalization where Third normal form (3NF) is fulfilled but Boyce–Codd normal form (BCNF) is not. Both are desirable forms in normal database formalization. What breaks the BCNF is the dependency topic_id->course_id. In plain English: if you know the topic_id you can deduce the course_id also so you don't need an explicit reference.

When you have user_topics relation with references only to user_id and topic_id you can easily fetch the courses of a user with a regular JOIN (via module to course).

Here is more formally put the dependency that is allowed in 3NF but not in BCNF (Third normal form - Wikipedia):

Every element of A-X, the set difference between A and X, is a prime attribute (i.e., each attribute in A-X is contained in some candidate key)

Boyce–Codd normal form (Wikipedia):

Only in rare cases does a 3NF table not meet the requirements of BCNF. A 3NF table which does not have multiple overlapping candidate keys is guaranteed to be in BCNF. Depending on what its functional dependencies are, a 3NF table with two or more overlapping candidate keys may or may not be in BCNF.