A course "has" a programme, and a programmer "consists of" a course? This is a rather ambiguous definition of the relationship. Generally speaking, relationships should be unidirectional.
I'm not sure what the difference is between "programme" and "subject". Can you give a concrete example? E.g., "a subject is a focused area of learning, while a programme provides an overview of the material to be learned with a scheduled ordering".
Kasey Speakman sounds like he's spent some time analysing this problem space.
In regards to uniqueness and set validation, I would say you have three categories of options:
Category 1. Prevent it from occurring on the client by using the read model before issuing the command. This works, but if you have multiple clients (native mobile vs HTML5 web application), then you need to duplicate this logic.
Category 2. Prevent it on the server as well. This typically uses a domain service. If you're doing strict eventual consistency (for distributed reasons), then there's a small window (milliseconds, probably) in which the uniqueness domain service is not up to date with the aggregate data.
Category 3. Detect it after the fact and compensate. I'm still learning that this (coupled with category 1) is often a good solution.
Note that I've used the word "category" above, because there are multiple ways to do it in each category. For example, to solve the age-old "unique username" scenario using category 2, you could have:
A. A "domain service" that is a wrapper around a simple SQL table.
B. A big fat aggregate containing a list of all usernames and the UUIDs to which they map.
C. A "lookup" aggregate, e.g., "UsernameList". The UUID of this aggregate is a deterministic UUID based on the username, and contains an array of the UUIDs of the users. That is, if person A registers with the username "michael", the system generates a deterministic UUID using this username to identify the UsernameList "e1ac86e6-dd0b-43e3-b9f8-122b81d26289". This UsernameList contains a single UUID pointing back to the user registered by person A. If person B also register with the username "michael", the same UsernameList would be loaded (because the UUID is deterministically generated based on the username "michael") and person B's UUID is added to the UsernameList.
There's 3 options in this one category, with option C effectively being a hash table of linked lists accessible to the domain. This can be distributed (unlike option A - you can't easily distribute a single SQL table), and is scalable with a smaller probability of contention that option B.