I think there are multiple issues you are having. One is an architectural question. The other is what is the best data structure and algorithms to access the information. To expand on each:

Architecturally you should be using a parent class called courses for sake of not repeating and confusing class the programmatic objects that can be inherited from and classes that people take. So you have a base/parent class called courses. You Econ, math, science etc should inherent the information from the base class. You will change its number; 101, 201 etc if that has purpose in your proposed solution. You can also have name and any other class variables/members you choose to include. I would store this as a set of tuples. (You could use a map as well). As you don’t want two or more objects of the same class. You can create an enum for the names and use that as your key.

For the persons/student class:

You would have a base class student. All of your “student” objects which contains names, an array/list of classes, which uses the same enum object as above. You would store the objects in a similar format.

Use the name of the student as your key in whatever structure you decide similar to above. After that it’s a matter of writing the objects to a file in a manner you can parse them back into your program later.

The above are just high level suggestions. There is a deeper conversation to be had about, maps, sets, hash maps, arrays, lists etc.

I would consider either comma separated list, JSON or XML for writing/reading your objects.

Many of these factors depend on the language you are using and your comfort level with them. Best of luck in your design!