I am in a graduate level (online) mathematics course. At the beginning of the course, the professor told us to post all of our homework solutions to the online learning forum which is open for everyone to see. While I do not have any issues with this per se, we are not graded on the homework nor are provided any feedback. The lack of involvement on the professors side has led to many students not even posting worked through solutions (i.e. provide a couple steps and skip to the solution). Moreover, we are given weekly reading out of the main text (usually a chapter) for which we are supposed to read, then watch the recorded lectures, and finally complete our problem set. That said, the lectures do not actually cover the reading in the book or provide any worked through examples. This is a theory based course and none of the proofs are worked through in the lectures either. The lectures simply consist of the professor reading aloud the theorems and moving on. The course costs nearly $5k and I am wondering where the value is. It would seem that the cost of the course is to have access to material, most of which is openly accessible to anyone with internet. I could just as easily buy the book and read it at home for free and get just as much out of it as I am going through this course. I know this is a bit of complaining on my part but I admit I am very frustrated that this has happened in more than one class. Do I have any grounds to go "up the chain" and file a complaint? Is a complaint of this matter likely to fall on deaf ears?
Yes, do complain. The value of a teacher is precisely to do things reading books and watching videos can't do: Answer questions, give feedback, help with gaining insight. If a professor does none of these things, then they're paid for a service they're not providing, and that should concern their employer.
So do go to the department head and complain about it. At the end of the semester, also make sure that you state your complaints in the course evaluation most universities have.
While you have the right to complain to a department head or other individual, my first step would be to discuss this with the instructor themselves. In our department, we would expect a student who complained to at least try to informally resolve the issue with the instructor before escalating it up the chain.
If the instructor has a very high grading load, there is a chance that they are not giving full feedback to all students under the misapprehension that the students don't want to engage with the feedback. Perhaps if you reached out to them, they would be happy to work with you on providing more fulsome feedback and helping you develop your skills.
(and, if not --- this would make your approach to the department head or chair even more convincing)