Dr$.$ Brown was an adjunct instructor at North State University $($NSU$)$ in Michigan. Each semester, near the beginning of each term, the parties executed a written contract that always included the following provision: $$The parties acknowledge that this agreement may be cancelled by NSU or the instructor at any time before the first class session.$$ In the spring semester of Brown$$s sixth year, he filed a complaint with NSU claiming that one of his students, Sylvia Davis, had engaged in inappropriate and disruptive classroom conduct. Brown gave her an $$incomplete$$ grade and asked NSU to request her to apologize as a condition of receiving a final grade. NSU claimed, and Brown denied, that he was told to assign Davis a grade if he wanted to teach in the fall. Toward the end of the semester, Brown was told which classes he would teach in the fall, but the parties did not sign a written contract. The Wednesday before classes began, NSU terminated him. Brown filed a suit against NSU and others, alleging breach of contract.

Did the parties have a contract?

If so$,$ what type of contract did they have.

Did NSU breach it$?$ Explain.