A good modern university program probably would have made you take "remedial" math courses first, where they don't assume that you already know general concepts

A good modern university program probably would have made you take "remedial" math courses first, where they don't assume that you already know general concepts like what a derivative is. Some classes (like proofs) introduce notation and get you comfortable with using definitions, but most people never take anything like that. It's normal not to really grasp a course until you take another one that relies on it.