Core courses are courses that students must complete in order to be awarded a degree. These courses are stated explicitly in the Faculty Handbook underneath your major/option/special or minor being pursued.
An anti-requisite is a course with substantially overlapping content as another course and which therefore cannot be taken by a student, for credit, who has already completed the course for which it is an anti-requisite.
A pre-requisite is a course listed in the Faculty Handbook or departmental handbook which must be completed before registration for another course is permitted. Usually, a pre-requisite course provides many of the fundamental concepts required for the more advanced course.