This work proposes to use a knowledge-based prerequisite framework (KPF) and presents a novel mathematical model that enables intelligent course planning for Science, Technology, Engineering, and Mathematics (STEM) education. This is done under the knowledge-based prerequisite framework with the consideration of hierarchical semantic relationships among knowledge terms. The knowledge-based prerequisite framework (KPF) is an alternative to the course-based prerequisite framework (CPF), which is widely used for curriculum design in the secondary and higher education. Prerequisite knowledge of a course is defined as a set of knowledge that students should acquire in order to take the course. Under the knowledge-based prerequisite framework, students may obtain prerequisite knowledge through a variety of ways, including taking micro courses from Massive Open Online Course (MOOC) providers. Comparing the two, the knowledge-based prerequisite framework is more flexible because it requires only essential prerequisite knowledge, while the course-based prerequisite framework is more rigid and students are usually required to take all prerequisite courses. Such flexibility can be obtained by verification of specific prerequisite knowledge terms for each course. Since the number of prerequisite knowledge terms is, in general, much greater than the number of prerequisite courses, flexibility can cause additional complexity in prerequisite verification. Furthermore, the knowledge-based prerequisite framework inevitably involves handling semantics of defined knowledge terms. This work presents a novel Artificial Intelligence (AI) Planning mathematical model that enables the knowledge-based prerequisite framework by automatically verifying prerequisite knowledge and incorporating hierarchical semantic relationships among knowledge terms into the model. The incorporation of semantics into the mathematical model significantly improves the quality of course planning solutions by finding hidden or better solutions that could not be obtained without semantics consideration. The results of the comprehensive experiments show the optimality of the solutions obtained by the mathematical model and demonstrate the outperformance of the semantics incorporation into the mathematical model in terms of the quality of solutions. Finally, the experimental results on scalability show the necessity of the development of efficient heuristic algorithms.