From the language of algebra to the logic of calculus, from motion in one dimension to the forces that govern complex systems, this class is built to take students beyond formulas and into structured scientific thinking. Students move from symbolic manipulation and functional relationships to vector analysis, trigonometric modeling, and rate-of-change reasoning, using mathematics not as a subject, but as a tool. Physics is developed through derivation, not memorization — kinematics expressed through equations, Newton’s laws framed through vectors, energy treated as a conserved quantity, and electrical and magnetic interactions analyzed quantitatively. Problems evolve from direct application to multi-step reasoning where assumptions, units, and mathematical structure matter. Throughout the course, mathematical methods are applied to physical systems: graphs become motion, equations become predictions, and variables represent reality. By the time students reach advanced topics, they are no longer “solving questions” — they are analyzing systems, building models, and testing results against physical meaning. This is a class for students who are ready to think precisely, reason mathematically, and treat Physics and Mathematics as disciplines, not subjects.