Geometry and Topology in the Plane
MIT OpenCourseWare offers this introductory mathematics course covering geometric and topological topics that can be visualized without heavy machinery. Subjects include hyperbolic geometry, billiards, and loops in the plane, moving from flatter, easier material to occasional harder patches described by the instructors as a moderate hike rather than a cliff climb. No prior background in differential geometry or topology is assumed, though the pace moves quickly from topic to topic. The course includes lecture notes and problem sets typical of MIT's OCW offerings, letting self-directed learners work through the material at their own speed. It suits students curious about how geometric intuition connects to topological reasoning, without requiring the formal prerequisites of a full differential geometry or topology sequence. Materials are freely available online with no certificate attached.