Month 01 — From Familiar Mathematics to Modern Mathematics
Move from familiar undergraduate mathematics toward some of the organizing ideas of modern mathematics: constructions, symmetry, invariants, intrinsic geometry, and emergence. Explore why the language changes, not just what the definitions say.
Explorations
- Week 01 — Field Extensions and Galois Theory
- Week 02 — Topology
- Week 03 — Geometry and Manifolds
- Week 04 — Probability Information and Emergence
These week labels organize a journey; they are not deadlines. Follow a question further whenever it becomes interesting. Session prompts invite a dialogue, predictions, examples and counterexamples rather than a textbook summary.
Keeping What I Learn
Write freely in the session notes. When an idea becomes worth revisiting independently, create a note in 02 Concepts and link to it. Record bridges between areas in 03 Connections, and test a prediction in 04 Problems and Experiments. Do not copy the same explanation into multiple notes.