CapstoneMath for LLMs5 hours

Implement Differential Geometry

Implement a portfolio-ready notebook experiment that proves you can use Differential Geometry, not just read about it.

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Build brief

You are turning the Differential Geometry module into a concrete artifact. Keep the scope small, make the behavior visible, and leave enough notes that another learner can understand the result.

Requirements

  • Use at least two ideas from Differential Geometry.
  • Keep the implementation small enough to explain in five minutes.
  • Add three test cases or examples that show normal and edge behavior.
  • Write a short reflection that explains what broke and how you fixed it.

Deliverables

  • A runnable notebook cell sequence for Differential Geometry.
  • A short explanation of the math idea in plain language.
  • At least one visualization, table, or numerical sanity check.

Project checklist

Source lessons

Notes25-Differential-Geometry/01-Manifolds/notes.mdOpenNotes25-Differential-Geometry/02-Riemannian-Geometry/notes.mdOpenNotes25-Differential-Geometry/03-Geodesics/notes.mdOpenNotes25-Differential-Geometry/04-Optimization-on-Manifolds/notes.mdOpenTheory Notebook25-Differential-Geometry/01-Manifolds/theory.ipynbOpenExercises Notebook25-Differential-Geometry/01-Manifolds/exercises.ipynbOpen
Run notebook

Milestones and skills

  1. 01Read the linked source lessons and note the key APIs or formulas.
  2. 02Sketch the smallest useful version of the notebook experiment.
  3. 03Build the core behavior before adding polish.
  4. 04Run the examples, notebook cells, or manual tests.
  5. 05Write the final explanation and mark the checklist complete.
Differential GeometryNumerical reasoningNotebook workflowPlanningTestingDebuggingExplanation