Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
5–10 weeks (6–8 hrs/week)
Take Differential Geometry for free and do the problem sets on curves, surfaces, curvature and geodesics. Write every solution up in LaTeX and keep the source and the PDF in one public repo as you go.
Proof required
Link your public repo with the LaTeX source and the PDF of the problem sets on curves, surfaces, curvature and geodesics, and show your self-check (Self-check without an answer key).
What gets checked
- Every computation shows its working.
- Curvature results are checked on a known surface (sphere, cylinder).
- Every proof is complete.
Common mistakes
- Copying posted solutions: verifiers read the reasoning and the history.
- A proof that skips the hard step.
- Asking for review before the self-check.
Powstik Guide
A public repo with your LaTeX write-ups of the problem sets on curves, surfaces, curvature and geodesics.
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: The course has no answer key. For each problem, name the definition or theorem every step uses; a step you cannot name is a gap. Then swap write-ups with a study partner before you ask for review.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Differential Geometry (MIT OpenCourseWare) What is here (problem sets, PDF): Self-check result: The hardest proof and why:
What gets sent back
- Answers with no reasoning.
- Photos of handwriting instead of typeset work.
- Self-check not shown.
Resources
Foundationstart here
Depthgo deeper
Masteryfor the dedicated
What a verifier looks for
- Every computation shows its working.
- Curvature results are checked on a known surface (sphere, cylinder).
- Every proof is complete.
- Pick two proofs and check every step: each argument must be correct and complete, not just present.
- Ask about one step; the answer should be clear.
You'll sign in first, then come straight back here.
Compute the curvature of a surface
1–3 weeks (5–8 hrs/week)
Use what you learned. Make a modelling notebook that computes the Gaussian curvature of three surfaces (a sphere, a torus and one you choose) by hand and in code, and checks the Gauss–Bonnet theorem on each. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link a modelling notebook that computes the Gaussian curvature of three surfaces (a sphere, a torus and one you choose) by hand and in code, and checks the Gauss–Bonnet theorem on each, in your public repo.
What gets checked
- Hand and code answers agree.
- Gauss–Bonnet is checked correctly, with the integral shown.
- Every step of the hand computation is correct.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
A modelling notebook that computes the Gaussian curvature of three surfaces (a sphere, a torus and one you choose) by hand and in code, and checks the Gauss–Bonnet theorem on each.
Steps
- Write one line: what you will prove or show.
- Draft it, then read it cold the next day.
- Ask someone to read it and mark the first step they doubt.
- Fix it and typeset the final version.
- Ask three people to check it.
Template
Title: What this shows: Main result (statement): Proof: What I would look at next:
What gets sent back
- A main step left unproved.
- Not clearly the person's own work.
- Claims more than it proves.
Resources
Foundationstart here
Depthgo deeper
Masteryfor the dedicated
What a verifier looks for
- Hand and code answers agree.
- Gauss–Bonnet is checked correctly, with the integral shown.
- Every step of the hand computation is correct.
- Every argument must be correct and complete; mark the first gap you find.
- Check that the work is the person's own.
You'll sign in first, then come straight back here.