Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
7–14 weeks (8–10 hrs/week)
Take Nonlinear Dynamics I: Chaos for free and do the problem sets (flows on the line and plane, bifurcations, limit cycles, the Lorenz equations). 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 (flows on the line and plane, bifurcations, limit cycles, the Lorenz equations), and show your self-check (Check each result numerically).
What gets checked
- Stability claims are proved by linearisation or a Lyapunov function.
- Each claim is matched by a simulation plot.
- Every argument 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 (flows on the line and plane, bifurcations, limit cycles, the Lorenz equations).
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 posts no solutions. Check every fixed point, stability claim and bifurcation by simulating the system.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Nonlinear Dynamics I: Chaos (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
What a verifier looks for
- Stability claims are proved by linearisation or a Lyapunov function.
- Each claim is matched by a simulation plot.
- Every argument 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.
Map a bifurcation
1–3 weeks (5–8 hrs/week)
Use what you learned. Make an expository write-up with code that finds and proves the bifurcations of one system (the logistic map or a pendulum with friction) and draws its bifurcation diagram. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link an expository write-up with code that finds and proves the bifurcations of one system (the logistic map or a pendulum with friction) and draws its bifurcation diagram, in your public repo.
What gets checked
- Each bifurcation point is found by hand and matches the diagram.
- The proofs of stability change are complete.
- The code reproduces the figure.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
An expository write-up with code that finds and proves the bifurcations of one system (the logistic map or a pendulum with friction) and draws its bifurcation diagram.
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
What a verifier looks for
- Each bifurcation point is found by hand and matches the diagram.
- The proofs of stability change are complete.
- The code reproduces the figure.
- 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.