Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
7–14 weeks (8–10 hrs/week)
Take Complex Variables with Applications for free and do the problem sets (analytic functions, Cauchy's theorem, residues, conformal maps). 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 (analytic functions, Cauchy's theorem, residues, conformal maps), and show your self-check (Problem sets with solutions).
What gets checked
- Answers are marked against the solutions.
- Every contour integral shows its contour and why the theorem applies.
- Each 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 (analytic functions, Cauchy's theorem, residues, conformal maps).
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: Do each problem set, then mark it against the posted solutions.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Complex Variables with Applications (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
- Answers are marked against the solutions.
- Every contour integral shows its contour and why the theorem applies.
- Each 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.
Evaluate real integrals with residues
1–3 weeks (5–8 hrs/week)
Use what you learned. Make an expository write-up that uses residues to evaluate three real integrals that are hard by other methods, with every contour argument justified and a numerical check. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link an expository write-up that uses residues to evaluate three real integrals that are hard by other methods, with every contour argument justified and a numerical check, in your public repo.
What gets checked
- Each contour and limit is justified.
- Numerical checks agree.
- Every step is correct.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
An expository write-up that uses residues to evaluate three real integrals that are hard by other methods, with every contour argument justified and a numerical check.
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 contour and limit is justified.
- Numerical checks agree.
- Every step 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.