Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
7–14 weeks (8–10 hrs/week)
Take Combinatorics for free and do the exercises on counting, recurrences, generating functions, graphs and inclusion–exclusion. 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 exercises on counting, recurrences, generating functions, graphs and inclusion–exclusion, and show your self-check (Check counts by computer).
What gets checked
- Every count has a proof, not just a number.
- Small cases are checked by program.
- Bijective proofs really are bijections (both directions shown).
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 exercises on counting, recurrences, generating functions, graphs and inclusion–exclusion.
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: For every counting answer, check small cases with a short program before you write the proof.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Combinatorics (Applied Combinatorics by Keller and Trotter (free book)) 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
- Every count has a proof, not just a number.
- Small cases are checked by program.
- Bijective proofs really are bijections (both directions shown).
- 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.
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Find and prove a counting formula
1–3 weeks (5–8 hrs/week)
Use what you learned. Make a proof set that finds a formula for a counting question you choose (tilings, paths on a grid, ways to make change), proves it two ways and checks it by program. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link a proof set that finds a formula for a counting question you choose (tilings, paths on a grid, ways to make change), proves it two ways and checks it by program, in your public repo.
What gets checked
- Both proofs are complete.
- The formula matches the program for small cases.
- The question is stated exactly.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
A proof set that finds a formula for a counting question you choose (tilings, paths on a grid, ways to make change), proves it two ways and checks it by program.
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
- Both proofs are complete.
- The formula matches the program for small cases.
- The question is stated exactly.
- 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.