Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
5–10 weeks (6–8 hrs/week)
Take Logic and Proof for free and do the book's exercises in natural deduction and in Lean (propositional logic, first-order logic, sets, induction). 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 book's exercises in natural deduction and in Lean (propositional logic, first-order logic, sets, induction), and show your self-check (Lean accepts the proof).
What gets checked
- Every Lean file compiles with no `sorry`.
- Paper proofs match the Lean proofs.
- The repo builds from the README.
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 book's exercises in natural deduction and in Lean (propositional logic, first-order logic, sets, induction).
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: Write each exercise's proof in Lean; it is right only when Lean accepts it with no `sorry`.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Logic and Proof (Logic and Proof by Jeremy Avigad and others (free book, Lean community)) 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 Lean file compiles with no `sorry`.
- Paper proofs match the Lean proofs.
- The repo builds from the README.
- 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.
Formalise a theorem in Lean
1–3 weeks (5–8 hrs/week)
Use what you learned. Make a Lean file that proves a theorem you choose from the core courses (for example, that √2 is irrational or that a group's identity is unique), with a paper proof alongside. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link a Lean file that proves a theorem you choose from the core courses (for example, that √2 is irrational or that a group's identity is unique), with a paper proof alongside, in your public repo.
What gets checked
- Lean accepts it with no `sorry`.
- The paper proof matches the Lean proof step for step.
- The statement in Lean really says what the theorem says.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
A Lean file that proves a theorem you choose from the core courses (for example, that √2 is irrational or that a group's identity is unique), with a paper proof alongside.
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
- Lean accepts it with no `sorry`.
- The paper proof matches the Lean proof step for step.
- The statement in Lean really says what the theorem says.
- 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.