Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
5–10 weeks (4 hrs/week)
Take Introduction to Mathematical Thinking for free and do the exercises in parts I–III (sets, logic, counting, direct proof, contrapositive, contradiction, induction). Write every solution up in LaTeX and keep the source and the PDF in one public repo as you go. OSSU lists a Coursera course whose graded track is paid. We use the free Book of Proof, which covers the same ground (logic, sets, direct proof, contradiction, induction) with solutions.
Proof required
Link your public repo with the LaTeX source and the PDF of the exercises in parts I–III (sets, logic, counting, direct proof, contrapositive, contradiction, induction), and show your self-check (Book of Proof solutions).
What gets checked
- Each proof states what it proves and every step follows from the one before.
- Odd-numbered answers match the book; even-numbered ones are argued in full.
- The work is typeset in LaTeX, not photographed.
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 in parts I–III (sets, logic, counting, direct proof, contrapositive, contradiction, induction).
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: Every odd-numbered exercise has a solution at the back of the book. Do the exercise first, then compare.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Introduction to Mathematical Thinking (Book of Proof by Richard Hammack (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
- Each proof states what it proves and every step follows from the one before.
- Odd-numbered answers match the book; even-numbered ones are argued in full.
- The work is typeset in LaTeX, not photographed.
- 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.
Write a proof set on numbers
1–3 weeks (5–8 hrs/week)
Use what you learned. Make a set of 10 proofs about whole numbers (even and odd, divisibility, primes, the irrationality of √2), each using a named method. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link a set of 10 proofs about whole numbers (even and odd, divisibility, primes, the irrationality of √2), each using a named method, in your public repo.
What gets checked
- Each proof names its method (direct, contradiction, induction).
- Every step is correct and nothing is skipped.
- At least two proofs use induction correctly (base case and step).
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
A set of 10 proofs about whole numbers (even and odd, divisibility, primes, the irrationality of √2), each using a named method.
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 proof names its method (direct, contradiction, induction).
- Every step is correct and nothing is skipped.
- At least two proofs use induction correctly (base case and step).
- 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.