Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
7–14 weeks (8–10 hrs/week)
Take Introduction to Analysis for free and do the 18.100A problem sets (real numbers, sequences, series, continuity, derivatives, the Riemann integral). 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 18.100A problem sets (real numbers, sequences, series, continuity, derivatives, the Riemann integral), and show your self-check (Introduction to Real Analysis by William Trench (free book, answers to selected exercises)).
What gets checked
- Every ε–δ and ε–N argument is complete and correct.
- Trench exercises are checked against the book's answers.
- No step relies on a fact that has not been proved yet.
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 18.100A problem sets (real numbers, sequences, series, continuity, derivatives, the Riemann integral).
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: The MIT problem sets post no solutions. For each topic, also do the matching exercises in Trench's free book and check them against its answers.
- 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 Analysis (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
Masteryfor the dedicated
What a verifier looks for
- Every ε–δ and ε–N argument is complete and correct.
- Trench exercises are checked against the book's answers.
- No step relies on a fact that has not been proved yet.
- 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 up one theorem in full
1–3 weeks (5–8 hrs/week)
Use what you learned. Make an expository write-up (3–5 pages) that proves one big theorem from the course from the axioms you used, such as the intermediate value theorem or the fundamental theorem of calculus, with a worked example and a counterexample when a condition is dropped. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link an expository write-up (3–5 pages) that proves one big theorem from the course from the axioms you used, such as the intermediate value theorem or the fundamental theorem of calculus, with a worked example and a counterexample when a condition is dropped, in your public repo.
What gets checked
- The proof is complete, with every lemma proved or cited from the course.
- The counterexample really breaks the dropped condition.
- It reads clearly to someone who has done calculus.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
An expository write-up (3–5 pages) that proves one big theorem from the course from the axioms you used, such as the intermediate value theorem or the fundamental theorem of calculus, with a worked example and a counterexample when a condition is dropped.
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
Masteryfor the dedicated
What a verifier looks for
- The proof is complete, with every lemma proved or cited from the course.
- The counterexample really breaks the dropped condition.
- It reads clearly to someone who has done calculus.
- 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.