Lecture Notes — Lecture 32: Capstone: The Method Applied
Companion to the lecture plan and the worked examples. Read the Definitions before class, the Explanation after it; the practice questions and the lecture quiz close the loop.
Definitions
- Capstone — unseen problems solved end-to-end under time pressure, then debriefed against the method.
- The method — specify, model, attempt, verify, compare, communicate - the course's spine in six verbs.
- Plan defence — a two-minute oral justification of approach, complexity, and test plan before coding.
- Post-mortem — the written what-happened, why, and what-check-would-have-caught-it.
- Transfer — applying the method to problems whose surface stories are new - the real learning outcome.
Explanation
The capstone format. Two unseen problems, 20 minutes each: 2 minutes specify, 2 minutes plan defence (oral, complexity and tests named), 12 minutes execute, 4 minutes verify and summarise. The clock is part of the lesson.
Problem A is a balancing task (assign people by skill to equal teams): greedy with a size cap, verified against brute force on small inputs - Block III's proof discipline applied.
Problem B is a route-and-budget task (visit required shelves within battery): BFS distances plus a knapsack-style selection - Block IV's modelling under a constraint.
The debrief maps every step to the method. Each team writes which of the six verbs was weakest under pressure; the class aggregates the histogram - the course's own retrospective.
After the capstone. The exam-style variants (provided for practice), the personal error taxonomy, and the honest-summary checklist are the take-home kit; the course ends by handing over its own tools.
Examples
The lecture's worked examples live in examples.md; the case studies this lecture builds on are worked in class from the projector. The case sequence with difficulties:
Common misconceptions
- Starting to code at minute one instead of specifying first - the capstone penalises it explicitly.
- Defending the plan with 'it should work' instead of named complexity and tests.
- Treating verification as optional when time is short - it is scored.
- Reading the post-mortem as blame; it is a checklist upgrade.
Summary and key takeaways
- Specify, defend, execute, verify - the method under a clock.
- Plan defence names complexity and tests BEFORE code.
- The post-mortem upgrades your personal checklist.
- Transfer is the goal: unseen stories, same method.
Practice questions
- Solve the exam-style variant of Problem A under a 20-minute clock; write the post-mortem.
- Solve the exam-style variant of Problem B; mark which method verb was weakest.
- Exchange post-mortems with a partner; adopt one of their checklist items.
- Assemble your personal error taxonomy from all eight quizzes into a one-page pre-exam checklist.
Where this leads
This is the final lecture - the capstone consolidates every phase of the method into exam-ready form.