Semester 2: Algorithms: Rubric and Passing Standards
Use this one decision rule for the exam, project and checkpoint. All six module gates must pass under their own rubrics, and each semester competency S1–S6 must reach level 2. Preserve project evidence, a fresh defense and delayed transfer. Exam points help locate gaps; no total percentage compensates for a failed competency.
Competency map
| ID | Independent outcome | Evidence | Critical error requiring repair |
|---|---|---|---|
| S1 | Derive costs under an explicit model | Module 1; E1; project ledger/admission limit | Unsupported tight bound; pseudopolynomial work called polynomial in bit length; hidden setup/copy cost |
| S2 | Preserve order, identity and search boundaries | Module 2; E2; project sort/predecessor code | Lost record identity/stability; wrong endpoint comparison; unsupported hash guarantee |
| S3 | Model graph constraints and check certificates | Module 3; E3; readiness stage | Hop count used as weighted readiness; partial cyclic result; missing/duplicate vertices |
| S4 | Derive sufficient state and return an optimal feasible witness | Module 4; E4; independent subset oracle | Budget/eligibility ignored; invalid witness; unjustified greedy rule; state reused after dependencies change |
| S5 | Preserve mutation/history contracts and justify sequence costs | Module 5; E5; version/atomicity checks | Corrupted old version; initial potential dropped; false-negative shortcut; unsupported logarithmic scheduler |
| S6 | Distinguish proof, tests, probability and measurement; adapt | E6; project comparison; Module 6 CA1–CA6 and solver-selection appendix; adversarial strand and delayed transfer | Fabricated measurements; unsafe pruning; heuristic claimed exact; reversed reduction; invalid approximation guarantee; missing independent explanation |
Module breadth remains in each module's evidence: the project need not include every graph algorithm or advanced heap. Preserve links to all module gates rather than replacing them with a single semester score.
Levels and scoring
| Level | Evidence |
|---|---|
| 0: absent/invalid | Missing required work or a critical contract/invariant fails |
| 1: assisted | Can follow a known example, but needs prompts to justify or repair |
| 2: independent | Correct contract/model, explanation or proof, relevant checks and fresh equivalent task without copied reasoning |
| 3: transfer | Adapts to an unseen changed requirement with a revised invariant, resource account and verification |
Use the worked key for the exam's 100-point diagnostic breakdown. A high score with an unsafe history or infeasible schedule still requires repair. A clerical error may be resolved on a fresh numeric case when the model is sound; a conceptual error requires a changed sequence/assumption and explanation.
Syntax documentation is allowed during project implementation. Record books, collaborators, tools and generated assistance. Assisted drafting can support learning; level 2 still requires an independent explanation and fresh performance. Imported reference code or self-reported confidence alone does not demonstrate that level.
Completion decision
Pass: all module gates, all six level-2 semester competencies, reproducible project, honest evidence/assistance record, and the delayed transfer are complete. Repair required: any required item is unresolved. The learner may study other material while repairing, but the semester is not signed off. There is no separate conditional or weak-pass rule. Transfer distinction: level 3 records stronger evidence; it is not an employment rank or population-percentile claim.
Repeat only affected work unless the error invalidates connected artifacts. For example, a changed endpoint convention requires recurrence, predecessor, witness and oracle rechecks; a corrected heading does not require redoing the entire project.
Review record and calibration
Keep a row for each S1–S6: evidence paths, initial level, assistance, critical error, repair, fresh-case result, delayed date, final level, reviewer and revision. Label self-assessment separately from independent review. Store raw exam/reviewer notes as checkpoint evidence; a public portfolio is optional.
Two reviewers should independently score a small shared sample, record disagreements and reconcile against observable evidence before altering the rubric. Capture actual effort, prerequisite strength, hints and 7–14-day retention. Independent technical review, inter-rater calibration and learner pilots for this revision remain pending; local code/build checks do not substitute for them.
Automata and computability evidence
Reuse the Module 6 bridge packet for S6: AC1–AC4 each require level 2 alongside CA1–CA6. Preserve the state invariant, language-boundary proof, impossibility/reduction argument and fresh transfer. A timeout called infeasible, or NP-completeness called undecidability, requires repair. This is module assessment evidence, not an additional timed exam or planner feature. Its 20–30 hours are counted in Module 6 (45–65 total), making the semester 465–660 hours.