D120 · English · shared course identity

Traceable Mathematical Work

A nine-unit English route for research reading, argument reconstruction, exposition, provenance, reproducible computation, errata, review, and auditable contribution work.

9units
71outcomes
54exercise–guidance pairs
14assessment designs

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Truth boundary: the 54 companion records are source guidance, not complete solutions. The backend defines routes and templates; it does not claim learner submissions, results, external participation, or credentials.

Learning sequence

Unit 1 · Reading Arguments as Networks of Claims 6 outcomes · 6 exercises

Open English unit · competency O017-COMP-U01 · assessment O017-ASMT-U01-COMPLETION

Outcomes

  1. O017-LO-U01-01 — distinguish definitions, assumptions, claims, illustrations, and conclusions in mathematical text;
  2. O017-LO-U01-02 — turn phrases such as *clearly* or *by an exchange argument* into explicit proof obligations;
  3. O017-LO-U01-03 — reconstruct omitted steps without illegitimately strengthening the claim;
  4. O017-LO-U01-04 — test the role of assumptions using examples and counterexamples;
  5. O017-LO-U01-05 — use computation as diagnostic empirical evidence, not as a substitute for proof; and
  6. O017-LO-U01-06 — record sources, interpretive decisions, and uncertainty in an auditable reading memo.

Practice and source guidance

Unit 2 · Searching the Literature and Assessing Source Authority 7 outcomes · 6 exercises

Open English unit · competency O017-COMP-U02 · assessment O017-ASMT-U02-COMPLETION

Outcomes

  1. O017-LO-U02-01 — turn a mathematical claim into a bounded, repeatable search question;
  2. O017-LO-U02-02 — distinguish search tools, metadata records, full texts, specific editions or versions, and correction records;
  3. O017-LO-U02-03 — assess a source's authority for a particular question, rather than relying only on reputation or search-result order;
  4. O017-LO-U02-04 — distinguish persistent identifiers for a work in general from identifiers for a particular version;
  5. O017-LO-U02-05 — draw citation chains as directed graphs with typed relationships;
  6. O017-LO-U02-06 — separate evidence that a source states a claim from proof that the claim is true; and
  7. O017-LO-U02-07 — record uncertainty without filling missing data with guesses.

Practice and source guidance

Unit 3 · Reconstructing Compressed or Omitted Proofs 8 outcomes · 6 exercises

Open English unit · competency O017-COMP-U03 · assessment O017-ASMT-U03-COMPLETION

Outcomes

  1. O017-LO-U03-01 — freeze the claim to be reconstructed without silently adding or removing hypotheses;
  2. O017-LO-U03-02 — expand the quantifiers, domains, and definitions that determine the proof target;
  3. O017-LO-U03-03 — turn compressed parts of a proof into obligations with clear inputs and outputs;
  4. O017-LO-U03-04 — draw dependency graphs between targets, lemmas, definitions, and hypotheses;
  5. O017-LO-U03-05 — select a lemma by its mathematical contract and check every hypothesis in the current context;
  6. O017-LO-U03-06 — connect forward planning from the hypotheses with backward planning from the conclusion;
  7. O017-LO-U03-07 — write a minimally sufficient reconstruction—complete enough to audit without turning one step into a new textbook; and
  8. O017-LO-U03-08 — distinguish closed gaps, gaps conditional on a reference, and gaps that remain unresolved.

Practice and source guidance

Unit 4 · Citation, Provenance, and Source Notebooks 8 outcomes · 6 exercises

Open English unit · competency O017-COMP-U04 · assessment O017-ASMT-U04-COMPLETION

Outcomes

  1. O017-LO-U04-01 — distinguish **citation**, **evidence provenance**, and **computational provenance** without substituting one for another;
  2. O017-LO-U04-02 — record works, versions, copies, and internal locations as distinct but connected objects;
  3. O017-LO-U04-03 — link a normalized claim to a locator precise enough for another reader to find the wording actually checked;
  4. O017-LO-U04-04 — preserve the basis for accepting, rejecting, or restricting a mathematical claim, not merely its bibliography;
  5. O017-LO-U04-05 — record corrections as relationships between versions without overwriting or deleting the old source's historical state;
  6. O017-LO-U04-06 — write structured uncertainty records and refuse to fill missing metadata with guesses;
  7. O017-LO-U04-07 — design a source notebook that can be updated, reviewed, and exported without losing its decision trail; and
  8. O017-LO-U04-08 — assemble a claim dossier combining citation, provenance, mathematical audit, and limits on the conclusion.

Practice and source guidance

Unit 5 · Writing Auditable Mathematical Exposition 8 outcomes · 6 exercises

Open English unit · competency O017-COMP-U05 · assessment O017-ASMT-U05-COMPLETION

Outcomes

  1. O017-LO-U05-01 — establish the audience, prerequisites, purpose, and scope of an exposition before choosing its level of detail;
  2. O017-LO-U05-02 — organize definitions, theorems, proofs, examples, and counterexamples as components with distinct functions;
  3. O017-LO-U05-03 — use typed notation, introduced before use and consistent throughout the document;
  4. O017-LO-U05-04 — give important claims local locators and cite external sources only for work those sources actually perform;
  5. O017-LO-U05-05 — provide local signposts so readers know the goal, why a step appears, and where the argument will return;
  6. O017-LO-U05-06 — revise drafts through a claim-dependency audit without hiding hypotheses, limitations, or uncertainty;
  7. O017-LO-U05-07 — distinguish proved statements from illustrations, counterexamples, heuristics, and historical comments; and
  8. O017-LO-U05-08 — turn written exposition into seminar notes that can be followed, questioned, and honestly corrected.

Practice and source guidance

Unit 6 · Reproducible Mathematical Computation 9 outcomes · 6 exercises

Open English unit · competency O017-COMP-U06 · assessment O017-ASMT-U06-COMPLETION

Outcomes

  1. O017-LO-U06-01 — separate claims about one execution, output repeatability, implementation correctness, finite results, and universal theorems;
  2. O017-LO-U06-02 — distinguish conjecture-generating experiments, counterexample searches, exhaustive finite checks, computational certificates, and proofs;
  3. O017-LO-U06-03 — freeze code, inputs, parameters, versions, dependencies, arithmetic models, random seeds, outputs, and execution procedures as one provenance package;
  4. O017-LO-U06-04 — rerun an artifact at least twice and compare actual bytes with expected outputs without silently updating the oracle;
  5. O017-LO-U06-05 — audit whether a program actually tests the stated claim, including its domain, index bounds, boundary cases, and numerical meaning;
  6. O017-LO-U06-06 — design falsification attempts that distinguish environment failures, nondeterminism, weak oracles, and mathematical errors;
  7. O017-LO-U06-07 — present machine outputs with plain-text summaries readable without color, plots, or particular software;
  8. O017-LO-U06-08 — assess exactly what computational witnesses for Cassini's identity establish and do not establish; and
  9. O017-LO-U06-09 — assemble a mathematical-computation dossier that another reader can audit.

Practice and source guidance

Unit 7 · Errata, Corrections, and Limits of Certainty 9 outcomes · 6 exercises

Open English unit · competency O017-COMP-U07 · assessment O017-ASMT-U07-COMPLETION

Outcomes

  1. O017-LO-U07-01 — distinguish typographical errors, local exposition defects, missing hypotheses, theorems false as written, ambiguous locators, and computational defects;
  2. O017-LO-U07-02 — separate **impact severity** from **confidence** in the diagnosis;
  3. O017-LO-U07-03 — freeze the version, copy, locator, and wording actually checked;
  4. O017-LO-U07-04 — construct a minimal reproducer that checks every hypothesis before demonstrating failure of the conclusion;
  5. O017-LO-U07-05 — distinguish what is observed, proved, provisionally inferred, and unknown;
  6. O017-LO-U07-06 — formulate a sufficiently narrow correction and prove that it is adequate;
  7. O017-LO-U07-07 — preserve correction records as append-only history without overwriting earlier claims or versions;
  8. O017-LO-U07-08 — write one concise, specific, actionable issue or erratum draft without contacting external parties; and
  9. O017-LO-U07-09 — stop or escalate an investigation when evidence, authority, or the scope of impact remains insufficient.

Practice and source guidance

Unit 8 · Seminar Notes, Referee Reports, and Responses to Criticism 8 outcomes · 6 exercises

Open English unit · competency O017-COMP-U08 · assessment O017-ASMT-U08-COMPLETION

Outcomes

  1. O017-LO-U08-01 — turn a mathematical talk into claim notes recording time, location, type, basis, verification status, and confidence;
  2. O017-LO-U08-02 — mark inaudible or unrecorded portions without inventing replacement content;
  3. O017-LO-U08-03 — distinguish summary, verification, questions, and objections, and separate issue severity from confidence in the diagnosis;
  4. O017-LO-U08-04 — write specific, evidence-bounded referee comments that respect the author and request feasible action;
  5. O017-LO-U08-05 — assess recommendations to accept, request minor or major revision, or reject by the state of the manuscript rather than the author's reputation or presumed intentions;
  6. O017-LO-U08-06 — respond to criticism by stating agreement or disagreement, action, evidence, change location, status, and unresolved matters;
  7. O017-LO-U08-07 — repair a theorem and proof without concealing the old wording or claiming a broader repair than has been proved; and
  8. O017-LO-U08-08 — produce an auditable seminar–review–response package without contacting external parties or publishing anything.

Practice and source guidance

Unit 9 · Bounded Community Contributions and an Auditable Portfolio 8 outcomes · 6 exercises

Open English unit · competency O017-COMP-U09 · assessment O017-ASMT-U09-CAPSTONE

Outcomes

  1. O017-LO-U09-01 — choose one small, useful, lawful community contribution that can be completed without silently expanding its scope;
  2. O017-LO-U09-02 — operationally distinguish the states **draft**, **prepared**, **submitted**, **acknowledged**, **accepted**, **merged**, and **published**;
  3. O017-LO-U09-03 — reject external-status claims unsupported by event evidence;
  4. O017-LO-U09-04 — package the target, locator, diagnosis, minimal repair, validation, scope, uncertainty, rights, and attribution as one contribution;
  5. O017-LO-U09-05 — write one concise, actionable message that respects maintainers without flooding the channel with separate comments;
  6. O017-LO-U09-06 — establish a path to stop, withdraw, correct, or reverse a contribution found to be wrong, obsolete, duplicate, or no longer authorized;
  7. O017-LO-U09-07 — assemble a portfolio mapping every competency claim to actual evidence from Units 1–8; and
  8. O017-LO-U09-08 — assess course completion by evidence quality, traceability, and limitations rather than file counts or activity claims.

Practice and source guidance