Schola Arcana — Cathedral Semester v2 (17 Weeks)

Axioms-first, concept-first — but now optimized for a real shipping semester: Logic & Proof + TOC (Sipser) + Linear Algebra (Axler) + Algorithms/DSA + Engineering Lane (React/TS during the 10-week build → backend/AI systems runway), with a Quantum thread that never dies.

10–12 hrs/week (minimum viable cathedral)
math → system translation is explicit now
flagship build = university system (10-week sprint)
Topics Atlas Proof Vault Journal Dossier Weekly/Daily Log
Weekly split (optimized for undergrad + startup runway)
Foundations 5h · Math 2h · Algo 1–2h · Eng 2–3h · QC 0.5–1h
Foundations 5h = TOC (3h) + Logic/Set/Discrete (2h). The Cathedral stays the Cathedral.
Weekly output rule (sacred)
1 artifact + drills
Target: TOC 6–10 ex · Proof/Discrete 6–10 · LA/Prob 6–10 · Algo 3–4 · QC 1–2.
End-of-semester assets
1 flagship shipped · proof vault · dossier v1
The flagship is your public-schools platform. Everything else supports coherence (masters + Vambe).

Cathedral rules how this stays sane

Your university may teach SWE unevenly. So we keep Schola Arcana as the high-signal layer: proof maturity, math foundations, and a disciplined engineering lane whose job is translating formal ideas into working systems. Not “random tutorials.” Structured output.

Foundations: Logic/Set/Discrete + TOC Math: Linear Algebra (ML/QC useful) + Probability (selected) Algo: patterns + invariants + complexity Engineering: React/TS sprint → backend/AI runway Quantum: weekly thread (tiny, consistent)

Translation rule math → system

  • Objects → data model: sets/structures become types + schemas.
  • Functions → APIs: maps become endpoints/modules.
  • Invariants → tests: proofs become test suites.
  • Reductions → pipelines: transform input until it fits the decision procedure.

17-week table v2: engineering lane added

Weeks 1–10 align with your 10-week university flagship build (React/TS). Weeks 11–17 pivot the engineering lane toward backend + AI systems (startup runway) while foundations continue.

Week Foundations A (Logic/Set/Discrete — axioms lane) Foundations B (TOC — Sipser) Math (LA/Prob — selected) Algorithms/DSA (patterns + proofs) Engineering Lane (ship) Quantum Thread Targets (exercises + artifact) Milestones (Flagship + Dossier)

Projects flagship + runway

Flagship — Public Schools Platform (Weeks 1–10) React + TS

Your real SWE artifact this semester. Treat it like a startup product: parents + students + teachers, workflows, permissions, analytics, and an MVP that actually ships.

  • MVP clarity: 8–12 core workflows max (don’t die building everything).
  • Architecture: roles + permissions, clean modules, stable API contracts.
  • Portfolio polish: README, screenshots, demo video link, architecture diagram.
  • Founder vibe: a “Product Spec Bible” (1–2 pages) + weekly changelog.
Runway — AI Backend Lab (Weeks 11–17) backend + AI

This is the bridge you asked for: math thinking → engineered system. Build a small service that looks like real AI product work.

  • Core: API + Postgres + auth + logging + tests.
  • AI layer: embeddings + retrieval (RAG) + eval harness.
  • Deliverable: “this service answers X with citations from Y” + metrics.
  • Stretch: queue/worker + caching + A/B evaluation.
Optional Mini — Automata Lab (compress) TOC concrete

Keep Automata Lab only if it feels joyful. Otherwise, treat TOC artifacts as proofs + small demos, not a second large build.

  • Mini-scope: NFA/DFA simulator + Graphviz export.
  • Do not let this compete with the flagship build or the AI backend lab.

Tech stack relevant + finishable

Your semester already uses TypeScript + React. The runway project can be FastAPI (AI-friendly) or Node/TS (stack-consistent).

  • Flagship: TypeScript + React (and whatever backend your team uses)
  • Runway backend: FastAPI + Postgres + pytest (or Node/TS equivalent)
  • AI layer: embeddings + vector store (simple) + evaluation harness
  • Docs: Markdown README + LaTeX proofs/writing samples
  • Repo hygiene: tests, examples, consistent formatting, changelog
Artifact cadence: weekly proof PDF (LaTeX) Ship cadence: weekly demo (flagship)

Dossier milestones masters + credibility

Not panic-based. Built slowly. Goal: CV + SOP bullets + writing sample + a portfolio repo that proves mathematical maturity and real shipping.

By Week 4 (traction) identity
  • Portfolio repo created (proofs + logs + flagship link).
  • CV v1 skeleton complete.
  • Flagship spec bible v1 (1–2 pages).
By Week 10 (flagship ship window) ship
  • Flagship MVP shipped with README + screenshots + architecture diagram.
  • SOP outline (bullets) + opening paragraph.
  • Writing sample intro + 2–3 pages drafted (choose a topic you can finish).
Weeks 11–14 (runway coherence) systems voice
  • AI backend lab core implemented (API + DB + RAG + eval skeleton).
  • Writing sample expands to 6–9 pages.
  • CV v2 polished with flagship impact bullets.
Week 16–17 packaging final
  • Writing sample finalized (8–12 pages is acceptable; 10–15 if natural).
  • CV formatted and consistent with theory + systems identity.
  • Portfolio cleaned: pinned flagship + runway + proof vault + weekly log.