Schola Arcana

cathedral semester — axioms first, always
10–12 hrs/week foundations first quantum thread ILLC · Oxford · ETH
The cathedral stays the cathedral. Logic and proof are the spine. TOC is the lens through which computation becomes mathematics. Linear algebra is the language quantum mechanics speaks. Algorithms are theorems in disguise. Every week, one proof. Every month, one step closer.
Atlas Proof Vault Journal Dossier Log Math Logic
rhythm

How the week works

Weekly split
Foundations 5h · Math 2h · Algo 1–2h · QC 0.5–1h
Foundations = TOC (3h) + Logic/Set/Discrete (2h). The cathedral stays the cathedral.
Weekly output rule (sacred)
1 artifact + drills
TOC 6–10 ex · Proof/Discrete 6–10 · LA/Prob 6–10 · Algo 3–4 · QC 1–2
End-of-semester assets
proof vault · dossier v1 · writing sample
Everything supports the masters application narrative.
the rule
one proof written in full · every week · no exceptions
LaTeX → Proof Vault → dated
structure

Cathedral rules

Foundations — Logic/Set/Discrete + TOC
The spine. Axioms-first thinking in logic and set theory, formal proof methods, and the full Sipser arc from automata through computability to complexity. This is what makes the rest rigorous.
  • Propositional and predicate logic — axioms, proof templates, ∀/∃
  • Set theory — sets, relations, functions, cardinality
  • TOC — automata, decidability, NP, reductions
  • Mathematical logic — completeness theorem (Enderton)
Math — Linear Algebra + Probability
Axler's Linear Algebra Done Right: vector spaces, linear maps, eigenvalues, inner products. Selected probability. Both feed quantum computing and theoretical ML foundations.
  • Vector spaces, linear maps, kernel/image
  • Spectral theorem, inner products, unitary operators
  • Probability axioms, Bayes, expectation, Markov chains
Algorithms/DSA — kept sharp
Patterns and correctness arguments, not just code. Invariants, induction, reduction schemas. Algorithms as theorems.
  • Hashmaps, two pointers, sliding window
  • BFS/DFS, heaps, greedy proofs
  • DP basics, invariants and correctness
Quantum Thread — small, consistent, never dies
Nielsen & Chuang as reference. Weekly thread — tiny, consistent. The goal is to arrive at de Wolf's course ready.
  • Postulates, gates, circuits
  • Entanglement + teleportation
  • Deutsch–Jozsa, Grover, Shor (conceptual)
  • BQP intuition
plan

The week table

Foundations A (Logic/Discrete) + Foundations B (TOC) + Math + Algorithms + Quantum thread + targets + milestones.

Week Foundations A — Logic/Discrete Foundations B — TOC (Sipser) Math — LA/Prob Algorithms/DSA Quantum Thread Targets + artifact Milestones
dossier

Milestones

pink, but lethal. 💗 the theory is the spine. the cathedral is built proof by proof.
schola arcana · cathedral semester · ILLC + Oxford MFoCS + ETH preparation