STAGE II: Structure

Weeks 15-42 · 5 Courses · 16 Credits · Rigorous formalization and engineering discipline

Question: How do we formalize system relationships and prevent information contamination?

In Stage II, students learn systematic decomposition, formal causal structure, state inference, population modeling, and channel separation. This stage transforms intuition from Stage I into rigorous, testable, verifiable knowledge.

The Five Courses

Course 5: Dynamic Systems Engineering

4 credits · 14 weeks · Prerequisite: Stage I complete

Systematic decomposition and component design. Learn to break complex systems into manageable pieces and understand how they fit together. Foundation for all subsequent formalization.

Course 6: Causal Structure & Dynamic Matrices

4 credits · 14 weeks · Prerequisite: Mathematics for Dynamic Systems

Formalize causality mathematically. Causal graphs, topological ordering, lower-triangular matrices, and how structure guarantees non-collapsibility through mathematical proof.

Course 7: Deterministic State Estimation

4 credits · 14 weeks · Prerequisite: Mathematics for Dynamic Systems + Dynamic Systems Analysis

Infer hidden state from observations. Observability, reconstruction, optimal estimation methods. Essential for diagnosis, control, and understanding what cannot be directly measured.

Course 8: Statistical Modeling & Synthetic Populations

3 credits · 14 weeks · Prerequisite: Stage I complete (no prior stats needed)

Build population-level models while preserving system structure. Distributions, conditional dependence, Simpson's paradox, synthetic populations. Move from single systems to aggregated ensembles.

Course 9: Channel Identification & Separation

3 credits · 14 weeks · Prerequisite: Introduction to NCFCA

Design systems maintaining NCFCA separation. Detect contamination, verify integrity, ensure S → D → I → C information flow never reverses. Make channel separation concrete and testable.

Parallelization

Option A (Recommended): Two 7-week clusters — Courses 5+6 (foundation), then Courses 7+8+9 (applications). Lighter than accelerated, reveals natural progression.

Option B: All 5 courses in parallel over 28 weeks (~60 hrs/week). Maximum integration, highest intensity.

Option C: Two semesters of sequential courses. Lightest load, longest duration.

After Stage II

Upon completion of Stage II, students have:

✓ Systematic decomposition and engineering discipline
✓ Formal causal structure and mathematical proof of non-collapsibility
✓ State inference from observations
✓ Population-level statistical modeling
✓ Channel separation design and verification

Ready for Stage III: Networks, where these individual-system tools scale to systems of systems, emergence, and collective behavior.

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