Syllabus

Mathematical Theory of Capital

A graduate monograph representing capital not as a quantity but as a structured state — the quadruple \(\mathbf{C} = (K, \mathcal{G}, Q, \Xi)\) of productive position, transformation architecture, information position, and meta-capacity.

Prerequisite. The author’s Mathematical Foundations of Modern Finance or equivalent: the earlier book’s stochastic-control, no-arbitrage, and information machinery is what the valuation chapters here draw upon.

The five parts

  1. The Problem of Capital and Its Representation (Ch 1–3) — why a scalar cannot carry the theory, and the forced four-coordinate representation.
  2. Transformation (Ch 4–7) — dynamics, networks, algebra, and geometry of the architecture \(\mathcal{G}\).
  3. Valuation (Ch 8–10) — pricing on a fixed map, architecture value, and the information position \(Q\).
  4. Formation, Degeneration, and Crisis (Ch 11–13) — the life of capital systems and the meta-capacity \(\Xi\) in motion.
  5. Institutions, Markets, and Equilibrium (Ch 14–16) — capital among its governors.

Tracks

The book separates a spine (definitions, main theorems, a worked miniature) from two optional tracks: an advanced track (starred, carrying the harder proofs and the dynamic-frontier material of Chapter 16) and a laboratory track (the computational modules on this site).

The running example

One example runs through all sixteen chapters — the signature network, a stylized house capital system founded in Chapter 5, priced across Parts II–III, killed in Chapter 12, coupled into crisis in Chapter 13, and governed in Part V. Its parameters are fixed once in Appendix B and honored everywhere; the laboratory reproduces those exact figures.