62 lines
2.0 KiB
TeX
62 lines
2.0 KiB
TeX
% preface.tex
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\documentclass[main.tex]{subfiles}
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\begin{document}
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\chapter*{Preface}
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\addcontentsline{toc}{chapter}{Preface}
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\section*{Philosophy}
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This book is intentionally small and opinionated:
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\begin{itemize}
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\item Each chapter is a self-contained unit you can compile on its own.
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\item Definitions are prioritized over intuition when the two conflict.
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\item Every theorem should have an explicit list of dependencies:
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what results it uses, and what background it assumes.
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\end{itemize}
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\section*{How to use the dependency graph}
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Think of the graph below as a diagnostic tool.
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If something feels like a black box, locate the nearest node you don’t fully own yet,
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then check the suggested “symptoms” under that node.
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\bigskip
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% --- Dependency tree graph (TikZ) ---
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\begin{figure}[ht]
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\centering
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\begin{tikzpicture}[
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node distance=10mm and 18mm,
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box/.style={draw, rounded corners, align=center, inner sep=4pt},
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arrow/.style={-Latex}
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]
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\node[box] (lin) {Linear Algebra\\(bases, maps, eigenvalues)};
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\node[box, right=of lin] (real) {Real Analysis\\(limits, continuity, measure-lite)};
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\node[box, below=of lin] (prob) {Probability\\(expectation, variance, concentration)};
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\node[box, below=of real] (top) {Topology/Geometry\\(metrics, compactness)};
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\node[box, below=12mm of prob] (func) {Functional Analysis\\($L^p$, Hilbert spaces, operators)};
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\node[box, below=12mm of top] (quant) {Quantum Formalism\\(states, observables, partial trace)};
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\node[box, below=14mm of func, xshift=25mm] (book) {This Book\\(Chapters 1--n)};
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\draw[arrow] (lin) -- (func);
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\draw[arrow] (real) -- (func);
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\draw[arrow] (prob) -- (func);
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\draw[arrow] (func) -- (quant);
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\draw[arrow] (lin) -- (quant);
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\draw[arrow] (top) -- (quant);
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\draw[arrow] (func) -- (book);
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\draw[arrow] (quant) -- (book);
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\draw[arrow] (prob) -- (book);
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\end{tikzpicture}
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\caption{Dependency tree: prerequisites and how they feed into the main text.}
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\label{fig:dependency-tree}
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\end{figure}
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\end{document}
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