Mathematics
The root page of this wiki. The spoke exists for a structural reason rather than a topical one: three mathematics texts arrived at the hub over five days, each was declined by the spoke nearest it, and each was declined for the same reason. The maths was infrastructure under that spoke and the subject of none of them. See synthesis for the argument; this page holds the map.
The corpus
| Body of theory | Source | Level |
|---|---|---|
| probability-theory | mcmullen-probability-theory — Harvard course notes, companion to Feller · stirzaker-elementary-probability — CUP course through Markov chains and Brownian motion | Terse notes with Feller assumed, and a self-contained 538-page course |
| vector-calculus | corral-vector-calculus — free 222-page Calculus III textbook | Undergraduate, self-rated 5/10 on rigour |
| fourier-analysis | thibos-fourier-analysis — vision-science methods coursenotes | Beginner, Matlab-based, applied |
| infinitesimal-calculus | keisler-elementary-calculus — the full calculus sequence on hyperreals | Freshman, published twice, foundations rebuilt |
| linear-algebra | hefferon-linear-algebra — free 4th-edition textbook, MAA Solow Award | Undergraduate, proves everything |
| real-analysis | trench-real-analysis — two-term course, rights reverted from Pearson | Undergraduate, rigorous, ε-δ made explicit |
| mathematical-statistics | larsen-marx-mathematical-statistics (theory) · herzog-understanding-statistics (practice and its failures) | Two-semester derivation, and a text with no derivations at all |
| abstract-algebra / group-theory | lal-algebra-1 — foundations-first, volume one of three · judson-abstract-algebra — applications-forward, Galois-complete | Two texts that disagree about what a first course is for |
| game-theory | osborne-rubinstein-course-in-game-theory — MIT Press graduate text, 1994 | Graduate, proof-complete, one semester |
| measurement-theory | mari-measurement-across-sciences — a concept system for measurement across physics and the human sciences | Research monograph, conceptual, not a textbook |
Twelve texts, pitched at as many levels and written for as many reasons. That spread is the corpus’s most useful feature. vector-calculus is now covered three times over and the accounts disagree about foundations while agreeing about results; statistics and probability are each covered twice, at different altitudes.
What is missing
The two founding holes closed on 2026-08-04: linear-algebra by Hefferon, real-analysis by Trench. What remains, in the order synthesis ranks it: a text that argues for the ε-δ foundation (three texts here assume it, one argues against it, nothing defends it), information and coding theory as a subject in its own right, abstract algebra and number theory, and numerical methods. Measure theory is still absent.
The odd one out
measurement-theory is not mathematics, and it is here anyway — no spoke in the hub owns measurement as a subject, and several borrow it. The routing is recorded as open question 7 in synthesis rather than presented as obvious.
The boundary
The rule this spoke was created to enforce: mathematics as the subject routes here; mathematics
as the method routes to whatever spoke owns the claim. A textbook teaching a body of theory from
first principles belongs here even when its examples come from optics or finance. A source using
that theory to say something about markets, audio or models belongs where the claim lives, with the
maths cross-linked. Full boundary in this spoke’s CLAUDE.md.
Related
probability-theory · vector-calculus · fourier-analysis · infinitesimal-calculus · linear-algebra · real-analysis · mathematical-statistics · abstract-algebra · game-theory · measurement-theory · synthesis