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 |
| stochastic-processes | lawler-stochastic-calculus — free maintained book, Itô through Black-Scholes · gamarnik-advanced-stochastic-processes and wu-introduction-stochastic-processes — two MIT courses, read as syllabi | One book at two levels in one file, and two courses that start in different places |
| 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 · gallier-quaintance-math-deep — Part I of the Penn manuscript, through SVD and graph Laplacians | Undergraduate proving everything, and a graduate treatment that starts where it stops |
| tensor-analysis / differential-forms / euclidean-manifold | bowen-wang-vectors-tensors-vol-2 — Bowen (Texas A&M) & Wang (Rice), vol. 2 of a two-volume text; the geometry volume only | Advanced undergraduate/graduate, proof-based, engineers' notation |
| topology | gallier-quaintance-math-deep — Part V, taught as the run-up to differential calculus | Graduate, proof-complete, not a dedicated text |
| 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 · gallier-quaintance-math-deep — Part IV, modules and tensor algebra | Two texts that disagree about what a first course is for |
| number-theory / cardinality-and-countability | baker-algebra-number-theory — Baker (Glasgow), third-year course notes, 73pp: arithmetic, groups and actions, arithmetic functions, countability | Third-year undergraduate, proof-based, no rings assumed |
| 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 |
| information-theory / coding-theory | information-theory-inference-learning-algorithms — MacKay, CUP 2003 — held in ../machine-learning-wiki, not here |
Graduate-level, and the only subject on this page whose source sits in another spoke |
The sources are pitched at as many levels as there are of them, 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), abstract algebra and number theory, and numerical methods. Measure theory is still absent, and the stochastic-processes sources added on 2026-08-16 make that absence louder: all three of them assume it, and one indents it as optional reading rather than teaching it.
Information and coding theory left that list on 2026-08-15 and only half-left it. The subject is
now paged out in eight pages from MacKay's book — but the book is held in ../machine-learning-wiki,
so this spoke teaches a subject it owns no copy of. A text of its own is still wanted.
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 · information-theory · coding-theory · synthesis