Contributing & corrections

What you can contribute

A useful contribution can be small: fix a hypothesis, explain a difficult example, improve a translation or recommend a particular chapter. This guide covers the whole Mathematics Resources area: the Library, learning paths, encyclopedia, terminology, web resources and Study & Careers.

Start with the existing page when one already answers the same question. An original encyclopedia explanation and an external reading guide are different kinds of content; recommending a link does not turn its contents into a site-authored article.

Reading needs no account. Submitting an issue or pull request uses a GitHub account; there is no separate site account. Contributions are reviewed before publication, not posted automatically. Reports are public: leave out private correspondence, account tokens and sensitive student information.

Choose a contribution

• Mathematical correction — A missing hypothesis, incorrect formula, proof gap or counterexample.
• Broken link — A missing file, moved page or link that opens the wrong work.
• Terminology suggestion — A mathematical sense, Chinese translation, alias or usage distinction.
• Resource recommendation — A specific book, lecture, course or advice article and what it helps readers learn.
• Article proposal — Suggest an explanation, worked example, learning guide or revision before writing it in full.
• Translation correction — An inaccurate translation, missing passage or wording that obscures the English original.

The forms ask for a page and a location. If you arrived here without a referring page, replace the guide URL with the affected page and quote its heading or a short passage. A section link is particularly helpful.

Editing an existing page

Use the entry’s source-edit link to propose a PR, or choose a form above if you would rather describe the change. Edit the source, not just the generated HTML. Explain what is wrong, why your replacement is better and which source supports it.

For a mathematical correction, include the hypotheses and enough of the argument to check it. For a translation, quote the English passage and proposed Chinese together; keep the same claim, conventions and qualifications. A smoother sentence should not make a theorem stronger.

For books and web links, identify the edition, exact reading location and access status: full text, preview, institutional access or purchase. For application information, cite the official programme and relevant year; do not infer funding, eligibility or an opening from an old announcement.

Proposing new content

An article proposal can be an outline. Tell us who it is for, the question it answers, related pages, primary sources with precise locators and what you would contribute. You do not need a finished article to start the discussion.

Before adding a record, read the content schema. Use one stable semantic concept ID; use separate IDs for genuinely different mathematical senses. Spelling variants, acronyms and Traditional Chinese forms belong in aliases, not duplicate entries. Check existing subject IDs and levels rather than inventing new taxonomy values.

A new encyclopedia article belongs in resources/content/encyclopedia/<area>/<id>.md; terminology records belong in resources/data/terminology-<area>.json. An encyclopedia article needs a corresponding terminology record. A well-sourced terminology record can stand alone without an empty article page.

Encyclopedia entries use the seven headings in the schema: Overview; Prerequisites; Definition and conventions; Intuition; Examples and non-examples; Important properties; Connections and further reading. State theorem assumptions, explain conventions and work through an example or non-example. Mark a proof sketch as a sketch. A research introduction may give an explicitly scoped formulation with a precise reference; it should not pretend to construct a whole theory in a few paragraphs.

Sources and translation evidence

Cite the author or institution, title, edition or version, public URL and exact section, definition, theorem or page you used. Prefer author, university, publisher or authorized archive sources. A forum can suggest a lead; check the underlying source before presenting it as evidence.

Evidence for a mathematical definition and evidence for a Chinese rendering are separate. An English textbook alone does not establish a Chinese term. Cite an explicit terminology standard, Chinese textbook or author’s notes that actually use the name. Record competing translations with their contexts. “Community usage” is not the same as a standardized term.

Use your own explanations. Link to source material instead of copying its prose, diagrams or exercises. Record an inspection date only when the source was actually read. Source checking is not external peer review; unchecked material remains a draft and does not count as a published entry.

Format and notation

Encyclopedia articles use Markdown with JSON front matter, not YAML, between --- lines. Follow the schema for required metadata and source fields. Aim for the length the explanation needs, usually 500–1000 words; published encyclopedia entries require 350–2000 words. These limits do not turn an external reading guide or a small correction into a full article.

Use $...$ for inline math and $$ on separate lines for display math. Standard KaTeX commands are supported; HTML, scripts, executable material, TikZ, custom macros, \label and \ref are not. Use ordinary Markdown links. The build renders formulas, including for readers without JavaScript.

Keep stable IDs and published anchors when editing. The builder creates the contents list, sources, related translation links and contribution controls; do not duplicate them inside the article.

A Markdown example

This is a body excerpt for the existing Sobolev-space topic, not a complete new entry or a publish-ready file. It shows a short argument and a specific source link. A new entry still needs schema-valid JSON metadata, all seven sections, appropriate length, genuine contributors and references with actual inspection dates. The English section heading is kept below because the current article-source schema requires it.

## Examples and non-examples

On $(-1,1)$, let $u(x)=|x|$. Its weak derivative is
$g(x)=-1$ for $x<0$ and $g(x)=1$ for $x>0$.
The value assigned to $g(0)$ does not change its $L^p$ class.

For $\varphi\in C_c^\infty(-1,1)$, integration by parts separately
on $(-1,0)$ and $(0,1)$ gives

$$
\int_{-1}^{1}|x|\varphi'(x)\,dx
=-\int_{-1}^{1}g(x)\varphi(x)\,dx.
$$

Thus $u\in W^{1,p}(-1,1)$ for every $1\le p\le\infty$,
although $u$ has no classical derivative at zero.

See [John K. Hunter, Notes on Partial Differential Equations,
Chapter 3, “Sobolev spaces”, §3.1 “Weak derivatives”](https://www.math.ucdavis.edu/~hunter/pdes/pde_notes.pdf).

Attribution and rights

Credit the people who wrote or revised the content and disclose AI-assisted drafting or translation in contributor metadata and the PR description. Do not attach the site owner’s name to text they did not write. Separate authorship, editing, source inspection and mathematical review; claim only work actually done.

New original encyclopedia and terminology contributions are offered under CC BY-SA 4.0. Retain attribution and comply with the licence when adapting compatible material. This does not relicense existing personal notes, external textbooks, quotations, images, dependency packages or the whole website. Other sections retain their existing terms; discuss rights for a new guide before publication rather than assuming this licence covers it.

Only submit material you wrote or have the right to contribute. Publicly readable is not the same as permission to copy or redistribute. Recommend an authorized link when you cannot supply the content itself.

Before a pull request is merged

For an existing page, keep the change focused and explain its reason. For a new page, include its record, references and relevant relations as well as the text. Use the repository’s PR checklist to separate what you checked from what still needs review.

• Check definitions, conventions, theorem assumptions, proof gaps and worked examples.
• Provide inspectable sources and concrete locators; keep mathematical and translation evidence separate.
• Check IDs, subject, level, aliases and existing senses; do not create empty or duplicate entries.
• Keep English and Chinese claims aligned, including notation, scope and qualifications. Flag a translation that needs review.
• Respect licences, attribution and privacy; report AI assistance and unresolved questions honestly.
• Check formula rendering, search, links, keyboard use and narrow-screen layout for the affected pages. Record which checks were actually run.

The maintainer installs the locked dependencies with npm ci --prefix resources --ignore-scripts, runs node resources/build.mjs and the content checks, and commits generated static pages before merging or publishing. The current workflow lists the full checks, including legacy content, formulas, search, links and repeat-build consistency. Its repository permissions are read-only: it does not auto-merge a PR or write to a contributor’s branch. A passing automated check does not replace editorial or mathematical review.

Contributions that would help

These are questions for a proposal, not links to unfinished articles. Check related pages first; a better example on an existing page may be more useful than a new entry.

• A worked localization-and-gluing example: show what the rings on two basic open sets retain and how agreement on the overlap is checked.
• An exercise on the weak derivative of the absolute-value function: use test functions, track the boundary terms and distinguish its first and second distributional derivatives.
• Conditional expectation on a finite probability space: compute it on a partition and explain what changes when the partition is refined.
• A first example of a site: compare an ordinary open cover with a covering family in the new setting, and identify the sheaf condition being used.

Revision record

19 October 2026 — Editorial revision of this guide: extended the instructions to all Mathematics Resources sections, added article and translation forms, and clarified the example, rights and review checklist.

Prepared with AI assistance. This date records the guide’s revision, not a new inspection of every linked source, external peer review or a mathematical check by Jiayu Chen.