About this handbook

The mathematics a physicist or applied scientist actually reaches for, written in small self-contained units, so you can take the few you need instead of carrying a twelve-hundred-page book.

Why it is built this way

Reference books are organised for the author's exposition, not for the reader's question. You want the residue theorem and its hypotheses; you get a chapter. Here each unit is one definition, one theorem with its proof, or one method, with its prerequisites named and linked. Tick the units you want anywhere in the contents and the site assembles a PDF of exactly those, with a reference list containing only the books those units cite.

How a unit is written

Every unit is written from a library of nineteen textbooks and rewritten in our own words. Each block carries a label — Original, Adapted or Quoted — and Adapted blocks name the work and pages they follow. This is enforced by software rather than good intentions: a unit whose prose shares twelve consecutive words with any book in the library, or whose argument tracks a source passage closely in order, cannot be published. The details, and a count of what this build actually contains, are on the provenance page.

How a unit gets published

Nothing appears here because it was written. A unit is published only after independent reviewers check its mathematics line by line — re-deriving proofs and recomputing the worked examples — and confirm every citation against the page it names. Theorem-heavy chapters get two reviewers; the rest get one. A unit that fails goes back and returns through the whole gate. Where a reviewer disagrees with a cited book rather than with us, the book stands and the disagreement is recorded separately, because a handbook that silently corrects its sources cannot be checked against them.

So the handbook is deliberately complete rather than provisionally complete: every unit the topic map plans has been written and has passed the gate. Nothing is shown here that has not.

Accuracy and corrections

Review catches errors; it does not catch all of them. Every unit here has passed independent review, and some will still contain mistakes — a wrong sign, a missing hypothesis, a page cited wrongly. Use the handbook as you would any reference: for anything that matters, check it against the cited page. That is what the citations are for.

Corrections are welcome. Open an issue on GitHub, or write to the address on the provenance page. A corrected unit goes back through the same review before it is published again.

The text is provided as it is, without warranty of any kind, as its licence states (CC BY-SA 4.0, section 5).

Who maintains it

The handbook is maintained by Sumangalam Avtar Sharma, a mathematics student at IISER Pune.

Licence

The text is licensed CC BY-SA 4.0 — use it, adapt it, credit it, share it alike. Quoted material and the cited books themselves are not covered. The software that builds and checks the handbook is MIT.