Mathematics · Print and keep

Reference sheets

Dense single-subject sheets meant to sit open beside you while you work: the identities, the transformations that generate them, and the traps, with nothing in between.

Each one is typeset in LaTeX and sized for paper rather than a screen. They are deliberately not tutorials — the explanatory material lives in the guides and the longer book editions. Every sheet is published in English and Japanese.

The sheets

Two · English & 日本語

Combinatorics: Permutations, Combinations & Identities Sampling with and without replacement, the core binomial identities, hockey stick and Vandermonde, stars and bars, inclusion–exclusion and derangements, the twelvefold way, Stirling, Bell and Catalan numbers, Lucas and Kummer, and entropy bounds. PDFEnglish 組合せ論 — 順列・組合せと二項係数の恒等式標本抽出の四類型、二項係数の主要な恒等式、ホッケースティックとヴァンデルモンドの畳み込み、仕切り棒法、包除原理と完全順列、十二通りの道、スターリング数・ベル数・カタラン数、リュカとクンマーの定理、そしてエントロピーによる評価。 PDF日本語 Products & ∏ Notation Telescoping, log–exp duality, falling and rising powers, Gamma and Gauss multiplication, roots of unity, q-products, convergence tests for infinite products, and Weierstrass–Hadamard factorisation. PDFEnglish 積の要約 — ∏ の恒等式と変形テレスコープ、対数と指数の双対性、下降べきと上昇べき、ガンマ関数とガウスの乗法公式、1 の冪根、q-積、無限積の収束判定、そしてワイエルシュトラス・アダマールの因数分解。 PDF日本語

How they are made

A sheet earns its place by what it leaves out.

Everything here is compiled from LaTeX sources: Palatino for the mathematics, Noto Serif CJK for the Japanese editions. The sheets are laid out in two columns on A4 and print cleanly in black and white, which is the only test that really matters for a page you intend to keep beside you.

Start with the interactive guides → See the longer editions →