mathematics.bigb

= Mathematics
{wiki}

= Infinity
{title2=$\infty$}
{parent=Mathematics}
{wiki}

Infinity denotes unbounded growth or an ideal quantity larger than every finite value; it is not a real number.

= Basel problem
{parent=Mathematics}
{c}
{wiki}

= Cantor function
{parent=Mathematics}
{c}
{wiki}

= Cayley-Hamilton theorem
{parent=Mathematics}
{c}
{wiki}

= Chinese remainder theorem
{parent=Mathematics}
{c}
{wiki}

For pairwise coprime positive integers $m_1,\ldots,m_r$, reduction induces a ring isomorphism
$$
\mathbb Z/(m_1\cdots m_r)\mathbb Z
\cong
\prod_{j=1}^r\mathbb Z/m_j\mathbb Z.
$$
Equivalently, every list of residue classes modulo the $m_j$ has a unique simultaneous residue class modulo their product.

= Lagrange theorem for polynomial congruences
{c}
{parent=Chinese remainder theorem}

A nonzero polynomial of degree $d$ over a field has at most $d$ roots. In particular, if a polynomial congruence $f(x)\equiv0\pmod p$ has degree $d$ and not all coefficients are divisible by the prime $p$, it has at most $d$ incongruent solutions modulo $p$.

= Chinese remainder theorem for unit groups
{parent=Chinese remainder theorem}
{c}

For coprime $m,n$, reduction gives $(\mathbb Z/mn\mathbb Z)^\times\cong(\mathbb Z/m\mathbb Z)^\times\times(\mathbb Z/n\mathbb Z)^\times$.

= Multiplicative order under the Chinese remainder theorem
{parent=Chinese remainder theorem for unit groups}

The order of a unit modulo a product of coprime moduli is the least common multiple of the orders of its components.

= Conjugacy class
{parent=Mathematics}
{wiki}

= Cycle decomposition of a permutation
{parent=Mathematics}
{wiki}

= Method of images
{parent=Mathematics}
{wiki}

= Metrizable space
{parent=Mathematics}
{wiki}

= Nakayama lemma
{parent=Mathematics}
{c}
{wiki}

= Newton law of cooling
{parent=Mathematics}
{c}
{wiki}

= Nilradical
{parent=Mathematics}
{wiki}

= Pattern waiting time
{parent=Mathematics}
{wiki}

= Period of a function
{title2=$T$}
{parent=Mathematics}
{wiki}

A nonzero number $T$ is a period of a <function> $f$ when $f(x+T)=f(x)$ throughout its domain.

= Periods
{synonym}

= Quasi-steady approximation
{parent=Mathematics}
{wiki}

= Rational root theorem
{parent=Mathematics}
{wiki}

If a primitive polynomial
$$
a_nX^n+\cdots+a_0\in\mathbb Z[X]
$$
has a rational root $r/s$ in lowest terms, then $r\mid a_0$ and $s\mid a_n$. In particular, a monic integer polynomial can have only integer rational roots dividing its constant term.

= Rodrigues rotation formula
{parent=Mathematics}
{c}
{wiki}

= Run of successes
{parent=Mathematics}
{wiki}

= Simultaneous diagonalization
{parent=Mathematics}
{wiki}

A finite family of pairwise commuting diagonalizable operators on a finite-dimensional complex vector space is simultaneously diagonalizable. In particular, commuting Hermitian operators admit an orthonormal common eigenbasis.

= Spectral mapping theorem
{parent=Mathematics}
{wiki}

= Termwise integration
{parent=Mathematics}
{wiki}

= Thomae function
{parent=Mathematics}
{c}
{wiki}

= Zero divisor
{parent=Mathematics}
{wiki}

= Area of mathematics
{parent=Mathematics}
{wiki=Areas_of_mathematics}

\Include[algebra]
\Include[analysis]
\Include[arithmetic]
\Include[combinatorics]
\Include[control-theory]
\Include[foundations-of-mathematics]
\Include[geometry-and-topology]
\Include[mathematical-optimization]
\Include[number-theory]
\Include[probability-and-statistics]