# 晴耕雨読

## working in the fields on fine days and reading books on rainy days

Math Pronunciation LaTeX
$\dfrac{1}{2}$ one over two \dfrac
$1.2$ one point two .
$\therefore$ therefore \therefore
$\because$ because \because
$\forall x$ for all $x$ \forall
$\exists x$ for some $x$ \exists
$p \wedge q$ $p$ and $q$ \wedge
$p \vee q$ $p$ or $q$ \vee
$\neg p$ not $p$ \neg
$p \rightarrow q$ $p$ implies $q$ \rightarrow
$p \Rightarrow q$ if $p$ then $q$ \Rightarrow
$p \leftrightarrow q$ $p$ is equivalent to $q$ \leftrightarrow
$p \Leftrightarrow q$ $p$ if and only if [iff] $q$ \Leftrightarrow
$a^\prime$ $a$ prime ^\prime
$a^{\prime\prime}$ $a$ double prime ^{\prime\prime}
$\bar{a}$ $a$ bar \var
$\widetilde{a}$ $a$ tilde \widetilde
$\hat{a}$ $a$ hat \hat
$a^*$ $a$ star ^*
$\pm a$ plus or minus $a$ \pm
$\lvert a\rvert$ absolute value of $a$ \lvert \rvert
$a^2$ $a$ square ^2
$a^3$ $a$ cube ^3
$a^n$ $a$ to the $n$ [$n$th (power)] ^n
$a_n$ $a$ sub $n$ _n
$\sqrt{a}$ square root of $a$ \sqrt
$\sqrt[3]{a}$ cube root of $a$ \sqrt[3]
$\sqrt[n]{a}$ $n$th root of $a$ \sqrt[n]
$a \approx b$ $a$ is approximately equal to $b$ \approx
$a \le b$ $a$ is greater then or equal to $b$ \le
$a \ge b$ $a$ is less then or equal to $b$ \ge
$a \times b$ $a$ times $b$ \times
$a \cdot b$ $a$ times $b$ \cdot
$a \div b$ $a$ by $b$ \div
$a \,/\, b$ $a$ by $b$ /
$a:b$ the ratio of $a$ to $b$ :
$(a + b)c$ $a$ plus $b$ in parentheses times $c$
$(a + b)(a - b)$ $a$ plus $b$ times $a$ minus $b$
$n!$ $n$ factorial !
$_nP_r$ permutation of $n$ things (taken) $r$ at a time _nP_r
$_nC_r$ combination of $n$ things (taken) $r$ at a time _nC_r
$a \equiv b \pmod{n}$ $a$ is congruent to $b$ modulo $n$ \equiv \pmod
$a \vert b$ $a$ is a divisor of $b$ \vert
$\vec{a}$ vector $a$ \vec
$$\begin{pmatrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{m1} & \cdots & a_{mn} \end{pmatrix}$$ $m$ times $n$ matrix $a$ one one to $a$ $m$ $n$ \begin{pmatrix} \cdots \vdots \ddots
$\left( a_{ij} \right)$ matrix $a$ $i$ $j$ _{ij}
$\det A$ determinant of $A$ \det
$\lvert A\rvert$ determinant of $A$ \lvert \rvert
$A^{-1}$ inverse of $A$ ^{-1}
$A^t$ transpose of $A$ ^t
$\mathrm{adj}\, A$ adjoint of $A$ \mathrm{adj}\,
$\mathrm{tr}\, A$ trace of $A$ \mathrm{tr}\,
$A \bigotimes B$ Kronecker product (tensor product) of $A$ $B$ \bigotimes
$$\{x\,\vert\,C\}$$ set of $x$ satisfying $C$ { \,\vert\, }
$$\{x_n\}$$ sequence $x$ sub $n$ {}
$x_1, x_2, \ldots$ $x$ one $x$ two and so on \ldots
$x \in \mathbb{Z}$ $x$ is an element of $\mathbb{Z}$ \in \mathbb
$\mathbb{Z} \ni x$ $\mathbb{Z}$ contains $x$ \mathbb \ni
$A \subset B$ $A$ is contained in $B$, $A$ is a subset of $B$ \subset
$A \supset B$ $A$ contains $B$ \supset
$A \varsubsetneqq B$ $A$ is properly contained in $B$ \varsubsetneqq
$A \cup B$ $A$ union $B$ \cup
$A \cap B$ $A$ intersection $B$ \cap
$\emptyset$ empty set \emptyset
$\dim A$ dimension of $A$ \dim
$\ln x$ natural logarithm of $x$ \ln
$\Re z$ real part of $z$ \Re
$\Im z$ imaginary part of $z$ \Im
$$\lim_{n\to\infty} x_n$$ limit of $x_n$ as $n$ tends to [approaches] infinity \lim \to \infty
$x_n \to -\infty \;(n\to\infty)$ $x_n$ tends to minus infinity as $n$ tends to [approaches] infinity \to \infty
$x_1 + \cdots + x_n$ the sum of the x's from sub one to sub $n$ \cdots
$$\sum_{k=1}^k x_k$$ sum of $x_k$ k equals one to $n$ \sum
$$\prod_{k=1}^k x_k$$ product of $x_k$ k equals one to $n$ \prod
$f: X \to Y$ function $f$ mapping $X$ into $Y$ \to
$f: x \mapsto x$ function $f$ mapping $x$ to $y$ \mapsto
$f \vert E$ $f$ restricted on $E$ \vert
$\mathrm{Im}\,f$ image of $f$ \mathrm{Im}\,
$\mathrm{Ker}\,f$ kernel of $f$ \mathrm{Ker}\,
$f \circ g$ $f$ composition $g$ \circ
$f * g$ $f$ convolution $g$ *
$f \sim g$ $f$ is equivalent to $g$ \sim
$\lVert x\rVert$ norm of $x$ \lVert \rVert
$\dfrac{dy}{dx}$ $d$ $y$ over [by] $d$ $x$ d
$\dfrac{d^2y}{dx^2}$ $d$ two $y$ over [by] $d$ $x$ square d^2
$\dfrac{\partial z}{\partial x}$ round $d$ $z$ over round $d$ $x$ \partial
$\varphi(x)$ phi of $x$ \varphi
$\nabla \cdot f$ nabla dot $f$ \nabla \cdot
$\Delta f$ Laplacian of $f$ \Delta
$\int y \,dx$ integral $y$ $d$ $x$ \int \,dx
$\int_a^b y \,dx$ integral from $a$ to $b$ of $y$ $d$ $x$ \int \,dx
$\iint f(x,y) \,dxdy$ double integral of $f$ of $x$ $y$ \iint \,dxdy
$\iint_E f(x,y) \,dxdy$ double integral over $E$ of $f$ of $x$ $y$ \iint \,dxdy
$f \bot g$ $f$ is orthogonal to $g$ \bot
$P(E)$ probability of $E$ P()
$P(E|F)$ probability of $E$ under the condition [when] $F$ P(|)
$$\bigcup\limits_{k=1}^{n} E_k$$ union of $E_k$ $k$ running from one to $n$ \bigcup\limits
$$\bigcap\limits_{k=1}^{n} E_k$$ intersection of $E_k$ $k$ running from one to $n$ \bigcap\limits