9720. MathJax Cheat Sheet for Mathematical Notation
MathJax and Time Complexity

Cheat sheet for displaying mathematical notations with MathJax.

1. MathJax

MathJax is a cross-browser JavaScript library that displays mathematical notation in web browsers. Read tutorial Jekyll - Math Symbols with MathJax to learn how to use MathJax in web page and Markdown.

2. MathJax Cheat Sheet

Title Formula Markdown
Variables $x_1$, $y_1$, $z_{3,4}$ $x_1$, $y_1$, $z_{3,4}$
Square $a^2$, $x^y$, $2^{n-1}$ $a^2$, $$x^y$, $2^{n-1}$
Square Root $\sqrt{9}$, $\sqrt{x}$, $\sqrt[n]{x}$ $\sqrt{9}$, $\sqrt{x}$, $\sqrt[n]{x}$
Logarithm $\log{}x$, $\log_{2}x$ $\log{}x$, $\log_{2}x$
Fraction $\frac{1}{2}$, $\left(-\frac{1}{2}\right)^n$ $\frac{1}{2}$, $\left(-\frac{1}{2}\right)^n$
Infinity $\infty$ $\infty$
Absolute Value $\vert{x}\vert$, $\vert\frac{x}{2}\vert$, $\lfloor{x}\rfloor$, $\lceil{x}\rceil$ $\vert{x}\vert$, $\vert\frac{x}{2}\vert$, $\lfloor{x}\rfloor$, $\lceil{x}\rceil$
Arithmetic Operation $2\times 3$, $6\div 3$ $2\times 3$, $6\div 3$
Factorial $n!$ $n!$
Trigonometric Functions $\sin\theta$, $\cos\theta$, $\tan\theta$ $\sin\theta$, $$\cos\theta$, $\tan\theta$
Greater or Less $a\gt b$, $a\geq b$, $a\lt b$, $a\leq b$ $a\gt b$, $a\geq b$, $a\lt b$, $a\leq b$
Equation $a=b$, $a\neq b$, $a\approx b$ $a=b$, $a\neq b$, $a\approx b$
Times Dot $a\cdot b=ab$ $a\cdot b=ab$
Divide Fraction $a/b=\frac{a}{b}$ $a/b=\frac{a}{b}$
Trinomial Equation $a^2 + b^2 = c^2$ $a^2 + b^2 = c^2$
Matrix Parentheses \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) $$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$
Matrix Brackets \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$
Matrix Equation \(\begin{vmatrix} a & b \\ c & d \end{vmatrix}=ad-bc\) $$\begin{vmatrix} a & b \\ c & d \end{vmatrix}=ad-bc$$
Set $x\in A$, $A\ni x$, $x\notin A$ $x\in A$, $A\ni x$, $x\notin A$
Subset $A\subset B$, $A\subseteq B$, $A \not \subset B$ $A\subset B$, $A\subseteq B$, $A \not \subset B$
Intersection & Union $A\cap B$, $A\cup B$, $\overline{A}$ $A\cap B$, $A\cup B$, $\overline{A}$
Quadratic formula $ x = {-b \pm \sqrt{b^2-4ac} \over 2a} $ $ x = {-b \pm \sqrt{b^2-4ac} \over 2a} $
Binomial $\sqrt{3x-1}+(1+x)^2$ $\sqrt{3x-1}+(1+x)^2$
Differentiation $f’$, $f^{(n)}$, $D_x f$ $f'$, $f^{(n)}$, $D_x f$
Integral $\int_0^1 f(x) dx$ $\int_0^1 f(x) dx$
Integral Large $\displaystyle \int_{-\infty }^{\infty}f(x)dx$ $\displaystyle \int_{-\infty }^{\infty}f(x)dx$
Max Sample \(\max(a,b)=\begin{cases}a&(a\geqq b)\\b&(a\lt b)\end{cases}\) $$\max(a,b)=\begin{cases}a&(a\geqq b)\\b&(a\lt b)\end{cases}$$
Name Notation Markdown
Big O [micron] $\mathcal{O}$ or $O$ $\mathcal{O}$ or $O$
Big Omega $\Omega$ $\Omega$
Big Theta $\Theta$ $\Theta$
Small O [micron] $o$ $o$
Small Omega $\omega$ $\omega$
On the order of $\sim$ $\sim$

4. Common Time and Space Complexity

Name Running Time Markdown
Constant Time $O(1)$ $O(1)$
Logarithmic Time $O(\log{}n)$ $O(\log{}n)$
Linear Time $O(n)$ $O(n)$
Quasilinear Time $O(n\log{}n)$ $O(n\log{}n)$
Quadratic Time $O(n^2)$ $O(n^2)$
Cubic Time $O(n^3)$ $O(n^3)$
Factorial Time $O(n!)$ $O(n!)$

5. References