Math Latex Examples
$\LaTeX$
LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. LaTeX is the de facto standard for the communication and publication of scientific documents.
For now, we will focus just on writing math equations inside of a Markdown file or a jupyter notebook cell.
In most Markdown editors, you write a math equation inside two single dollar signs $eqt$, or double dollar signs
$$
eqt
$$
Operators
\cos (2\theta) = \cos^2 \theta - \sin^2 \theta
$$ \cos (2\theta) = \cos^2 \theta - \sin^2 \theta $$
limits
\lim_{x \to \infty} \exp(-x) = 0
$$ \lim_{x \to \infty} \exp(-x) = 0 $$
Powers and indices
n^{22}
$n^{22}$
f(n) = n^5 + 4n^2 + 2 |_{n=17}
$$ f(n) = n^5 + 4n^2 + 2 |_{n=17} $$
Fractions and Binomials
\frac{n!}{k!(n-k)!} = \binom{n}{k}
$$ \frac{n!}{k!(n-k)!} = \binom{n}{k} $$
\frac{\frac{1}{x}+\frac{1}{y}}{y-z}
$$ \frac{\frac{1}{x}+\frac{1}{y}}{y-z} $$
Sums and integrals
\sum_{i=1}^{10} t_i
$$ \sum_{i=1}^{10} t_i $$
\displaystyle\sum_{i=1}^{10} t_i
$$ \displaystyle\sum_{i=1}^{10} t_i $$
\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x
$$ \int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x $$
\sum_{\substack{
0<i<m \\
0<j<n
}}
P(i,j)
$$
\sum_{\substack{
0<i<m
0<j<n
}}
P(i,j)
$$
Brackets, braces and delimiters
( a ), [ b ], \{ c \}, | d |, \| e \|,
\langle f \rangle, \lfloor g \rfloor,
\lceil h \rceil, \ulcorner i \urcorner
$$ ( a ), [ b ], { c }, | d |, | e |, \langle f \rangle, \lfloor g \rfloor, \lceil h \rceil, \ulcorner i \urcorner $$
Manual sizing
( \big( \Big( \bigg( \Bigg( word \Bigg) \bigg) \Big) \big) )
$$ ( \big( \Big( \bigg( \Bigg( word \Bigg) \bigg) \Big) \big) ) $$
\frac{\mathrm d}{\mathrm d x} \left( k g(x) \right)
$$ \frac{\mathrm d}{\mathrm d x} \left( k g(x) \right) $$
Color
k = {\color{red}x} \mathbin{\color{blue}-} 2
$$ k = {\color{red}x} \mathbin{\color{blue}-} 2 $$
Manually Specifying Formula Style
\begin{equation}
C^i_j = {\textstyle \sum_k} A^i_k B^k_j
\end{equation}
$$ \begin{equation} C^i_j = {\textstyle \sum_k} A^i_k B^k_j \end{equation} $$
\newcommand{\tsum}[1]{{\textstyle \sum_{#1}}}
$$ \newcommand{\tsum}[1]{{\textstyle \sum_{#1}}} $$
$$ \begin{equation} x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \end{equation} $$
\begin{equation}
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\end{equation}
List of mathematical symbols
Trigonometric Functions
| Symbol | Script | Symbol | Script | Symbol | Script | Symbol | Script |
|---|---|---|---|---|---|---|---|
| $\sin$ | \sin |
$\arcsin$ | \arcsin |
$\sinh$ | \sinh |
$\sec$ | \sec |
| $\cos$ | \cos |
$\arccos$ | \arccos |
$\cosh$ | \cosh |
$\csc$ | \csc |
| $\tan$ | \tan |
$\arctan$ | \arctan |
$\tanh$ | \tanh |
$\cot$ | \cot |
Other Symbols
| Symbol | Script | Symbol | Script | Symbol | Script | Symbol | Script | Symbol | Script |
|---|---|---|---|---|---|---|---|---|---|
| $\partial$ | \partial |
$\imath$ | \imath |
$\Re$ | \Re |
$\nabla$ | \nabla |
$\aleph$ | \aleph |
| $\eth$ | \eth |
$jmath$ | \jmath |
$\Im$ | \Im |
$\Box$ | \Box |
$\beth$ | \beth |
| $\hbar$ | \hbar |
$\ell$ | \ell |
$\wp$ | \wp |
$\infty$ | \infty |
$\gimel$ | \gimel |
Greek Letters
| Symbol | Script | Symbol | Script |
|---|---|---|---|
| A and $\alpha$ | A and \alpha |
N and $\nu$ | N and \nu |
| B and $\beta$ | B and \beta |
$\Xi$ and $\xi$ | \Xi and \xi |
| $\Gamma$ and $\gamma$ | \Gamma and \gamma |
O and o | O and o |
| $\Delta$ and $\delta$ | \Delta and \delta |
$\Pi$, $\pi$, and $\varpi$ | \Pi, \pi and \varpig |
| E, $\epsilon$, and $\varepsilon$ | E, \epsilon, and \varepsilon |
P, $\rho$ and $\varrho$ | P, \rho and \varrho |
| Z and $\zeta$ | Z and \zeta |
$\Sigma$, $\sigma$ and $\varsigma$ | \Sigma, \sigma and \varsigma |
| H and $\eta$ | H and \eta |
T and $\tau$ | T and \tau |
| $\Theta$, $\theta$ and $\vartheta$ | \Theta, \theta and \vartheta |
$\Upsilon$ and $\upsilon$ | \Upsilon ,\upsilon |
| I and $\iota$ | I and \iota |
$\Phi$, $\phi$ and $\varphi$ | \Phi, \phi and \varphi |
| K, $\kappa$, $\varkappa$ | K, \kappa, \varkappa |
X, $\chi$ | X, \chi |
| $\Lambda$, $\lambda$ | \Lambda, \lambda |
$\Psi$, $\psi$ | \Psi, \psi |
| M, $\mu$ | M, \mu |
$\Omega$, $\omega$ | \Omega, \omega |
Delimeters
| Symbol | Script | Symbol | Script | Symbol | Script |
|---|---|---|---|---|---|
| $\uparrow$ | \uparrow |
${$ | \{ |
$}$ | \} |
| $\downarrow$ | \downarrow |
$\Uparrow$ | \Uparrow |
$\Downarrow$ | \Downarrow |
Relation Symbols
| Symbol | Script | Symbol | Script | Symbol | Script | Symbol | Script | Symbol | Script |
|---|---|---|---|---|---|---|---|---|---|
| $<$ | < |
$>$ | > |
$=$ | = |
$\parallel$ | \parallel |
$\nparallel$ | \nparallel |
| $\leq$ | \leq |
$\geq$ | \geq |
$\doteq$ | \doteq |
$\asymp$ | \asymp |
$\bowtie$ | \bowtie |
| $\ll$ | \ll |
$\gg$ | \gg |
$\equiv$ | \equiv |
$\vdash$ | \vdash |
$\dashv$ | \dashv |
| $\subset$ | \subset |
$\supset$ | \supset |
$\approx$ | \approx |
$\in$ | \in |
$\ni$ | \ni |
| $\sqsubset$ | \sqsubset |
$\sqsupset$ | \sqsupset |
$\sim$ | \sim |
$\perp$ | \perp |
$\mid$ | \mid |
| $\sqsubseteq$ | \sqsubseteq |
$\sqsupseteq$ | \sqsupseteq |
$\propto$ | \propto |
$\prec$ | \prec |
$\succ$ | \succ |
| $\preceq$ | \preceq |
$\succeq$ | \succeq |
$\neq$ | \neq |
$\sphericalangle$ | \sphericalangle |
$\measuredangle$ | \measuredangle |
Binary Operations
| Symbol | Script | Symbol | Script | Symbol | Script | Symbol | Script |
|---|---|---|---|---|---|---|---|
| $\pm$ | \pm |
$\cap$ | \cap |
$\diamond$ | \diamond |
$\oplus$ | \oplus |
| $\mp$ | \mp |
$\cup$ | \cup |
$\bigtriangleup$ | \bigtriangleup |
$\ominus$ | \ominus |
| $\times$ | \times |
$\uplus$ | \uplus |
$\triangleleft$ | \triangleleft |
$\otimes$ | \otimes |
| $\ast$ | \ast |
$\sqcap$ | \sqcap |
$\triangledown$ | \triangledown |
$\odot$ | \dot |
| $\star$ | \star |
$\vee$ | \vee |
$\bigcirc$ | \bigcirc |
$\circ$ | \circ |
| $\dagger$ | \dagger |
$\wedge$ | \wedge |
$\bullet$ | \bullet |
$\setminus$ | \setminus |
| $\ddagger$ | \ddagger |
$\cdot$ | \cdot |
$\wr$ | \wr |
$\amalg$ | \amalg |