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(2θ)=cos2θ−sin2θ

limits

\lim_{x \to \infty} \exp(-x) = 0

limx→∞exp(−x)=0

Powers and indices

n^{22}

n22

f(n) = n^5 + 4n^2 + 2 |_{n=17}

f(n)=n5+4n2+2|n=17

Fractions and Binomials

\frac{n!}{k!(n-k)!} = \binom{n}{k}

n!k!(n−k)!=(nk)

\frac{\frac{1}{x}+\frac{1}{y}}{y-z}

1x+1yy−z

Sums and integrals

\sum_{i=1}^{10} t_i

10∑i=1ti

\displaystyle\sum_{i=1}^{10} t_i

10∑i=1ti

\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x

∫∞0e−xdx

\sum_{\substack{
   0<i<m \\
   0<j<n
  }} 
 P(i,j)

∑0<i<m0<j<nP(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|,⟨f⟩,⌊g⌋,⌈h⌉,⌜

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

References

  1. https://en.wikibooks.org/wiki/LaTeX/Mathematics
  2. https://en.wikibooks.org/wiki/LaTeX/Introduction