Introduction to LaTeX

Mathematics > Logic

LaTeX is the document preparation and typesetting system used for scientific publications. LaTeX is based on the idea that ‘it is better to leave document design to document designers’, so the user can focus on the content. It requires a greater technical understanding than typical simple note-taking systems; however, because it is incredibly descriptive and produces aesthetically-appealing output, it is becoming more popular. This post provides a reference to configuration and syntax.

LaTeX Beginnings

Tex is the actual low-level language created by Donald Knuth in 1978. Leslie Lamport created an alternative, high-level, macro file called lplain (“l” for Lamport), with a set of much-easier-to-use commands. The latex script ran the macros, first, then compiled the Tex language and outputs to a PostScript file that another program converts to a document. This evolved into the LaTeX program.

The LaTeX site provides the open source software distribution that compiles your LaTeX markup. Getting this set-up and using it can be quite involved and most workflows don’t allow for such complexities.

Also, most users don’t have to worry about becoming comfortable with the LaTeX markup. There are many templates available, including:

Large journal publications provide their own templates for document preparation, such as IEEE. However, some users may want to customize their own output. An example document could include the following.

\begin{document}
  \begin{environment1}
    \begin{environment2}
    \end{environment2}
  \end{environment1}
\end{document}

There is an interesting post describing how to create a business card in LaTeX. This is ridiculous! For more graphic-intensive work there are much better options, such Photoshop or even PowerPoint. For more information, look into latex tutorial.

Typical Usage

Jupyter

More commonly, simple snippets or blocks of LaTeX are used within common markdown or HTML to display mathematical text or special symbols. Pandoc can be used to convert simple markdown into other formats, including a PDF file with LaTeX.

Jupyter notebook uses MathJax to render LaTeX inside html/markdown. Just put your LaTeX math inside \\(.

The inline notation \\)c = \sqrt{a^2 + b^2}\\( becomes: \)c = \sqrt{a^2 + b^2}$

The display mode notation \\[c = \\sqrt{a^2 + b^2}\\] becomes:

\[c = \sqrt{a^2 + b^2}\]

Or place it in an individual cell.

from IPython.display import Math
Math(r'F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx')

$\displaystyle F(k) = \int_{-\infty}^{\infty} f(x) e^{2\pi i k} dx$

You can enter latex directly with the %%latex cell magic, within a Markdown cell:

%%latex
\begin{aligned}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\
\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{aligned}

%%latex \begin{aligned} \nabla \times \vec{\mathbf{B}} -, \frac1c, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \ \nabla \times \vec{\mathbf{E}}, +, \frac1c, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}

MathJax

Superscripts and Subscripts, use ^ and _. For example

  • x_i^2: \(x_i^2\)
  • \log_2 x: \(\log_2 x\)

Groups, Superscripts, Subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces {…}. If you do 10^10, you will get a surprise: 1010

But 10^{10} gives what you probably wanted: \(10^{10}\). Use curly braces to delimit a formula to which a superscript or subscript applies:

  • x^5^6 is an error
  • {x^y}^z is \({x^y}^z\)
  • x^{y^z} is \(x^{y^z}\)

Observe the difference between x_i^2 \(x_i^2\) and x_{i^2} \(x_{i^2}\)

Parentheses and Ordinary symbols ()[] make parentheses and brackets \((2+3)[4+4]\) Use \{ and \} for curly braces \(\{\}\)

These do not scale with the formula in between, so if you write (\frac{\sqrt x}{y^3}) the parentheses will be too small: \((\frac{\sqrt x}{y^3})\)

Using \left(…\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac{\sqrt x}{y^3}\right) is \(\left(\frac{\sqrt x}{y^3}\right)\)

\left and \right apply to all the following sorts of parentheses:

  • ( ) \((𝑥)\)
  • [ ] \([𝑥]\)
  • \{ \} \(\{𝑥\}\)
  • | \(|𝑥|\)
  • \vert \(\vert x\vert\)
  • \Vert \(\Vert x\Vert\)
  • \langle and \rangle \(\langle x \rangle\)
  • \lceil and \rceil \(\lceil x \rceil\)
  • \lfloor and \rfloor \(\lfloor x \rfloor\)
  • \middle can be used to add additional dividers

There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is \(\left.\frac12\right\rbrace\)

If manual size adjustments are required: \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) gives \(\Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr)\)

Sums and integrals \sum and \int; the subscript is the lower limit and the superscript is the upper limit, so for example \sum_1^n \(\sum_1^n\). Don’t forget {…} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is \(\sum_{i=0}^\infty i^2\). Similarly, \prod \(\prod\), \int \(\int\), \bigcup \(\bigcup\), \bigcap \(\bigcap\), \iint \(\iint\), \iiint \(\iiint\), \idotsint \(\idotsint\)

Fractions There are three ways to make these. \frac ab applies to the next two groups, and produces \(\frac ab\); for more complicated numerators and denominators use {…}: \frac{a+1}{b+1} is \(\frac{a+1}{b+1}\). If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in: {a+1\over b+1} is \({a+1\over b+1}\). Using \cfrac{a}{b} command is useful for continued fractions \(\cfrac{a}{b}\), more details for which are given in this sub-article.

Radical signs use sqrt, which adjusts to the size of its argument: \sqrt{x^3} \(\sqrt{x^3}\); \sqrt[3]{\frac xy} \(\sqrt[3]{\frac xy}\). For complicated expressions, consider using {...}^{1/2} \({…}^{1/2}\) instead.

Special functions, such as “lim”, “sin”, “max”, “ln”, and so on are normally set in roman font instead of italic font. Use \lim \(\lim\), \sin \(\sin\), etc. to make these: \sin x \(\sin x\), not sin x \(sin x\). Use subscripts to attach a notation to \lim: \lim_{x\to 0} \(\lim_{x\to 0}\).

There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:

\lt \gt \le \leq \leqq \leqslant \(\lt \gt \le \leq \leqq \leqslant\)

\ge \geq \geqq \geqslant \neq \(\ge \geq \geqq \geqslant \neq\)

You can use \not to put a slash through almost anything: \not\lt \(\not\lt\), but it often looks bad.

\times \div \pm \mp \(\times \div \pm \mp\)

\cup \cap \setminus \subset \subseteq \subsetneq \supset \(\cup \cap \setminus \subset \subseteq \subsetneq \supset\)

\in \notin \emptyset \varnothing \(\in \notin \emptyset \varnothing\)

\cdot is a centered dot: \(x \cdot y\)

{n+1 \choose 2k} \({n+1 \choose 2k}\) or \binom{n+1}{2k} \(\binom{n+1}{2k}\)

\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto \(\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto\)

\land \lor \lnot \forall \exists \top \bot \vdash \vDash \(\land \lor \lnot \forall \exists \top \bot \vdash \vDash\)

\star \ast \oplus \circ \bullet \(\star \ast \oplus \circ \bullet\)

\approx \sim \simeq \cong \equiv \prec \lhd \therefore \(\approx \sim \simeq \cong \equiv \prec \lhd \therefore\)

\infty \aleph_0 \(\infty \aleph_0\)

\nabla \partial \(\nabla \partial\) \Im \Re \(\Im \Re\)

For modular equivalence, use \pmod like this: a\equiv b\pmod n \(a\equiv b\pmod n\)

\ldots is the dots in \(a1,a2,\ldots,an\)

\cdots is the dots in \(a1+a2+\cdots+an\)

Some Greek letters have variant forms: \epsilon \varepsilon \(\epsilon\) \(\varepsilon\) and \phi \varphi \(\phi \varphi\) and others

Script lowercase l is \(\ell\)

Formula to code can be done with Detexify which lets you draw a symbol on a web page and then lists the 𝑇𝐸𝑋 symbols that seem to resemble it. These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains a list of currently supported 𝐿𝐴𝑇𝐸𝑋 commands, and one can also check Dr. Carol JVF Burns’s page of 𝑇𝐸𝑋

Spaces MathJax usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJax puts in: a b and a b are both ab

  • To add more space: use \, for a thin space \(a\,b\); and use\; for a wider space \(a\;b\). \quad and \qquad are large spaces: \(a \quad b\) adn \(a \qquad b\)
  • To set plain text, use \text{…}: \(\{x\in s\mid x\text{ is extra large}\}\). You can nest \\(…\\) inside of \text{…}.
  • Accents and diacritical marks use \hat for a single symbol \(\hat{x}\), \widehat for a larger formula \(\hat{xy}\). If you make it too wide, it will look silly. Similarly, there are \bar \(\bar{x}\) and \overline \(\overline{xyz}\), and \vec \(\vec{x}\) and \overrightarrow \(\overrightarrow{xy}\) and \overleftrightarrow \(\overleftrightarrow{xy}\). For dots, as in \(\frac d{dx}x\dot x = \dot x^2 + x\ddot x\), use \dot \(\dot\) and \ddot \(\ddot\).
  • Special characters used for MathJax interpreting can be escaped using the \ character: \$ \( , \\{ {, \\_ _, etc. If you want \\ itself, you should use \\backslash \)∖$, because \\ is for a new line.

References

To see how any formula was written in any question or answer, including this one, right-click on the expression it and choose “Show Math As > TeX Commands”.

This small mathjax post on stackexchange provided the best mathjax examples I’ve seen. The docs are useful, but a bit wordy.

The wikipedia page provides some nice LaTeX references.

Tables

MathJax does not implement LaTeX tables.

%%latex \begin{array}{|c|c|} \hline X & P(X = i) \\hline 1 & 1/6 \\hline 2 & 1/6 \\hline 3 & 1/6 \\hline 4 & 1/6 \\hline 5 & 1/6 \\hline 6 & 1/6 \\hline \end{array}

Greek letters

%%latex \begin{array}{|c|c|c|c|} \hline \alpha & \theta & o & \tau \\hline \beta & \vartheta & \pi & \upsilon \\hline \gamma & \gamma & \varpi & \phi \\hline \delta & \kappa & \rho & \varphi \\hline \epsilon & \lambda & \varrho & \chi \\hline \varepsilon & \mu & \sigma & \psi \\hline \zeta & \nu & \varsigma & \omega \\hline \eta & \xi & & \\hline
\end{array}

%%latex \begin{array}{|c|c|c|c|} \hline \Gamma & \Lambda & \Sigma & \Psi \\hline \Delta & \Xi & \Upsilon & \Omega \\hline \Theta & \Pi & \Phi & - \\hline \end{array}

Notation

%%latex \begin{array}{|c|c|c|c|c|} \hline \hat{a} & \acute{a} & \bar{a} & \dot{a} & \breve{a} \\hline \check{a} & \grave{a} & \vec{a} & \ddot{a} & \tilde{a} \\hline \end{array}

%%latex \begin{array}{|c|c|} \hline \widetilde{abc} & \widehat{abc} \\hline \overleftarrow{abc} & \overrightarrow{abc} \\hline \overline{abc} & \underline{abc} \\hline \overbrace{abc} & \underbrace{abc} \\hline \sqrt{abc} & \sqrt[n]{abc} \\hline f’ & \frac{abc}{xyz} \\hline \end{array}

Basic arrows and symbols

%%latex \begin{array}{|c|c|c|} \hline \leftarrow & \longleftarrow & \uparrow \\hline \Leftarrow & \Longleftarrow & \Uparrow \\hline
\rightarrow & \longrightarrow & \downarrow \\hline
\Rightarrow & \Longrightarrow & \Downarrow \\hline
\leftrightarrow & \longleftrightarrow & \updownarrow \\hline
\Leftrightarrow & \Longleftrightarrow & \Updownarrow \\hline
\mapsto & \longmapsto & \nearrow \\hline
\hookleftarrow & \hookrightarrow & \searrow \\hline
\leftharpoonup & \rightharpoonup & \swarrow \\hline
\leftharpoondown & \rightharpoondown & \nwarrow \\hline
\rightleftharpoons & \leadsto & \\hline \end{array}

Logic, set, and operator symbols

%%latex \begin{array}{|c|c|c|c|} \hline \forall & \complement & \therefore & \emptyset \\hline \exists & \subset & \because & \empty \\hline \exist & \supset & \mapsto & \varnothing \\hline \nexists & \mid & \to & \implies \\hline \in & \land & \gets & \impliedby \\hline \isin & \lor & \leftrightarrow & \iff \\hline \notin & \ni & \notni & \neg or \lnot \\hline \end{array}

%%latex \begin{array}{|c|c|c|c|} \hline \pm & \cap & \diamond & \oplus \\hline
\mp & \cup & \bigtriangleup & \ominus \\hline
\times & \uplus & \bigtriangledown & \otimes \\hline
\div & \sqcap & \triangleleft & \oslash \\hline
\ast & \sqcup & \triangleright & \odot \\hline
\star & \vee & \lhd\(^b\) & \bigcirc \\hline
\circ & \wedge & \rhd\(^b\) & \dagger \\hline
\bullet & \setminus & \unlhd\(^b\) & \ddagger \\hline
\cdot & \wr & \unrhd\(^b\) & \amalg \\hline

  •       &         -          &                              &                \\\hline

\end{array}

Relation symbols

%%latex \begin{array}{|c|c|c|c|} \hline \leq & \geq & \equiv & \models \\hline
\prec & \succ & \sim & \perp \\hline
\preceq & \succeq & \simeq & \mid \\hline
\ll & \gg & \asymp & \parallel \\hline
\subset & \supset & \approx & \bowtie \\hline
\subseteq & \supseteq & \cong & \Join\(^b\) \\hline
\sqsubset\(^b\) & \sqsupset\(^b\) & \neq & \smile \\hline
\sqsubseteq & \sqsupseteq & \doteq & \frown \\hline
\in & \ni & \propto & = \\hline
\vdash & \dashv & < & > \\hline
: & & & \\hline \end{array}

Miscellaneous symbols

%%latex \begin{array}{|c|c|c|c|} \hline \ldots & \cdots & \vdots & \ddots \\hline
\ldots & \cdots & \vdots & \ddots \\hline
\aleph & \prime & \forall & \infty \\hline
\hbar & \emptyset & \exists & \Box\(^b\) \\hline
\imath & \nabla & \neg & \Diamond\(^b\) \\hline
\jmath & \surd & \flat & \triangle \\hline
\ell & \top & \natural & \clubsuit \\hline
\wp & \bot & \sharp & \diamondsuit \\hline
\Re & | & \backslash & \heartsuit \\hline
\Im & \angle & \partial & \spadesuit \\hline
\mho\(^b\) & . & | & \\hline \end{array}

%%latex \begin{array}{|c|c|c|c|c|c|c|} \hline \arccos & \cos & \csc & \exp & \ker & \limsup & \min & \sinh \\hline
\arcsin & \cosh & \deg & \gcd & \lg & \ln & \Pr & \sup \\hline
\arctan & \cot & \det & \hom & \lim & \log & \sec & \tan \\hline
\arg & \coth & \dim & \inf & \liminf & \max & \sin & \tanh \\hline \end{array}

Variable-sized symbols

%%latex \begin{array}{|c|c|c|} \hline \sum & \bigcap & \bigodot \\hline
\prod & \bigcup & \bigotimes \\hline
\coprod & \bigsqcup & \bigoplus \\hline
\int & \bigvee & \biguplus \\hline
\oint & \bigwedge & \\hline \end{array}

Delimiters

%%latex \begin{array}{|c|c|c|c|} \hline ( & ) & \uparrow & \Uparrow \\hline
[ & ] & \downarrow & \Downarrow \\hline
{ & } & \updownarrow & \Updownarrow \\hline
\lfloor & \rfloor & \lceil & \rceil \\hline
\langle & \rangle & / & \backslash \\hline
| & | & & \\hline \end{array}

%%latex \begin{array}{|c|c|c|c|} \hline \rmoustache & \lmoustache & \rgroup & \lgroup \\hline \arrowvert & \Arrowvert & \bracevert & \\hline \end{array}

Matrix symbols

\[\begin{matrix} a & b \\ c & d \end{matrix}\]

%%latex

\begin{pmatrix} a & b \ c & d \end{pmatrix}

\[\begin{bmatrix} 1 & 2 & -1 \\ 3 & 0 & 1 \\ 0 & 2 & 4 \end{bmatrix}\]

\[\left( \frac{p}{q} \right)\]

Geometry symbols

%%latex

\begin{array}{|c|c|} \hline \angle & \measuredangle \\hline \triangle & \square \\hline \cong & \ncong \\hline \sim & \nsim \\hline | & \nparallel \\hline \perp & \not \perp \\hline \end{array}

Algebraic symbols

\[\sum_{n=0}^{\infty}\]

\[\prod_{n=0}^{\infty}\]

Calculus symbols

\[\int_a^b\]

\[\lim_{x \to a}\]

\[ f’(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x - a}\]

\[\lim_{x \to a^-} f(x) = f(a) = \lim_{x \to a^+} f(x)\]

Conclusion

Remembering these symbols’ code may be difficult when only writing intermitently; however, this reference should provide any required information, quickly.

References