Coding Guide in MathJax (LaTeX)

Contributors:

Erica Madebeykin, MBA
🇬🇧MBA Merit
🇬🇧MSc Comp Sci student

Nikita Madebeykin
ML Engineer

Start Creation Date: October 24, 2024 🔄 Continuously updated

LaTeX (MathJax) Basic Tutorials and Coding Guide

✅ Useful code snippets and explanations for understanding and documenting with MathJax (LaTeX). Perfect for students, educators, and programmers! 😻

Just click the "copy code" button below 'markdown'!

Summary Overview

Group	Section	What you'll learn	Key commands
Getting started	1.1 Inline vs Display Maths	maths inside a sentence or on its own line	$ $, $$ $$
	1.2 Superscripts and Subscripts	powers, indices and grouping	^, _, { }
	1.3 Fractions	fractions in every size	\frac, \dfrac, \tfrac, \cfrac
	1.4 Roots	square roots and n-th roots	\sqrt{}, \sqrt[n]{}
Building blocks	1.5 Greek Letters	symbols used in ML and statistics	\alpha, \theta, \sigma, \lambda
	1.6 Brackets that Resize	brackets that fit tall formulas	\left( \right), \{ \}, \lvert \rvert
	1.7 Operators and Relations	the punctuation of maths	\times, \le, \neq, \approx
	1.8 Big Operators with Limits	sums, products, integrals and limits	\sum, \prod, \int, \lim
	1.9 Function Names	upright names such as log and max	\log, \exp, \operatorname{}
	1.10 Fonts and Accents	bold vectors, hats and bars	\mathbf, \mathbb, \hat, \bar
	1.11 Sets and Logic	writing definitions	\in, \forall, \cup, \mid
Layout	1.12 Ellipses	the different kinds of dots	\ldots, \cdots, \vdots, \ddots
	1.13 Space Commands	spaces from tiny to wide, and line breaks	\,, \;, \quad, \\
	1.14 Matrix Environments	matrix bracket styles	pmatrix, bmatrix, vmatrix
	1.15 Special Characters	printing symbols such as the percent and dollar signs	\%, \$, \_, \&
	1.16 Boxes, Colour and Equation Numbers	boxed answers, colour and numbered equations	\boxed{}, \color{}, \tag{}

1.1 Inline vs Display Maths

1.1.1 Inline Maths

Inline Maths: one dollar sign on each side

Example:

The area of a circle is $\pi r^2$, where $r$ is the radius.

Inline maths sits inside a sentence. On this website, \( \) does not display, so always use dollar signs.

Where it's used: symbols and short formulas inside explanations.

The area of a circle is $\pi r^2$, where $r$ is the radius.

1.1.2 Display Maths

Display Maths: two dollar signs on their own lines

Example:

$$A=\pi r^2$$

Display maths is centred on its own line, and big symbols like sums get more room.

Where it's used: main formulas and step-by-step solutions.

$$
A = \pi r^2
$$

1.2 Superscripts and Subscripts

1.2.1 Superscripts and Subscripts

Superscript "^" and Subscript "_"

Example:

$$x^2{x}_i{x}_i^2$$

^ raises the next character and _ lowers it. You can use both on the same symbol.

Where it's used: powers, and indices such as the $i$-th value $x_i$.

$$
x^2 \qquad x_i \qquad x_i^2
$$

1.2.2 Group with Curly Brackets

Group with Curly Brackets "{ }"

Example:

$$x^{10}\text{vs}{x}^{1}0x_{ij}{e}^{-x^2}$$

Without curly brackets, only the first character is raised or lowered, so x^10 shows as $x^{1}0$. Put anything longer than one character inside { }.

Where it's used: any power or index with more than one character. This is the most common beginner mistake.

$$
x^{10} \quad \text{vs} \quad x^10 \qquad x_{ij} \qquad e^{-x^2}
$$

1.2.3 Primes and Training Example Notation

Primes and Nested Indices

Example:

$$f^{\prime }(x)f^{″}(x)x_j^{(i)}$$

Use ' for derivatives. In Machine Learning, $x_j^{(i)}$ is the $j$-th feature of the $i$-th training example.

Where it's used: derivatives, and Machine Learning notation for datasets.

$$
f'(x) \qquad f''(x) \qquad x_j^{(i)}
$$

1.3 Fractions

1.3.1 Basic Fraction

Fraction: "\frac{}{}"

Example:

$$\frac{a}{b}\frac{x+1}{x-1}$$

The first { } is the numerator and the second is the denominator.

Where it's used: everywhere: rates, probabilities, averages and formulas.

$$
\frac{a}{b} \qquad \frac{x + 1}{x - 1}
$$

1.3.2 Display and Text Size

Fraction Sizes: "\dfrac" and "\tfrac"

Example:

Inline: $\frac{1}{2}$ and ${\displaystyle \frac{1}{2}}$

$$\frac{1}{2}\frac{1}{2}$$

\frac changes size depending on where it is. \dfrac always uses the full size, and \tfrac always uses the small size.

Where it's used: making fractions easier to read inside sentences and tables.

Inline: $\frac{1}{2}$ and $\dfrac{1}{2}$

$$
\frac{1}{2} \qquad \tfrac{1}{2}
$$

1.3.3 Continued Fractions

Continued Fraction: "\cfrac"

Example:

$$x=\frac{1}{\frac{9}{20}}\frac{1}{1+\frac{1}{1+\frac{1}{2}}}$$

\cfrac keeps every level full size, while a \frac inside a \frac gets smaller and harder to read.

Where it's used: dividing by a fraction, like the multiplicative inverse steps in the practice sheets.

$$
x = \cfrac{1}{\cfrac{9}{20}} \qquad \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{2}}}
$$

1.4 Roots

1.4.1 Square Root

Square Root: "\sqrt{}"

Example:

$$\sqrt{x}\sqrt{x^2+y^2}$$

Where it's used: standard deviation, distances between points, and vector norms.

$$
\sqrt{x} \qquad \sqrt{x^2 + y^2}
$$

1.4.2 n-th Root

n-th Root: "\sqrt[n]{}"

Example:

$$\sqrt[3]{8}=2x^{\frac{a}{b}}=\sqrt[b]{x^a}$$

The number in square brackets [ ] sets the root.

Where it's used: cube roots and fractional exponents.

$$
\sqrt[3]{8} = 2 \qquad x^{\frac{a}{b}} = \sqrt[b]{x^a}
$$

1.5 Greek Letters Cheat Sheet

These symbols appear everywhere in Machine Learning, AI and Data Science papers.

Symbol	Code	Common meaning in ML and statistics
$\alpha$	\alpha	learning rate; significance level in hypothesis tests
$\beta$	\beta	regression coefficients
$\theta$	\theta	model parameters
$\lambda$	\lambda	regularisation strength; eigenvalue
$\mu$	\mu	mean
$\sigma$	\sigma	standard deviation; sigmoid function
$\mathrm{\Sigma }$	\Sigma	covariance matrix (not the same as the sum sign \sum)
$ϵ$	\epsilon	error or noise term
$\eta$	\eta	learning rate (another common symbol)
$\gamma$	\gamma	discount factor in reinforcement learning
$\delta$	\delta	a small change; error term in backpropagation
$\mathrm{\Delta }$	\Delta	change in a value, such as $\mathrm{\Delta }x$
$\varphi$	\phi	feature map or basis function
$\pi$	\pi	the number pi; policy in reinforcement learning
$\rho$	\rho	correlation coefficient
$\tau$	\tau	time step; temperature in softmax
$\chi$	\chi	chi-squared test, written ${\chi }^2$
$\mathrm{\nabla }$	\nabla	gradient
$\partial$	\partial	partial derivative

Capital letters start with a capital: \Gamma, \Delta, \Theta, \Lambda, \Sigma, \Pi, \Phi and \Omega. Some letters also have a second shape: \varepsilon gives $\epsilon$ and \varphi gives $\phi$.

1.6 Brackets that Resize

1.6.1 Automatic Sizing

Resizing Brackets: "\left" and "\right"

Example:

$${\left(\frac{a}{b}\right)}^2\text{vs}(\frac{a}{b}{)}^2$$

\left and \right make brackets grow to fit what is inside. They always come in pairs.

Where it's used: brackets around fractions, sums and other tall expressions.

$$
\left( \frac{a}{b} \right)^2 \quad \text{vs} \quad ( \frac{a}{b} )^2
$$

1.6.2 Bracket Types

Looks like	Code	Use it for
$(x)$	( )	grouping
$[x]$	[ ]	intervals and matrices
$\{x\}$	\{ \}	sets
$⟨x,y⟩$	\langle \rangle	inner products
$|x|$	\lvert \rvert	absolute value
$\Vert x\Vert$	\lVert \rVert	norms of vectors
$\lfloor x\rfloor$	\lfloor \rfloor	rounding down (floor)
$\lceil x\rceil$	\lceil \rceil	rounding up (ceiling)

1.7 Operators and Relations

These are the punctuation of maths.

Symbol	Code	Meaning
$\times$	\times	multiplication
$\cdot$	\cdot	multiplication (dot)
$÷$	\div	division
$\pm$	\pm	plus or minus
$\ne$	\neq	not equal to
$\approx$	\approx	approximately equal to
$\equiv$	\equiv	identical to
$:=$	:=	defined as, or update in an algorithm
$\le$	\le	less than or equal to
$\ge$	\ge	greater than or equal to
$\ll$	\ll	much less than
$\propto$	\propto	proportional to
$\sim$	\sim	distributed as
$\to$	\to	tends to, or maps to
$\Rightarrow$	\Rightarrow	implies
$⟺$	\iff	if and only if

1.8 Big Operators with Limits

1.8.1 Sum, Product, Integral and Limit

Big Operators

Example:

$$\sum _{i=1}^n{x}_i\prod _{i=1}^n{p}_i{\int }_0^{\mathrm{\infty }}{e}^{-x}dx\underset{x\to 0}{lim}\frac{\sin x}{x}$$

Use _ for the lower limit and ^ for the upper limit.

Where it's used: totals and averages (sum), likelihoods (product), areas and probabilities (integral), and derivatives (limit).

$$
\sum_{i=1}^{n} x_i \qquad \prod_{i=1}^{n} p_i \qquad \int_{0}^{\infty} e^{-x} \, dx \qquad \lim_{x \to 0} \frac{\sin x}{x}
$$

1.8.2 Limits in Inline Maths

Forcing Limits: "\limits"

Example:

Inline: $\sum _{i=1}^n{x}_i$ and $\sum _{i=1}^n{x}_i$

In inline maths, limits move to the side to keep the line short. \limits puts them back above and below.

Where it's used: sums inside sentences, when you want the limits in the usual place.

Inline: $\sum_{i=1}^{n} x_i$ and $\sum\limits_{i=1}^{n} x_i$

1.9 Function Names

1.9.1 Built-in Function Names

Upright Function Names

Example:

$$\log (x)\ln (x)\exp (x)\sin (\theta )max(a,b)\text{vs}log(x)$$

Commands like \log, \ln, \exp, \sin, \cos, \tan, \max, \min and \det print upright names with correct spacing. Typing plain log gives slanted letters, as if you were multiplying $l$, $o$ and $g$.

Where it's used: log-likelihood, exponential growth, and choosing the largest or smallest value.

$$
\log(x) \qquad \ln(x) \qquad \exp(x) \qquad \sin(\theta) \qquad \max(a, b) \quad \text{vs} \quad log(x)
$$

1.9.2 Your Own Function Names

Custom Names: "\operatorname{}"

Example:

$$\mathrm{softmax}(\mathbf{z})\mathrm{ReLU}(x)\mathrm{Var}(X)$$

Use \operatorname{} for names without a built-in command. It adds the same spacing as \log.

Where it's used: Machine Learning functions such as softmax and ReLU, and statistics such as Var and Cov.

$$
\operatorname{softmax}(\mathbf{z}) \qquad \operatorname{ReLU}(x) \qquad \operatorname{Var}(X)
$$

1.10 Fonts and Accents

Looks like	Code	Use it for
$\mathbf{x}$	\mathbf{x}	vectors and matrices
$\mathit{\beta }$	\boldsymbol{\beta}	bold Greek letters
$\mathbb{R}$	\mathbb{R}	number sets such as $\mathbb{R}$, $\mathbb{N}$ and $\mathbb{Z}$
$\mathcal{N}$	\mathcal{N}	distributions and loss functions
$\mathrm{d}x$	\mathrm{d}x	upright letters, such as the d in $\mathrm{d}x$
$\hat{y}$	\hat{y}	predictions and estimates
$\overline{x}$	\bar{x}	the mean
$\tilde{x}$	\tilde{x}	approximations or noisy values
$\overrightarrow{v}$	\vec{v}	vectors, in physics style
$\dot{x}$	\dot{x}	rate of change over time
$\widehat{xy}$	\widehat{xy}	a hat over several letters

1.11 Sets and Logic

1.11.1 Writing Definitions

Sets and Logic in a Formula

Example:

$$\mathrm{\forall }x\in \mathbb{R},x^2\ge 0A=\{x\in \mathbb{N}\mid x<10\}$$

This reads: "for all $x$ in the real numbers, $x^2$ is at least 0", and "$A$ is the set of natural numbers less than 10".

Where it's used: definitions, proofs, and describing datasets and feature spaces.

$$
\forall x \in \mathbb{R}, \; x^2 \ge 0 \qquad A = \{ x \in \mathbb{N} \mid x < 10 \}
$$

Symbol	Code	Meaning
$\in$	\in	is an element of
$\notin$	\notin	is not an element of
$\subset$	\subset	is a subset of
$\subseteq$	\subseteq	is a subset of, or equal to
$\cup$	\cup	union
$\cap$	\cap	intersection
$\setminus$	\setminus	set difference
$\mathrm{\varnothing }$	\emptyset	empty set
$\mathrm{\forall }$	\forall	for all
$\mathrm{\exists }$	\exists	there exists
$\mathrm{\neg }$	\neg	not
$\wedge$	\land	and
$\vee$	\lor	or

1.12 Ellipses in Different Use Cases

1.12.1 Ellipsis Centered : "\cdots"

Centered Ellipsis : "\cdots"

Example Use Case: Sequences in Summation

• In the contexts where terms are arranged in a sequence horizontally (such as in summation formulas), $\cdots$ can be used to indicate continuation.

$$\sum _{i=1}^n{a}_i=a_1+a_2+\cdots +a_n$$

 $$
 \sum_{i=1}^n a_i = a_1 + a_2 + \cdots + a_n
 $$

Other Use Cases of Centered Ellipsis:

1. Products:

   • When writing a product of several factors, $\cdots$ shows that the multiplication continues.

   Product of several factors, for example:

   $$a_1\cdot a_2\cdots a_n$$

   • This suggests a multiplication of the terms from $a_1$ to $a_n$.

    $$
    a_1 \cdot a_2 \cdots a_n
    $$

2. Matrices:

   • In matrix notation, $\cdots$ can be used to indicate the continuation of entries in a row.

   Matrix Notation example:

   $$\left[\begin{array}{cccc}1& 2& \cdots & n\\ a& b& \cdots & z\end{array}\right]$$

   • This shows that the entries continue horizontally.

    $$
    \begin{bmatrix}
    1 & 2 & \cdots & n \\
    a & b & \cdots & z
    \end{bmatrix}
    $$

1.12.2 Ellipsis Horizontal : "\ldots"

Horizontal Ellipsis : "\ldots" for "lowered dots"

Example

$$1,2,\dots ,n$$

 $$
 1, 2, \ldots, n
 $$

1.12.3 Ellipsis Vertical : "\vdots"

Vertical Ellipsis: "\vdots"

Example:

$$\left(\begin{array}{c}a\\ ⋮\\ c\end{array}\right)$$

 $$
 \begin{pmatrix} a \\ \vdots \\ c \end{pmatrix}
 $$

1.12.4 Ellipsis Diagonal : "\ddots"

Diagonal Ellipsis: "\ddots"

Example:

$$I=\left(\begin{array}{cccc}1& 0& \cdots & 0\\ 0& 1& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \cdots & 1\end{array}\right)$$

This is the identity matrix $I$. \ddots shows that the 1s continue down the diagonal.

 $$
 I = \begin{pmatrix} 1 & 0 & \cdots & 0 \\ 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & 1 \end{pmatrix}
 $$

1.12.5 Smart Dots

Smart Dots: "\dots"

Example:

$$x_1,x_2,\dots ,x_n{x}_1+x_2+\cdots +x_n$$

\dots chooses the height for you: low dots after commas, and centred dots between operators like $+$. For full control, you can also use \dotsc (commas), \dotsb (operators like $+$ and $=$), \dotsm (multiplication) and \dotsi (integrals).

Where it's used: everyday writing, when you are not sure whether to use \ldots or \cdots.

$$
x_1, x_2, \dots, x_n \qquad x_1 + x_2 + \dots + x_n
$$

1.12.6 Ellipsis in Sets, Lists and Indices

Ellipsis in Sets, Lists and Indices

Example:

$$S=\{x_1,x_2,\dots ,x_n\}f(x_1,\dots ,x_n)i=1,2,\dots ,n$$

Use \{ and \} for curly brackets. Plain { and } are used for grouping in LaTeX, so they do not show on the page.

Where it's used: describing a dataset as a set of samples, functions with many inputs, and index ranges in sums and loops.

$$
S = \{ x_1, x_2, \ldots, x_n \} \qquad f(x_1, \ldots, x_n) \qquad i = 1, 2, \ldots, n
$$

1.12.7 Vertical Dots in a System of Equations

Vertical Dots in Equations: "\vdots"

Example:

$$\begin{array}{rl}{a}_{11}{x}_1+a_{12}{x}_2+\cdots +a_{1n}{x}_n& =b_1\\ a_{21}{x}_1+a_{22}{x}_2+\cdots +a_{2n}{x}_n& =b_2\\ & ⋮\\ a_{m1}{x}_1+a_{m2}{x}_2+\cdots +a_{mn}{x}_n& =b_m\end{array}$$

\vdots skips the rows in the middle, while \cdots skips the terms within each row.

Where it's used: writing out a system of linear equations, which is the long form of the matrix equation $A\mathbf{x}=\mathbf{b}$ in Linear Algebra.

$$
\begin{aligned}
a_{11} x_1 + a_{12} x_2 + \cdots + a_{1n} x_n &= b_1 \\
a_{21} x_1 + a_{22} x_2 + \cdots + a_{2n} x_n &= b_2 \\
&\;\vdots \\
a_{m1} x_1 + a_{m2} x_2 + \cdots + a_{mn} x_n &= b_m
\end{aligned}
$$

1.12.8 Which Dots Should I Use?

Command	Looks like	Use it for	Example
\ldots	$\dots$	lists separated by commas	$x_1,x_2,\dots ,x_n$
\cdots	$\cdots$	between operators like $+$, $\cdot$ and $=$	$a_1+a_2+\cdots +a_n$
\vdots	$⋮$	skipping rows in vectors, matrices and systems of equations	see 1.12.3 and 1.12.7
\ddots	$\ddots$	skipping along the diagonal of a matrix	see 1.12.4
\dots	$\dots$	when unsure, it chooses the height automatically	see 1.12.5

1.13 Space Commands

1.13.1 Wide Space (Quad)

Space (Quad): "\quad"

Example:

$$x+yz$$

\quad adds a wide space, about the width of the letter M. For smaller gaps, use \, for a thin space or \ for a normal space.

 $$
 x + y \quad z
 $$

1.13.2 Double Wide Space (Double Quad)

Double Space (Double Quad): "\qquad"

Example:

$$x+yz$$

 $$
 x + y \qquad z
 $$

1.13.3 Thin, Medium and Thick Spaces

Thin, Medium and Thick Spaces

Example:

$${\int }_0^1{x}^{2}dx9.8{\text{m/s}}^2{\theta }^{\ast }=\underset{\theta }{\arg min}J(\theta )$$

\, adds a thin space, \: a medium space and \; a thick space. They are all smaller than \quad.

Where it's used: \, before $dx$ in integrals and between a number and its unit, and \; to give an operator like $\arg min$ some room.

$$
\int_{0}^{1} x^2 \, dx \qquad 9.8 \, \text{m/s}^2 \qquad \theta^{*} = \underset{\theta}{\arg\min} \; J(\theta)
$$

1.13.4 Normal Space and Words in Maths

Normal Space and Words in Maths

Example:

$$\text{if }x>0x\text{and}y$$

LaTeX ignores normal spaces in maths, so typing a b shows $ab$. Use \ (backslash and a space) for a normal space, or put the spaces inside \text{ }.

Where it's used: conditions like "if $x>0$" in piecewise functions, and short words such as "and" or "for all" inside formulas.

$$
\text{if } x > 0 \qquad x \ \text{and} \ y
$$

1.13.5 Negative Space

Negative Space

Example:

$$\int {\int }_{D}f(x,y)dxdy\text{vs}\int {\int }_{D}f(x,y)dxdy$$

\! removes a thin space and pulls symbols closer together. For double integrals, \iint is a ready-made shortcut.

Where it's used: tightening a gap that looks too wide, such as between two integral signs.

$$
\int\!\!\int_{D} f(x, y) \, dx \, dy \qquad \text{vs} \qquad \int\int_{D} f(x, y) \, dx \, dy
$$

1.13.6 Custom Width

Custom Width: "\hspace{}"

Example:

$$abab$$

\hspace{} adds a space of the exact width you choose, using units such as cm, em or pt.

Where it's used: lining up symbols when none of the standard spaces fit.

$$
a \hspace{1cm} b \qquad a \hspace{2em} b
$$

1.13.7 Line Breaks and Vertical Spacing

Line Breaks and Vertical Spacing

Example:

$$\begin{array}{rl}f(x)& =(x+1{)}^2\\ & =x^2+2x+1\\ f^{\prime }(x)& =2x+2\end{array}$$

Inside aligned, \\ starts a new line, \\[2ex] adds extra space before the next line, and & lines up the equals signs.

Where it's used: step-by-step derivations and worked solutions, like the ones in the practice sheets.

$$
\begin{aligned}
f(x) &= (x + 1)^2 \\
&= x^2 + 2x + 1 \\[2ex]
f'(x) &= 2x + 2
\end{aligned}
$$

1.13.8 Space Commands at a Glance

From smallest to largest. One em is about the width of the letter M.

Command	Name	Size	Example
\!	negative thin space	−3/18 em	$ab$
none	no space	0	$ab$
\,	thin space	3/18 em	$ab$
\:	medium space	4/18 em	$ab$
\;	thick space	5/18 em	$ab$
\	normal space	about 1/3 em	$ab$
\quad	quad	1 em	$ab$
\qquad	double quad	2 em	$ab$

1.14 Matrix Environments

1.14.1 Bracket Styles

Matrix Bracket Styles

Example:

$$\begin{array}{cc}a& b\\ c& d\end{array}\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|\left\{\begin{array}{cc}a& b\\ c& d\end{array}\right\}$$

& separates columns and \\ starts a new row. From left to right: matrix (no brackets), pmatrix (round), bmatrix (square), vmatrix (straight lines, for determinants) and Bmatrix (curly).

Where it's used: vectors, weight matrices and determinants. bmatrix is the most common style in Machine Learning.

$$
\begin{matrix} a & b \\ c & d \end{matrix} \quad \begin{pmatrix} a & b \\ c & d \end{pmatrix} \quad \begin{bmatrix} a & b \\ c & d \end{bmatrix} \quad \begin{vmatrix} a & b \\ c & d \end{vmatrix} \quad \begin{Bmatrix} a & b \\ c & d \end{Bmatrix}
$$

1.15 Special Characters

Some characters have a special job in LaTeX, so you need a backslash to print them.

1.15.1 Printing Special Characters

Escaping Special Characters

Example:

$$\text{accuracy}=95\mathrm{\%}S=\{a,b,c\}\text{Q\&A}$$

Where it's used: percentages, sets, and any formula that mentions these characters.

$$
\text{accuracy} = 95\% \qquad S = \{ a, b, c \} \qquad \text{Q\&A}
$$

Code	Prints	Why it needs a backslash
\%	percent sign	% starts a comment in LaTeX
\$	dollar sign	a dollar sign starts and ends maths
\_	underscore	_ makes a subscript
\#	hash sign	# is used inside commands
\&	ampersand	& separates columns
\{ \}	curly brackets	{ } group things together
\backslash	backslash	\ starts every command

1.16 Boxes, Colour and Equation Numbers

1.16.1 Box a Final Answer

Boxed Answer: "\boxed{}"

Example:

$$15\cdot \frac{4}{13}\cdot \frac{26}{15}=\boxed{{\displaystyle 8}}$$

Where it's used: highlighting the final answer of a worked solution.

$$
15 \cdot \frac{4}{13} \cdot \frac{26}{15} = \boxed{8}
$$

1.16.2 Colour

Colour: "\color{}"

Example:

$$f(x)=3x^2+2x+1$$

Put \color{} and the part you want to colour inside { }, so the colour stops there.

Where it's used: pointing out the part of a formula you are explaining.

$$
f(x) = {\color{red} 3}x^2 + {\color{blue} 2}x + 1
$$

1.16.3 Equation Numbers

Equation Number: "\tag{}"

Example:

$$\begin{array}{}\text{(1)}& \hat{y}={\mathbf{w}}^{\mathrm{\top }}\mathbf{x}+b\end{array}$$

Where it's used: numbering important equations so you can refer back to them, such as "from Equation (1)".

$$
\hat{y} = \mathbf{w}^{\top} \mathbf{x} + b \tag{1}
$$

More LaTeX Quick Code

Ready for formulas? Each subject has its own page:

• LaTeX for Calculus
• LaTeX for Linear Algebra and Matrices
• LaTeX for Statistics and Probability
• LaTeX for Machine Learning