Tips for LaTeX Math Formatting
How to avoid some of the most common pitfalls leading to ugly LaTeX.
Text Inside of Equations
Use $\textrm{my_variable} = 2$
$\textrm{my_variable} = 2.$
Not $my_variable = 2$
$my_variable = 2.$
Parentheses Around Fractions
Use $\left( \dfrac{1}{2} \right)$
$\left( \dfrac{1}{2} \right).$
Not $( \dfrac{1}{2} )$
$( \dfrac{1}{2} ).$
This applies to brackets, braces, absolute value signs, etc as well.
Exponents and Subscripts
Use $2^{10}$
$2^{10}.$
Not $2^10$
$2^10.$
Vertical Bars
Whenever you want to use a vertical bar $|$
$\vert,$ it has to be in a math environment (e.g. between dollar signs, or in an align environment).
Otherwise, if you try to use it as plain text, it will turn into a horizontal bar: |
———.
Integral Formatting
Use $\displaystyle \int x \, \mathrm{d}x$
$\displaystyle \int_0^1 x \, \mathrm{d}x.$
Not $\int x dx$
$\int_0^1 x dx.$
Evaluating at Bounds
Use $\left. \dfrac{x^2}{2} \right|{12}^{15}$
$\left. \dfrac{x^2}{2} \right\vert_{12}^{15}.$
Not $\frac{x^2}{2} \right|_12^15$
$\frac{x^2}{2} \vert_12^15.$
Arrows Under Limits
Use $\lim\limits_{x \to 0} f(x)$
$\lim\limits_{x \to 0} f(x).$
Not $\lim_{x \to 0} f(x)$
$\lim_{x \to 0} f(x).$
Expectation and Variance
Use $\mathrm{E}[X] \mathrm{Var}[X]$
$\mathrm{E}[X] \, \mathrm{Var}[X].$
Not $E[X] Var[X]$
$E[X] \, Var[X].$
Conditional Probability
Use $P(\textrm{new event} \, | \, \textrm{old event})$
$P(\textrm{new event} \, \vert \, \textrm{old event}).$
Not $P(new event | old event)$
$P(new event \vert old event).$
Multiplication
Use $P(A)P(B), \, P(A) \cdot P(B), \, P(A) \times P(B)$
$P(A)P(B), \, P(A) \cdot P(B), \, P(A) \times P(B).$
Not $P(A) * P(B)$
$P(A) * P(B).$
Align Environments
Whenever you are manipulating an equation, use an align environment:
\begin{align*}
3x+2 &= 5 \\
3x &= 3 \\
x &= 1
\end{align*}
Likewise, whenever you are simplifying an expression through multiple steps, use an align environment:
\begin{align*}
\int_1^2 x \, \textrm{d}x &= \left. \dfrac{x^2}{2} \right|_1^2 \\
&= \dfrac{2^2}{2} - \dfrac{1^2}{2} \\
&= \dfrac{4}{2} - \dfrac{1}{2} \\
&= \dfrac{3}{2}
\end{align*}
Running Off the Page
If a line of math is running off the page, break it after a term midway and put the rest on the next line like this:
\begin{align*}
\int (x + x^2 + x^3 + x^4 + x^5 + x^6) \, \textrm{d}x
&= \int x \, \textrm{d}x + \int x^2 \, \textrm{d}x + \int x^3 \, \textrm{d}x \\
&\quad + \int x^4 \, \textrm{d}x + \int x^5 \, \textrm{d}x + \int x^6 \, \textrm{d}x \\
&\quad + \int x^7 \, \textrm{d}x + \int x^8 \, \textrm{d}x + \int x^9 \, \textrm{d}x
\end{align*}
Don’t keep it all on one line. So, don’t do this:
</code> \begin{align*} \int (x + x^2 + x^3 + x^4 + x^5 + x^6) \, \textrm{d}x = \int x \, \textrm{d}x + \int x^2 \, \textrm{d}x + \int x^3 \, \textrm{d}x + \int x^4 \, \textrm{d}x + \int x^5 \, \textrm{d}x + \int x^6 \, \textrm{d}x + \int x^7 \, \textrm{d}x + \int x^8 \, \textrm{d}x + \int x^9 \, \textrm{d}x \end{align*} </code>