# More on: Mathematics

## Further amsmath alignments

In addition to the align* environment shown in the main lesson, amsmath has several other display math constructs, notably gather for multi-line displays that do not need alignment, and multline for splitting a larger single expression over multiple lines, aligning the first line to the left, and the last to the right. In all cases the * form omits the equation numbers by default.

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}

\usepackage{amsmath}

\begin{document}

Gather
\begin{gather}
P(x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+ex +f\\
x^2+x=10
\end{gather}

Multline
\begin{multline*}
(a+b+c+d)x^{5}+(b+c+d+e)x^{4} \\
+(c+d+e+f)x^{3}+(d+e+f+a)x^{2}+(e+f+a+b)x\\
+ (f+a+b+c)
\end{multline*}
\end{document}


### Columns in math alignments

The amsmath alignment environments are designed to take pairs of columns with the first column of each pair aligned to the right and the second aligned to the left. This allows multiple equations to be shown, each aligned towards its relation symbol.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\begin{document}
Aligned equations
\begin{align*}
a &= b+1   &  c &= d+2  &  e &= f+3   \\
r &= s^{2} &  t &=u^{3} &  v &= w^{4}
\end{align*}

\end{document}


In addition there are variants of the display environments ending in ed that make a subterm inside a larger display. For example, aligned and gathered are variants of align and gather respectively.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\begin{document}
Aligned:
\left.\begin{aligned} a&=b\\ c&=d \end{aligned}\right\} \Longrightarrow \left\{\begin{aligned} b&=a\\ d&=c \end{aligned}\right.
\end{document}


aligned takes a positional optional argument similar to tabular. This is often useful to align an inline math formula on its top row; compare the items in the list in the following example.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\begin{document}
\begin{itemize}
\item
\begin{aligned}[t] a&=b\\ c&=d \end{aligned}
\item
\begin{aligned} a&=b\\ c&=d \end{aligned}
\end{itemize}
\end{document}


## Bold Math

Standard LaTeX has two methods to give bold symbols in math. To make an entire expression bold, use \boldmath before entering the expression. The command \mathbf is also available to set individual letters or words in upright bold roman.

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}

\begin{document}

$(x+y)(x-y)=x^{2}-y^{2}$

{\boldmath $(x+y)(x-y)=x^{2}-y^{2}$ $\pi r^2$}

$(x+\mathbf{y})(x-\mathbf{y})=x^{2}-{\mathbf{y}}^{2}$
$\mathbf{\pi} r^2$ % bad use of \mathbf
\end{document}


If you want to access bold symbols (as would be used by \boldmath) within an otherwise normal weight expression, then you can use the command \bm from the bm package. Note that \bm also works with symbols such as = and Greek letters. (Note that \mathbf has no effect on \pi in the example above.)

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{bm}

\begin{document}

$(x+\mathbf{y})(x-\mathbf{y})=x^{2}-{\mathbf{y}}^{2}$

$(x+\bm{y})(x-\bm{y}) \bm{=} x^{2}-{\bm{y}}^{2}$

$\alpha + \bm{\alpha} < \beta + \bm{\beta}$

\end{document}


## Mathtools

The package mathtools loads amsmath and adds several additional features, such as variants of the amsmath matrix environments that allow the column alignment to be specified.

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{mathtools}

\begin{document}

$\begin{pmatrix*}[r] 10&11\\ 1&2\\ -5&-6 \end{pmatrix*}$

\end{document}


## Unicode Math

As will be seen in Lesson 14, there are variant TeX engines that use OpenType fonts. By default, these engines still use classic TeX math fonts but you may use the unicode-math package to use OpenType Math fonts. The details of this package are beyond this course and we refer you to the package documentation. However, we give a small example here.

% !TEX lualatex
\documentclass[a4paper]{article}
\usepackage{unicode-math}
\setmainfont{TeX Gyre Pagella}
\setmathfont{TeX Gyre Pagella Math}

\begin{document}

One two three
$\log \alpha + \log \beta = \log(\alpha\beta)$

Unicode Math Alphanumerics
$A + \symfrak{A}+\symbf{A}+ \symcal{A} + \symscr{A}+ \symbb{A}$

\end{document}