Part III: the ne points of looking good
 Math in text
 Dots
 Big delimiters
 Spacing tricks
 Common ugly constructions
31
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Putting it all in math mode
Acommon mistake:
We see that $x$ $+$ $y$ $=$ $z$ $+$ $23$.
We see that x + y = z + 23.
Put the entire equation or expression in math mode:
We see that $x + y = z + 23$.
We see that x+y = z+23.
32
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Punctuation around formulae
In text math mode, commas and periods that are part of the
sentence should be outside math mode:
Because $f(a,b) = 0$, it follows that $f(2a, b-a) = 4$.
Because f(a;b) = 0, it follows that f(2a;b a) = 4.
In display math mode, there should (usually) be a comma,
semicolon, or period inside the display.
We find therefore that \[ x^{n} + y^{n} \ne z^{n}. \]
We nd therefore that
x
n
+y
n
6= z
n
:
33
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Dots
The AMS packages have introduced convenient abbreviations
for dierent kinds of dots in math mode. This is a good idea,
since then it is possible to change all of the style consistently
throughout a document by adding a single line to the preamble
(instead of doing a search and replace potentially across several
les). Here they are:
 \dotsc for dots with commas, as in $a_1, \dotsc, a_n$ for
a
1
;:::;a
n
;
 \dotsmfordots with multiplication, as in $1 \cdot 2 \dotsm n$
for 12n;
34
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More dots
 \dotsb for dots with binary operators or relations, as in
$1 + \dotsb + n$ for 1++n;
 \dotsi for dots with integrals, as in
\[ \int_A \int_B \dotsi \int_Z \] for
Z
A
Z
B

Z
Z
;
 \dotso for \other."
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Even more dots
 In text mode just use \dots; it’ll make something like this...
 To force low horizontal dots in math mode, use \ldots.
 To force centered horizontal dots in math mode, use \cdots.
 In matrices with rows or columns left out, you may need
\vdots (
.
.
.) and \ddots (
.
.
.
)as well.
36
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Dots in a matrix
\[ \begin{matrix}
a_{11} & \cdots & a_{1n} \\
\vdots & \ddots & \vdots \\
a_{n1} & \cdots & a_{nn}
\end{matrix} \]
a
11
 a
1n
.
.
.
.
.
.
.
.
.
a
n1
 a
nn
37
Delimiter height, part 1: automatic expansion
Using \left and \right in front of delimiters (parentheses,
brackets, etc.) makes them expand to enclose a tall expression
(fraction, sum, integral, etc.).
Thus $\left(\frac{x^2}{y^2}\right)$ gives
x
2
y
2
.
By contrast $(\frac{x^2}{y^2})$ gives (
x
2
y
2
).
\left and \right must be properly nested.
38
Delimiter height, part 2: doing it yourself
You can (and sometimes should) choose the size yourself:
$(\ldots)$
(:::)
$\bigl(\ldots\bigr)$
:::
$\Bigl(\ldots\Bigr)$
:::
$\biggl(\ldots\biggl)$
:::
!
$\Biggl(\ldots\Biggr)$
0
@
:::
1
A
These need not be properly nested (so be careful).
39
Delimiter height, part 3: examples
f\bigl((x + 1)^{4} + 1\bigr)
f
(x+1)
4
+1
\biggl(\sum_{n\ge 1} a_{n} n^{-s}\biggr)^2
X
n1
a
n
n
s
!
2
40
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