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Short Math Guide for L
A
T
E
X
Michael Downes, updated by Barbara Beeton
American Mathematical Society
Version 2.0 (2017/12/22), currently available from a link at
https://www.ams.org/tex/amslatex
Contents
1 Introduction 3
2 Inline math formulas and displayed equations 3
2.1 The fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Automatic numbering and cross-referencing . . . . . . . . . . . . . . . . . . 5
3 Math symbols and math fonts 6
3.1 Classes of math symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Some symbols intentionally omitted here . . . . . . . . . . . . . . . . . . . . 6
3.3 Alphabets and digits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.1 Latin letters and Arabic numerals . . . . . . . . . . . . . . . . . . . 7
3.3.2 Greek letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.3 Other “basic” alphabetic symbols . . . . . . . . . . . . . . . . . . . . 8
3.3.4 Math font switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3.5 Blackboard Bold letters (msbm; no lowercase) . . . . . . . . . . . . . 9
3.3.6 Calligraphic letters (cmsy; no lowercase) . . . . . . . . . . . . . . . . 9
3.3.7 Non-CM calligraphic and script letters . . . . . . . . . . . . . . . . . 9
3.3.8 Fraktur letters (eufm) . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4 Miscellaneous simple symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.5 Binary operator symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.6 Relation symbols: < = > ∼ and variants . . . . . . . . . . . . . . . . . . 10
3.7 Relation symbols: arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.8 Relation symbols: miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . 11
3.9 Cumulative (variable-size) operators . . . . . . . . . . . . . . . . . . . . . . 12
3.10 Punctuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.11 Pairing delimiters (extensible) . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.12 Nonpairing extensible symbols . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.13 Extensible vertical arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.14 Math accents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.15 Named operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Notations 13
4.1 Top and bottom embellishments . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Extensible arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 Affixing symbols to other symbols . . . . . . . . . . . . . . . . . . . . . . . 14
4.4 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.5 Math spacing commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.6 Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.7 Nonbreaking dashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.8 Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.9 Boxed formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1
Short Math Guide for L
A
T
E
X, version 2.0 (2017/12/22) 2
5 Fractions and related constructions 16
5.1 The \frac, \dfrac, and \tfrac commands . . . . . . . . . . . . . . . . . . 16
5.2 The \binom, \dbinom, and \tbinom commands . . . . . . . . . . . . . . . . 16
5.3 The \genfrac command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.4 Continued fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6 Delimiters 17
6.1 Delimiter sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.2 Vertical bar notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7 The \text command 18
7.1 \mod and its relatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
8 Integrals and sums 18
8.1 Altering the placement of limits . . . . . . . . . . . . . . . . . . . . . . . . . 18
8.2 Multiple integral signs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
8.3 Multiline subscripts and superscripts . . . . . . . . . . . . . . . . . . . . . . 19
8.4 The \sideset command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
9 Changing the size of elements in a formula 19
10 Other packages of interest 20
11 Other documentation of interest 21
Acknowledgments and plans for future work
Thanks to all who contributed suggestions, assistance and encouragement. Special thanks
to David Carlisle for repairing unruly macros and to Jennifer Wright-Sharp for applying
consistent editing in AMS style.
Plans for a future edition include addition of an index.
Reports concerning errors and suggestions for improvement should be sent to
Short Math Guide for L
A
T
E
X, version 2.0 (2017/12/22) 3
1. Introduction
This is a concise summary of recommended features in L
A
T
E
X and a couple of extension
packages for writing math formulas. Readers needing greater depth of detail are referred
to the sources listed in the bibliography, especially [Lam], [AMUG], and [LFG]. A certain
amount of familiarity with standard L
A
T
E
X terminology is assumed; if your memory needs
refreshing on the L
A
T
E
X meaning of command, optional argument, environment, package,
and so forth, see [Lam].
Most of the features described here are available to you if you use L
A
T
E
X with two ex-
tension packages published by the American Mathematical Society: amssymb and amsmath.
Thus, the source file for this document begins with
\documentclass{article}
\usepackage{amssymb,amsmath}
The amssymb package might be omissible for documents whose math symbol usage is rela-
tively modest; in Section 3, the symbols that require amssymb are marked with
a
or
b
(font
msam or msbm). In Section 3.3, a few additional fonts are included; the necessary packages
are identified there.
Many noteworthy features found in other packages are not covered here; see Section 10.
Regarding math symbols, please note especially that the list given here is not intended to be
comprehensive, but to illustrate such symbols as users will normally find already present in
their L
A
T
E
X system and usable without installing any additional fonts or doing other setup
work.
If you have a need for a symbol not shown here, you will probably want to consult The
Comprehensive L
A
T
E
X Symbol List [CLSL]. If your L
A
T
E
X installation is based on T
E
X Live,
and includes documentation, the list can also be accessed by typing texdoc comprehensive
at a system prompt.
2. Inline math formulas and displayed equations
2.1. The fundamentals. Entering and leaving math mode in L
A
T
E
X is normally done
with the following commands and environments.
inline formulas displayed equations
$ . . . $
\( . . . \)
\[...\] unnumbered
\begin{equation*}
. . .
\end{equation*}
unnumbered
\begin{equation}
. . .
\end{equation}
automatically
numbered
Note 1. Do not leave a blank line between text and a displayed equation. This allows a page break at that
location, which is bad style. It also causes the spacing between text and display to be incorrect, usually
larger than it should be. If a visual break is desired in the input, insert a line containing only a % at the
beginning. Leave a blank line between a display and following text only if a new paragraph is intended.
Note 2. Do not group multiple display structures in the input (\[...\], equation, etc.). Instead, use a
multiline structure with substructures (split, aligned, etc.) as appropriate.
Note 3. The alternative environments \begin{math} . . . \end{math} and
\begin{displaymath} . . . \end{displaymath} are seldom needed in practice. Using the plain T
E
X notation
$$ . . . $$ for displayed equations is strongly discouraged. Although it is not expressly forbidden in L
A
T
E
X,
it is not documented anywhere in the L
A
T
E
X book as being part of the L
A
T
E
X command set, and it interferes
with the proper operation of various features such as the fleqn option.
Note 4. The eqnarray and eqnarray* environments described in [Lam] are strongly discouraged because
they produce inconsistent spacing of the equal signs and make no attempt to prevent overprinting of the
equation body by the equation number.
Environments for handling equation groups and multiline equations are shown in Table 1.
Short Math Guide for L
A
T
E
X, version 2.0 (2017/12/22) 4
Table 1: Multiline equations and equation groups
(vertical lines indicate nominal margins).
\begin{equation}\label{xx}
\begin{split}
a& =b+c-d\\
& \quad +e-f\\
& =g+h\\
& =i
\end{split}
\end{equation}
a = b + c −d
+ e −f
= g + h
= i
(1.1)
\begin{multline}
a+b+c+d+e+f\\
+i+j+k+l+m+n\\
+o+p+q+r+s
\end{multline}
a + b + c + d + e + f
+ i + j + k + l + m + n
+ o + p + q + r + s (1.2)
\begin{gather}
a_1=b_1+c_1\\
a_2=b_2+c_2-d_2+e_2
\end{gather}
a
1
= b
1
+ c
1
(1.3)
a
2
= b
2
+ c
2
− d
2
+ e
2
(1.4)
\begin{align}
a_1& =b_1+c_1\\
a_2& =b_2+c_2-d_2+e_2
\end{align}
a
1
= b
1
+ c
1
(1.5)
a
2
= b
2
+ c
2
− d
2
+ e
2
(1.6)
\begin{align}
a_{11}& =b_{11}&
a_{12}& =b_{12}\\
a_{21}& =b_{21}&
a_{22}& =b_{22}+c_{22}
\end{align}
a
11
= b
11
a
12
= b
12
(1.7)
a
21
= b
21
a
22
= b
22
+ c
22
(1.8)
\begin{alignat}{2}
a_1& =b_1+c_1& &+e_1-f_1\\
a_2& =b_2+c_2&{}-d_2&+e_2
\end{alignat}
a
1
= b
1
+ c
1
+ e
1
− f
1
(1.9)
a
2
= b
2
+ c
2
− d
2
+ e
2
(1.10)
\begin{flalign}
a_{11}& =b_{11}&
a_{12}& =b_{12}\\
a_{21}& =b_{21}&
a_{22}& =b_{22}+c_{22}
\end{flalign}
a
11
= b
11
a
12
= b
12
(1.11)
a
21
= b
21
a
22
= b
22
+ c
22
(1.12)
Note 1. Applying * to any primary environment will suppress the assignment of equation numbers. How-
ever, \tag may be used to apply a visible label, and \eqref can be used to reference such manually tagged
lines. Use of either * or a \tag on a subordinate environment is an error.
Note 2. The split environment is something of a special case. It is a subordinate environment that can
be used as the contents of an equation environment or the contents of one “line” in a multiple-equation
structure such as align or gather.
Note 3. The primary environments gather, align and alignat have subordinate “-ed” counterparts
(gathered, aligned and alignedat) that can be used as components of more complicated displays, or
within in-line math. These “-ed” environments can be positioned vertically using an optional argument
[t], [c] or [b].
Note 4. The name flalign is meant as “full length”, not “flush left” as often mistakenly reported. However,
since a display occupying the full width will often begin at the left margin, this confusion is understandable.
The indent applied to flalign from both margins is set with \multlinegap.
Short Math Guide for L
A
T
E
X, version 2.0 (2017/12/22) 5
2.2. Automatic numbering and cross-referencing. To get an auto-numbered equa-
tion, use the equation environment; to assign a label for cross-referencing, use the \label
command:
\begin{equation}\label{reio}
...
\end{equation}
To get a cross-reference to an auto-numbered equation, use the \eqref command:
... using equations~\eqref{ax1} and~\eqref{bz2}, we
can derive ...
The above example would produce something like
using equations (3.2) and (3.5), we can derive
In other words, \eqref{ax1} is equivalent to (\ref{ax1}), but the parentheses produced
by \eqref are always upright.
To give your equation numbers the form m.n (section-number.equation-number), use
the \numberwithin command in the preamble of your document:
\numberwithin{equation}{section}
For more details on custom numbering schemes see [Lam, §6.3, §C.8.4].
The subequations environment provides a convenient way to number equations in a
group with a subordinate numbering scheme. For example, supposing that the current
equation number is 2.0, write
\begin{equation}\label{first}
a=b+c
\end{equation}
some intervening text
\begin{subequations}\label{grp}
\begin{align}
a&=b+c\label{second}\\
d&=e+f+g\label{third}\\
h&=i+j\label{fourth}
\end{align}
\end{subequations}
to get
a = b + c (2.1)
some intervening text
a = b + c (2.2a)
d = e + f + g (2.2b)
h = i + j (2.2c)
By putting a \label command immediately after \begin{subequations} you can get a
reference to the parent number; \eqref{grp} from the above example would produce (2.2)
while \eqref{second} would produce (2.2a).
An example at https://tex.stackexchange.com/questions/220001/ shows a variant
of the above example, with numbering like (2.1), (2.1a), . . . , rather than (2.1), (2.2a), . . . .
This is accomplished by using \tag with a cross-reference to the principal component of
the subequation number.
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