Hardcore L
A
T
E
XMath
RSI 2011 Sta
June 18, 2011
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Part I: basic features
 Review
 Theorems and proofs such
2
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Entering math mode
Use $...$ or \(...\) for text math mode and \[...\] or $$...$$
for display math mode:
This sentence refers to integers $n$ and \(m\) and
reminds you that
\[ \int_0^\infty e^{-t} dt = 1. \]
This sentence refers to integers n and m and reminds you that
Z
1
0
e
t
dt= 1:
It’s probably better to use $...$ than \(...\), because dollar
signs are more traditional, and thus easier to read. But for
displayed equations, \[...\] is preferable.
3
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Punctuation
Inline equations should not contain punctuation belonging to
the sentence.
Because the ideal $I$ contains $x$, ...
Displayed equations that end sentences should contain a period.
Therefore, the value of the integral is
\[ \int_0^\infty e^{-t} dt = 1. \]
4
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Numbered equations
Use the equation environment to create a numbered equation.
Put a label inside it using \label{foo} and then use \ref{foo}
to typeset the equation number. Preferred: You can type
\eqref{foo} to add parentheses automatically.
It follows that
\begin{equation}
\label{verywrong}
6 \times 9 = 42.
\end{equation}
From \eqref{verywrong} we can deduce we screwed up somewhere.
It follows that
69= 42:
(1)
From (1) we can deduce we screwed up somewhere.
5
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Variables
For most variables with one-character names, just type the
character in math mode: $x + y$ for x+y.
For Greekletters,backslashtheirnames:$\alpha, \beta, \Gamma$
for ;; . (There is no $\Alpha$; simply use $A$.)
For long names, there are two tasteful options:
\[ \mathit{long\_variable\_name} + \text{roman name} = 240 \]
long
variable
name
+roman name= 240
Don’t just type a long name into math mode or you’ll get
long
v
ariable
n
ame:
6
Variables in other fonts
A
\mathbf{A}
F
\mathcal{F}
(capitals only)
Z
\mathbb{Z}
(capitals only)
ab \mathfrak{ab}
L
\mathscr{L}
(capitals only; requires mathrsfs package)
Put only the variable inside the font-changing command:
\[ \mathfrak{c}(\mathfrak{a} + \mathfrak{b}) \]
c(a+b)
7
Roman operators
Many notations like sin(x) and log(x) are typeset in upright
characters. Say \sin(x), \log(x), etc. For comparison, sin(x)
produces sin(x), which is italicized.
For the condition under \lim, \max, or the like, use a subscript:
\[ \lim_{x\to \infty} 1/x = 0 \]
lim
x!1
1=x= 0
(Note that subscripts and superscripts which are more than one
character need brackets. For instance, 10^10 appears as 10
1
0.)
8
Dening your own operators
To dene your own, say
\DeclareMathOperator{\spec}{Spec}
in preamble.tex and then use $\spec A[x]$ for SpecA[x]. You
can also type $\operatorname{Spec} A[x]$ to get the same result
without dening a command.
9
Big operators
For big operators such as sums (\sum), products (\prod), and
integrals (\int), use subscripts and superscripts to get the
limits:
\[ \int_{1}^{\infty} \frac{dx}{x^2} = 1. \]
Z
1
1
dx
x
2
=1:
\[ \sum_{k=1}^{\infty} \frac{1}{k^2} = \frac{\pi^2}{6}. \]
1
X
k=1
1
k
2
=
2
6
:
10
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