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X Math for Undergrads
Rule One Any mathematics at all, even a single character,
goes in a mathematical setting. Thus, for ``the value of xis
7'' enter `the value of \textbackslash ( x \textbackslash ) is \textbackslash ( 7 \textbackslash )'.
Template Your document should contain at least this.
\textbackslash do c um en t cl a ss \{ a r ti cl e \}
\textbackslash us ep a ck a ge \{ a ms ma t h , amss y mb , a ms t hm \}
\textbackslash us ep a ck a ge [ u tf 8 ]\{ in pu t en c \}
\textbackslash b e gi n \{ d oc u me n t \}
-- d oc u m en t bod y here --
\textbackslash e n d \{ do c u me n t \}
Common constructs
x2x\textasciicircum 2 \surd 2,n
\surd 3\textbackslash sqrt\{2\},\textbackslash sqrt[n]\{3\}
xi,j x\]\{i,j\} 2
3,2/3\textbackslash frac\{2\}\{3\},2/3
Calligraphic letters Use as \textbackslash ( \textbackslash mathcal\{A\} \textbackslash ).
\scrA \scrB \scrC \scrD \scrE \scrF \scrG \scrH \scrI \scrJ \scrK \scrL \scrM \scrN \scrO \scrP \scrQ \scrR \scrS \scrT \scrU \scrV \scrW \scrX \scrY \scrZ
Greek
\alpha \textbackslash alpha \xi ,\Xi \textbackslash xi,\textbackslash Xi
\beta \textbackslash beta oo
\gamma ,\Gamma \textbackslash gamma,\textbackslash Gamma \pi ,\Pi \textbackslash pi,\textbackslash Pi
\delta ,\Delta \textbackslash delta,\textbackslash Delta \varpi \textbackslash varpi
\epsilon \textbackslash epsilon \rho \textbackslash rho
\varepsilon \textbackslash varepsilon \varrho \textbackslash varrho
\zeta \textbackslash zeta \sigma ,\Sigma \textbackslash sigma,\textbackslash Sigma
\eta \textbackslash eta \varsigma \textbackslash varsigma
\theta \Theta \textbackslash theta,\textbackslash Theta \tau \textbackslash tau
\vargamma \textbackslash vartheta \upsilon ,\Upsilon \textbackslash upsilon,\textbackslash Upsilon
\iota \textbackslash iota \phi ,\Phi \textbackslash phi,\textbackslash Phi
\kappa \textbackslash kappa \varphi \textbackslash varphi
\lambda \Lambda \textbackslash lambda,\textbackslash Lambda \chi \textbackslash chi
\mu \textbackslash mu \psi ,\Psi \textbackslash psi,\textbackslash Psi
\nu \textbackslash nu \omega ,\Omega \textbackslash omega,\textbackslash Omega
Sets and logic
\cup \textbackslash cup \BbbR \textbackslash mathbb\{R\} \forall \textbackslash forall
\cap \textbackslash cap \BbbZ \textbackslash mathbb\{Z\} \exists \textbackslash exists
\subset \textbackslash subset \BbbQ \textbackslash mathbb\{Q\} \neg \textbackslash neg
\subseteq \textbackslash subseteq \BbbN \textbackslash mathbb\{N\} \vee \textbackslash vee
\supset \textbackslash supset \BbbC \textbackslash mathbb\{C\} \wedge \textbackslash wedge
\supseteq \textbackslash supseteq \varnothing \textbackslash varnothing \vdash \textbackslash vdash
\in \textbackslash in \emptyset \textbackslash emptyset | =\textbackslash models
\ni \textbackslash ni \aleph \textbackslash aleph \Rightarrow \textbackslash Rightarrow
/\in \textbackslash notin \setminus \textbackslash setminus \nRightarrow \textbackslash nRightarrow
\not \in \textbackslash not\textbackslash in \equiv \textbackslash equiv
Negate an operator, as in \not \subset , with \textbackslash not\textbackslash subset. Get the
set complement A\sansc with A\textasciicircum \{\textbackslash mathsf\{c\}\}, get A\complement with
A\textasciicircum \{\textbackslash complement\}, or get \=
Awith \textbackslash bar\{A\}.
Decorations
f\prime f' \.a\textbackslash dot\{a\} \~x\textbackslash tilde\{x\}
f\prime \prime f'' \"a\textbackslash ddot\{a\} \=x\textbackslash bar\{x\}
\Sigma \ast \textbackslash Sigma\textasciicircum \{*\} \^x\textbackslash hat\{x\} \vec{}x \textbackslash vec\{x\}
If the decorated letter is ior jthen some decorations need
\textbackslash imath or \textbackslash jmath, as in \textbackslash vec\{\textbackslash imath\}. Some authors use
boldface for vectors: \textbackslash boldsymbol\{x\}.
Entering \textbackslash overline\{x+y\} produces x+y, and
\textbackslash widehat\{x+y\} gives \widehat
x+y. Comment on an expression as
here (there is also \textbackslash overbrace\{..\}).
x+y
\underbrace{} \underbrace{}
| A|
\textbackslash underbrace\{x+y\}\]\{|A|\}
Dots Use low dots in a list \{ 0,1,2, . . .\} , entered as
\textbackslash \{0,1,2,\textbackslash ,\textbackslash ldots\textbackslash \}. (If you use \textbackslash ldots in plain text as
London, Paris, \textbackslash ldots\{\}\textbackslash ,. note the thinspace \textbackslash , be-
fore the period.) Use centered dots in a sum or product
1 + \cdot \cdot \cdot + 100, entered as 1+\textbackslash cdots+100. You can also get
vertical dots \textbackslash vdots and diagonal dots \textbackslash ddots.
Roman names Enter \textbackslash tan(x), with a backslash, instead
of tan(x). These get the same treatment.
sin \textbackslash sin sinh \textbackslash sinh arcsin \textbackslash arcsin
cos \textbackslash cos cosh \textbackslash cosh arccos \textbackslash arccos
tan \textbackslash tan tanh \textbackslash tanh arctan \textbackslash arctan
sec \textbackslash sec coth \textbackslash coth min \textbackslash min
csc \textbackslash csc det \textbackslash det max \textbackslash max
cot \textbackslash cot dim \textbackslash dim inf \textbackslash inf
exp \textbackslash exp ker \textbackslash ker sup \textbackslash sup
log \textbackslash log deg \textbackslash deg lim inf \textbackslash liminf
ln \textbackslash ln arg \textbackslash arg lim sup \textbackslash limsup
lg \textbackslash lg gcd \textbackslash gcd lim \textbackslash lim
Other symbols
<<\angle \textbackslash angle \cdot \textbackslash cdot
\leq \textbackslash leq \measuredangle \textbackslash measuredangle \pm \textbackslash pm
>>\ell \textbackslash ell \mp \textbackslash mp
\geq \textbackslash geq \| \textbackslash parallel \times \textbackslash times
\not =\textbackslash neq 45\circ 45\textasciicircum \{\textbackslash circ\} \div \textbackslash div
\ll \textbackslash ll \sim
=\textbackslash cong \ast \textbackslash ast
\gg \textbackslash gg \ncong \textbackslash ncong | \textbackslash mid
\approx \textbackslash approx \sim \textbackslash sim \nmid \textbackslash nmid
\asymp \textbackslash asymp \simeq \textbackslash simeq n!n!
\equiv \textbackslash equiv \nsim \textbackslash nsim \partial \textbackslash partial
\prec \textbackslash prec \oplus \textbackslash oplus \nabla \textbackslash nabla
\preceq \textbackslash preceq \ominus \textbackslash ominus \hbar \textbackslash hbar
\succ \textbackslash succ \odot \textbackslash odot \circ \textbackslash circ
\succeq \textbackslash succeq \otimes \textbackslash otimes \star \textbackslash star
\propto \textbackslash propto \oslash \textbackslash oslash \surd \textbackslash surd
.
=\textbackslash doteq \upharpoonright \textbackslash upharpoonright \checkmark \textbackslash checkmark
Enter a|b for the divides relation a| b. Use \textbackslash mid as in
\textbackslash \{a\textbackslash in S\textbackslash mid\textbackslash text\{\textbackslash (a=0\textbackslash ) or \textbackslash (a\textbackslash ) is odd\}\textbackslash \} for the
set \{ a\in S| a= 0 or ais odd\} .
Variable-sized operators The summation \sum 3
j=0 j2
\textbackslash sum\]\{j=0\}\textasciicircum 3 j\textasciicircum 2 and the integral \int 3
x=0 x2dx
\textbackslash int\]\{x=0\}\textasciicircum 3 x\textasciicircum 2\textbackslash ,dx expand when displayed.
3
\sum
j=0
j2\int 3
x=0
x2dx
These do the same.
\int \textbackslash int \int \int \int \textbackslash iiint \bigcup \textbackslash bigcup
\int \int \textbackslash iint \oint \textbackslash oint \bigcap \textbackslash bigcap
