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TEXAMS-LATEX13.1LATEXmathematics\(\)$$\begin{math}\end{math}Add$a$squaredand$b$squaredtoget$c$squared.Or,usingamoremathematicalapproach:$c^{2}=a^{2}+b^{2}$Addasquaredandbsquaredtogetcsquared.Or,usingamoremathematicalapproach:c2=a2+b2\TeX{}ispronouncedas$\tau\epsilon\chi$.\\[6pt]100~m$^{3}$ofwater\\[6pt]Thiscomesfrommy$\heartsuit$TEXispronouncedas¿²Â.100m3ofwaterThiscomesfrommy~\[\]\begin{displaymath}\end{displaymath}LATEXequation1CTAN:/tex-archive/macros/latex/required/amslatex38Add$a$squaredand$b$squaredtoget$c$squared.Or,usingamoremathematicalapproach:\begin{displaymath}c^{2}=a^{2}+b^{2}\end{displaymath}Andjustonemoreline.Addasquaredandbsquaredtogetcsquared.Or,usingamoremathematicalapproach:c2=a2+b2Andjustonemoreline.\label\ref\begin{equation}\label{eq:eps}\epsilon0\end{equation}From(\ref{eq:eps}),wegather\ldots²0(3.1)From(3.1),wegather...$\lim_{n\to\infty}\sum_{k=1}^n\frac{1}{k^2}=\frac{\pi^2}{6}$limn!1Pnk=11k2=¼26\begin{displaymath}\lim_{n\to\infty}\sum_{k=1}^n\frac{1}{k^2}=\frac{\pi^2}{6}\end{displaymath}limn!1nXk=11k2=¼261.\,\quad\qquad2.3.\textrm{...}\begin{equation}\forallx\in\mathbf{R}:\qquadx^{2}\geq0\end{equation}8x2R:x2¸0(3.2)3.239\begin{equation}x^{2}\geq0\qquad\textrm{forall}x\in\mathbf{R}\end{equation}x2¸0forallx2R(3.3)blackboardboldamsfontsamssymb\mathbb\begin{displaymath}x^{2}\geq0\qquad\textrm{forall}x\in\mathbb{R}\end{displaymath}x2¸0forallx2R3.2{...}\begin{equation}a^x+y\neqa^{x+y}\end{equation}ax+y6=ax+y(3.4)3.3503.10LowercaseGreekletters\alpha,\beta,\gamma,...\Gamma,\Delta,...2$\lambda,\xi,\pi,\mu,\Phi,\Omega$¸;»;¼;¹;Φ;Ω^_2LATEX2AlphaA40$a_{1}$\qquad$x^{2}$\qquad$e^{-\alphat}$\qquad$a^{3}_{ij}$\\$e^{x^2}\neq{e^x}^2$a1x2e¡®ta3ijex26=ex2squareroot\sqrtn:\sqrt[n]LATEX\surd$\sqrt{x}$\qquad$\sqrt{x^{2}+\sqrt{y}}$\qquad$\sqrt[3]{2}$\\[3pt]$\surd[x^2+y^2]$pxpx2+py3p2p[x2+y2]\overline\underline$\overline{m+n}$\qquad$\underline{m+n}$m+nm+n\overbrace\underbrace$\underbrace{a+b+\cdots+z}_{26}$a+b+¢¢¢+z|{z}26˜tilde503.1\widetilde\widehat'0prime\begin{displaymath}y=x^{2}\qquady'=2x\qquady''=2\end{displaymath}y=x2y0=2xy00=2Vectorsarrowsymbols\vec\overrightarrow\overleftarrowAB\begin{displaymath}\veca\quad\overrightarrow{AB}\end{displaymath}~a¡¡!AB\cdot3.341\begin{displaymath}v={\sigma}_1\cdot{\sigma}_2{\tau}_1\cdot{\tau}_2\end{displaymath}v=¾1¢¾2¿1¢¿2LATEX\arccos\cos\csc\exp\ker\limsup\min\arcsin\cosh\deg\gcd\lg\ln\Pr\arctan\cot\det\hom\lim\log\sec\arg\coth\dim\inf\liminf\max\sin\sinh\sup\tan\tanh\[\lim_{x\rightarrow0}\frac{\sinx}{x}=1\]limx!0sinxx=1modulofunction\bmod“amodb”\pmod“x´a(modb)”fraction\frac{...}{...}1=2$1\frac{1}{2}$~hours\begin{displaymath}\frac{x^{2}}{k+1}\qquadx^{\frac{2}{k+1}}\qquadx^{1/2}\end{displaymath}112hoursx2k+1x2k+1x1=2{...\choose...}{...\atop...}3\begin{displaymath}{n\choosek}\qquad{x\atopy+2}\end{displaymath}µnk¶xy+2\stackrel3amsmath\binom\genfracnnewcommandfnnewatopg[2]%ngenfracfgfgf0ptgf1gf#1gf#2gg\atop42\begin{displaymath}\intf_N(x)\stackrel{!}{=}1\end{displaymath}ZfN(x)!=1integraloperator\intsumoperator\sumproductoperator\prod^_4\begin{displaymath}\sum_{i=1}^{n}\qquad\int_{0}^{\frac{\pi}{2}}\qquad\prod_\epsilon\end{displaymath}nXi=1Z¼20Y²bracesdelimitersTEX[hkl\{\updownarrow523.8\begin{displaymath}{a,b,c}\neq\{a,b,c\}\end{displaymath}a;b;c6=fa;b;cg\leftTEX\right\left‘\right.’!\begin{displaymath}1+\left(\frac{1}{1-x^{2}}\right)^3\end{displaymath}1+µ11¡x2¶3\big,\Big,\bigg\Bigg54AMS-LATEX/511pt12ptexscaleamsmath3.443$\Big((x+1)(x-1)\Big)^{2}$\\$\big(\Big(\bigg(\Bigg($\quad$\big\}\Big\}\bigg\}\Bigg\}$\quad$\big\|\Big\|\bigg\|\Bigg\|$³(x+1)(x¡1)´2¡³µÃªo¾)°°°°°°°°°°°°°°threedots\ldots\cdots\vdots\ddotsdiagonaldots3.5\begin{displaymath}x_{1},\ldots,x_{n}\qquadx_{1}+\cdots+x_{n}\end{displaymath}x1;:::;xnx1+¢¢¢+xn3.4TEX\,318quad(),\:418quad()\;518quad()\Ã\quad()\qquad()\quad‘M’\!¡318quad()\newcommand{\ud}{\mathrm{d}}\begin{displaymath}\int\!\!\!\int_{D}g(x,y)\,\udx\,\udy\end{displaymath}insteadof\begin{displaymath}\int\int_{D}g(x,y)\udx\udy\end{displaymath}ZZDg(x;y)dxdyinsteadofZZDg(x;y)dxdy‘d’AMS-LATEX\iint,\iiint,\iiiint\idotsintamsmath44\newcommand{\ud}{\mathrm{d}}\begin{displaymath}\iint_{D}\,\udx\,\udy\end{displaymath}ZZDdxdytestmath.texAMS-LATEX“TheLaTeXCompanion”3.5arraysarrayarraystabular\\\begin{displaymath}\mathbf{X}=\left(\begin{array}{ccc}x_{11}&x_{12}&\ldots\\x_{21}&x_{22}&\ldots\\\vdots&\vdots&\ddots\end{array}\right)\end{displaymath}X=0BB@x11x12:::x21x22:::.........1CCAarray“.”\begin{displaymath}y=\left\{\begin{array}{ll}a&\textrm{if$dc$}\\b+x&\textrm{inthemorning}\\l&\textrm{alldaylong}\end{array}\right.\end{displaymath}y=8:aifdcb+xinthemorninglalldaylongtabulararray\begin{displaymath}\left(\begin{array}{c|c}1&2\\\hline3&4\end{array}\right)\end{displaymath}Ã1234!3.545equationsystemeqnarrayeqnarray*equationeqnarrayeqnarray*eqnarrayeqnarray*{rcl}\\\begin{eqnarray}f(x)&=&\cosx\\f'(x)&=&-\sinx\\\int_{0}^{x}f(y)dy&=&\sinx\end{eqnarray}f(x)=cosx(3.5)f0(x)=¡sinx(3.6)Zx0f(y)dy=sinx(3.7)\setlength\arraycolsep{2pt}{\setlength\arraycolsep{2pt}\begin{eqnarray}\sinx&