\fbox{..}---make a box
\hfill ----make line space
\hrule ---draw a line
\newpage
\frak{F}---------fourier

\begin{description}
\item{(1)} $T_X$ is bounded below, i.e., $\|T_X c\|_H \geq K \|c\|_{l_2(X)} \; \; \forall c\in l_2(X)\;$ for some positive constant $K$.
\item{(2)} $\ran T_X$ is closed and $\ker T_X=\{0\}.$
\item{(3)} There exists $R\in bL(H)$ s.t.\ $\langle R x, x'\rangle=\delta_{x x'} \;\;\; \forall x,x'\in X.$
\end{description}

\begin{verbatim}
function [r] = lattice(m, n, s)
% function [r] = lattice(m, n, s)
% m and n are integers and s is a 2-by-2 invertible integer
% matrix.
\end{verbatim}

$c_0(k) = \left\{ \matrix{e^{-i\theta_1} & if & j\ge 0 \cr
                                                               0 & if & j<0 \cr} \right. $
$$B_1(t):=\cases{1, &  $ 0 \le t \le 1$   \cr
                             0,  & otherwise.  \cr}$$
$$ A+B=C \eqno{(1)} $$   print the eqation # to right. (\leqno--> left)

In a file
\documentclass[11pt,epic,eepic]{article}
\usepackage{ graphicx, latexsym, amssymb, amscd, psfrag}

\newcommand{\R}{{\mathbb R}}
\newcommand{\Z}{{\mathbb Z}}
\newcommand{\N}{{\mathbb N}}
\newcommand{\T}{{\mathbb T}}
\newcommand{\C}{{\mathbb C}}
\newcommand{\qed}{\hfill $\Box$ \hfill \\}
\newcommand{\hence}{.^{\textstyle\cdot}.~~}
\newcommand{\since}{.^{\kern-6.5pt{\textstyle\cdot\kern5pt\cdot}}~~}
\newcommand{\lined}{\hfill \hrule\hfill\vspace{1mm} \\}

%\newcommand{\nRightarrow}{ \Rightarrow {\kern-13,5pt{\backslash}}~~}
%\newcommand{\nLeftarrow}{ \Leftarrow {\kern-11pt{\slash}}~~}
\input amssym.def

\begin{document}

\end{document}


Drawing
1 plot any function in maple
2 export to latex with file name like try4
3 go to your tex directory, you can find the try401.eps file there
4 in the tex file which you want to put the graph, begin with the following (1) and (2)
\documentclass{article} %%---(1)
\usepackage{graphicx, latexsym} %% ---(2)
5 in tex file where you want to put the graph, do the following
\begin{center}
\includegraphics[height=5cm,width=5cm,angle=30]{try201.eps}
\end{center}
6. (ex. /public/html/teaching/math113/spring06> gvim formula.tex)
\begin{center}
\psfrag {1}{$\sqrt{3}$}
\psfrag {2}{$1$}
\psfrag {c}{$45^\circ=\frac{\pi}{4} $}
\psfrag {d}{Reference triangles}
\includegraphics[height=3cm,width=10cm]{ref.eps}
\end{center}


> xfig & (in the cmdtool)
after finishing drawing, click Export
determine the output filename ex) rectangle.eps
in Language bar: Encapsulated Postscript
put the file in the directory
click export
make rectangle.fig file if you want to modify the figure later
do just \includegraphics[height=5cm, width=2cm]{rectangle.eps} in your tex file (like math722.tex)

Color


\usepackage[usenames]{color}
\begin{document}
\pagecolor[named]{GreenYellow} %background color
{\color{BrickRed} This color is BrickRed}
\end{document}
68 named colors:
GreenYellow, Yellow, Goldenrod, Dandelion, Apricot, Peach, Melon, YellowOrange, Orange, BurntOrange, Bittersweet, RedOrange, Mahogany, Maroon, BrickRed, Red, OrangeRed, RubineRed, WildStrawberry, Salmon, CarnationPink, Magenta, VioletRed, Rhodamine, Mulberry, RedViolet, Fuchsia, Lavender, Thistle, Orchid, DarkOrchid, Purple, Plum, Violet, RoyalPurple, BlueViolet, Periwinkle, CadetBlue, CornflowerBlue, MidnightBlue, NavyBlue, RoyalBlue, Blue, Cerulean, Cyan, ProcessBlue, SkyBlue, Turquoise, TealBlue, Aquamarine, BlueGreen, Emerald, JungleGreen, SeaGreen, Green, ForestGreen, PineGreen, LimeGreen, YellowGreen, SpringGreen, OliveGreen, RawSienna, Sepia, Brown,Tan,Gray  click here to see the colors(pdf)

If you need more colors, you can define your own color;
\definecolor{myred}{rgb}{.7,0.3,0.45}
{\color{myred}This color is myred}


Basics

Links
Latex;help
Latex
TeX Users Group Home Page
Search the Comprehensive TeX Archive Network
texman-- easy to see about table, matrix, ...
symbols.pdf
How to format Matlab code for LATEX
LATEX@dd: Hints


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