thesis notes - wikispacesnotes.pdfthesis notes 9 messages mani thu, ... {this is first chapter}...
TRANSCRIPT
1/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
usman chaudry <[email protected]>
Thesis Notes9 messages
Mani <[email protected]> Thu, Aug 9, 2012 at 12:59 AMTo: usman chaudry <[email protected]>
Personal Agents:ECAI2012DocSymposiumChair
ECAI2012GeneralChair
ECAI2012IntlRuleChalChair
ECAI2012IntlRuleChalSteerCommitChair
ECAI2012LiaisonChair
ECAI2012LocalChair
ECAI2012MetaAndSocialChair
ECAI2012PanelChair
ECAI2012ProgramChair
ECAI2012PublicityChair
ECAI2012SteeringChair
STRUCT2012AdvisoryBoard
STRUCT2012CEI
STRUCT2012CoChairs
STRUCT2012DefeasibleLogic
STRUCT2012MAS
STRUCT2012ModalLogic
STRUCT2012PSOA
STRUCT2012ReactionRules
STRUCT2012TGAgent
STRUCT2012UnCertReason
Organizational Agents:
SymposiumPlanner Super-Organizational Agent (RuleML-2012 & RuleML Structure)
Sub-Organizational Agent (RuleML-2012)
Sub-Organizational Agent (RuleML Structure)
Mani <[email protected]> Thu, Aug 9, 2012 at 1:00 AMTo: usman chaudry <[email protected]>
UNBThesis2.tex
\documentclass[12pt]{unbthesis}
%\usepackage[left=4cm, right=2.5cm, top=2.5cm, bottom=2.5cm]{geometry}
\usepackage{graphicx}
\usepackage{subfig}
\usepackage[subfigure]{tocloft} % no number for Vita in ToC
\usepackage{fancyhdr}
\usepackage[english]{babel}
\usepackage{footmisc}
\usepackage{algorithmic}
\usepackage{listings}
\usepackage{fancyvrb}
\title{Type Title of Thesis here}
\author{Name of Candidate}
\predegree{Previous Degrees (i.e. Degree, University, Year)\\
Bachelor of Arts, UNB, 1999}
\degree{Name of Degree}
\gau{your GAU}
\supervisor{name1,degree department/field\\ & name2, degree
department/field}
\examboard{name1, degree, department/field,
Chair\\ & name2, degree, department}
\externalexam{name, degree,
department/field, institution}
\date{Month, Year of submission to Graduate School}
\copyrightyear{Year of graduation}
\setlength\parindent{0pt}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{definition}{Definition}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{notation}{Notation}[section]
\begin{document}
\unbtitlepage
\setcounter{secnumdepth}{3} \setcounter{tocdepth}{3}
2/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
\pagenumbering{roman} \setcounter{page}{1}
\include{dedication}
\include{abstract}
\include{acknowledgments}
%%-----------Table of Contents------------------
\renewcommand{\contentsname}{Table of Contents}
\tableofcontents{}
\addcontentsline{toc}{chapter}{Table of Contents}
%%------------List of Tables----------------------
\listoftables{}
\addcontentsline{toc}{chapter}{List of Tables}
%%------------List of Figures----------------------
\listoffigures{}
\addcontentsline{toc}{chapter}{List of Figures}
\include{abbreviations}
%%-------------change single space to double space--------
\doublespacing \pagenumbering{arabic} \setcounter{page}{1}
\include{chapter1}
\include{chapter2}
\include{chapter3}
\include{chapter4}
\include{chapter5}
%\include{bibliography}
% changes default name Bibliography to References
%\renewcommand{\bibname}{References}
\bibliographystyle{amsplain}
\bibliography{mybibliography}
\addcontentsline{toc}{chapter}{Bibliography}
\include{appendices2}
\include{glossary}
\include{vita}
\end{document}
Mani <[email protected]> Thu, Aug 9, 2012 at 1:01 AMTo: usman chaudry <[email protected]>
%%-----------Chapters start-------------------------------------
%%-----------Chapter 1------------------------------------------
\chapter{This is first chapter}
%\setcounter{secnumdepth}{3} \pagenumbering{arabic}
%\setcounter{page}{1} \pagestyle{myheadings}
%\markboth{}{}\markright{} \rhead{\thepage} \setcounter{page}{1}
%\pagestyle{myheadings} \pagenumbering{arabic} \rhead{\thepage}
%\setcounter{page}{1}
\section{ A section}
\subsection{A subsection}
This is a subsection. This is a subsection. This is a subsection.
This is a subsection. This is a subsection. This is a subsection.
This is a subsection. This is \hfill a subsection.
Mani <[email protected]> Thu, Aug 9, 2012 at 1:05 AMTo: usman chaudry <[email protected]>
%%----------Chapter 2------------------------------------------
\chapter{This is second chapter}
\section{Example citation}
%%---------------example citation---------------------
Start writing from here. Here is a citation~\cite{Knuth92}
\section{Example Tables}
\subsection{A table with border} another paragraph and more text
and more and more and more and more and more text
3/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
%%------------------example table--------------------
\begin{table}[!h]
\caption{Example table}
\begin{center}
\begin{tabular}{| l || r | r | r | c |}
\hline
Name&Exam1&Exam2&Exam3&Grade\\
\hline\hline
John&19& 28&33&C \\
\hline
Smith&49& 35&60&B \\
\hline
Peter&76& 38&59&A \\
\hline
\end{tabular}
\end{center}
\end{table}
\subsection{A table without border}
Here is another example table without border. some symbols with
label can be refereed later on.
\begin{table}[!h]
\caption{Variable-sized Symbols}
\begin{center}
\begin{tabular}{l l l l l l}
$\sum$ \label{p1}&$\backslash$sum &$\bigcap$ \label{p2}&$\backslash$bigcap &$\bigodot$ &$\backslash$bigodot \\
$\prod$ &$\backslash$prod &$\bigcup$ &$\backslash$bigcup &$\bigotimes$ &$\backslash$bigotimes\\
$\coprod$ &$\backslash$coprod &$\bigsqcup$ &$\backslash$bigsqcup &$\bigoplus$ &$\backslash$bigoplus \\
$\int$ &$\backslash$int &$\bigvee$ &$\backslash$bigvee &$\biguplus$ &$\backslash$biguplus\\
$\oint$ &$\backslash$oint &$\bigwedge$ &$\backslash$bigwedge
\end{tabular}
\end{center}
\end{table}
\section{Example List}
\subsection{Example dotted list}
%%-----------------example dotted list--------------------
4/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
\smallskip
\textbf{Some special characters in TeX:}
\begin{itemize}
\item Accents
\item Braces
\item Dollar signs
\end{itemize}
\subsection{Example numbered list}
%%----------------example numbered list---------------------
\smallskip
\textbf{Some special characters in TeX:}
\begin{enumerate}
\item Accents
\item Braces
\item Dollar signs
\end{enumerate}
\section{Math Example}
\subsection{Inline math mode}
%%-------------------example math equation----------
Mathematical material to be typeset inline must be surrounded by a
single dollar sign. For example: $a2 + b2 = c2$.
\subsection{Displayed math}
This is a displayed math example without numbering.
\[
\lim_{x \to a}f(x)
\]
\[
\left|\sum_{i=1}n a_ib_i\right| \le \left(\sum_{i=1}n
a_i2\right){1/2} \left(\sum_{i=1}n b_i2\right){1/2}
\]
This is a math equation with numbering.
\begin{equation}
(a+b)3 = (a+b)2(a+b)
\end{equation}
%%-----------------example aligned equation------------------
This is multiline equation example.
\begin{align}
(a+b)3 &= (a+b)2(a+b)\\
&=(a2+2ab+b2)(a+b)\\
&=(a3+2a2b+ab2) + (a2b+2ab2+b3)\\
&=a3+3a2b+3ab2+b3
\end{align}
%%--------------example matrix-------------------------------
This is a matrix
5/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
\[
\begin{matrix}
a+b & uv & x-y & 5\\
a+b+c & u+v &x+y & 10
\end{matrix}
\]
%%------------example cases----------------------------------
This is a case
\[
f(x)=
\begin{cases}
-x{2}, &\text{if $x<0$;}\\
\alpha+x, &\text{if $0 \leq x \leq 1$;}\\
x{2}, &\text{otherwise.}
\end{cases}
\]
%%-----------example theorem, definition, notation and lemma-----------
\subsection{math theorem, definition, notation and lemma}
\begin{theorem} A polynomial $p(z)$ of degree $n$ over $C$ has $n$ roots.
\end{theorem}
\begin{lemma} A polynomial $p(z)$ of degree $n>0$ over $C$ has at least
one root.
\end{lemma}
\begin{definition}
Let $D_{i}$, $i \in I$, be complete distributive
lattices satisfying condition~\textup{(J)}. Their
$\Pi{*}$ product is defined as follows:
\[
\Pi{*} ( D_{i} \mid i \in I ) =
\Pi ( D_{i}{-} \mid i \in I ) + 1;
\]
that is, $\Pi{*} ( D_{i} \mid i \in I )$ is
$\Pi ( D_{i}{-} \mid i \in I )$ with a new unit element.
\end{definition}
\begin{theorem}
If a lexicographic bottleneck problem can be solved in $O(f(m))$
time, then the type-1 lexicographic balanced optimization problem
can be solved in $O(mf(m))$ time.
\end{theorem}
\begin{theorem}The lexicographic bottleneck problem can be
solved in polynomial time if and only if LBaOP1 can be solved in
polynomial time.
\end{theorem}
\begin{notation}
If $i \in I$ and $d \in D_{i}{-}$, then
\[
\langle \dots, 0, \dots, \overset{i}{d}, \dots, 0,
\dots \rangle
\]
is the element of $\Pi{*} ( D_{i} \mid i \in I )$ whose
$i$th component is $d$ and all the other components
are $0$.
\end{notation}
%%---------------------------example proof---------------------
\subsection{math proof}
\begin{proof}[math theorem proof]
Let the length of every Hamiltonian path in $G$ be $\alpha .$ For
any edge $e=(i,j)\in E(G),$ let $w(e)=c_{ij}.$ Let $H$ be an
arbitrary Hamiltonian cycle in $G$ with
$E(H)=\{e_{1},e_{2},...,e_{n}\}$. For any $i\in \{1,\ldots ,n\},$
$C(H-e_{i})=\alpha .$ Hence $w(e_{i})=\alpha/(n-1)$ for $i=1,\ldots
,n.$ Since $H$ is arbitrary and $G$ is strongly Hamiltonian,
$w(e)=\alpha /(n-1)$ for all $e\in E(G).$
\end{proof}
\section{Graphics example}
\subsection{UNB logo}
%%--------------------example figure-------------------
6/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
The ideal graphics format for inclusion in a LaTex document is
"encapsulated postscript" or eps. Here is an example figure.
\begin{figure}[!hbp]
\begin{center}
\includegraphics{unblogo}
\caption{UNB logo}
\end{center}
\end{figure}
Mani <[email protected]> Thu, Aug 9, 2012 at 1:09 AMTo: usman chaudry <[email protected]>
%%--------------------Chapter 3------------------------
\chapter{This is third chapter}
\section{A section}
%%--------------------example citation-----------------
Start writing from here~\cite{ConcreteMath}
\subsection{A subsection}
some text with footnote\footnote{A first}. more
text\footnote{second} and more.
%%-----------------text superscript, subscript--------------------
A sentence with superscript.\textsuperscript{superscript}. A
sentence with subscript.$_{\mbox{\footnotesize{subscript}}}$
%%-----------------printing verbatim--------------------------------
7/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
\subsection{Printing Verbatim}
\begin{verbatim}
THIS TEXT WILL BE DIRECTLY PRINTED AS IF TYPED ON A TYPEWRITER, WITH
ALL LINE BREAKS AND SPACES, without any LaTex command
being executed.
public class BasicsDemo{
public static void main(String[] args){
int sum = 0;
for (int current = 1; current <= 10; current++){
sum += current;
}
System.out.println("Sum = " + sum);
}
}
\end{verbatim}
\begin{Verbatim}[frame=single, xrightmargin=2pc]
public class BasicsDemo{
public static void main(String[] args){
int sum = 0;
for (int current = 1; current <= 10; current++){
sum += current;
}
8/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
System.out.println("Sum = " + sum);
}
}
\end{Verbatim}
%%---------------program code-------------------------------------
\section{A section}
\subsection{Pretty-printing program code}
\singlespacing
\begin{algorithmic}
\IF {$i\leq0$} \STATE $i\gets1$ \ELSE \IF {$i\geq0$} \STATE
$i\gets0$ \ENDIF \ENDIF
\end{algorithmic}
\subsubsection{Example Java code}
The following is an code example:
\begin{lstlisting}[language=Java]
public class BasicsDemo{
public static void main(String[] args){
int sum = 0;
for (int current = 1; current <= 10; current++){
sum += current;
}
System.out.println("Sum = " + sum);
}
}
\end{lstlisting}
\doublespacing
Mani <[email protected]> Thu, Aug 9, 2012 at 1:10 AMTo: usman chaudry <[email protected]>
9/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
%%----------------Bibliography--------------------------------
\begin{thebibliography}{99}
\addcontentsline{toc}{chapter}{Bibliography}
\bibitem{k1} R.J. Drofnats, \emph{Proof of the Riemann
Hypothesis}, preprint, available at
\texttt{http://www.drofnats.com/riemann.ps}.
\bibitem{k2} P. Erd\H os, \emph{A selection of problems and
results in combinatorics}, Recent trends in combinatorics
(Matrahaza, 1995), Cambridge Univ. Press, Cambridge, 2001, pp. 1--6.
\bibitem{k3}
R.L. Graham, D.E. Knuth, and O. Patashnik, \emph{Concrete
mathematics}, Addison-Wesley, Reading, MA, 1989.
\bibitem{Knuth92} D.E. Knuth, \emph{Two notes on notation}, Amer.
Math. Monthly \textbf{99} (1992), 403--422.
\bibitem{Drofnats} R.J. Drofnats, \emph{Proof of the Riemann
Hypothesis}, preprint, available at
\texttt{http://www.drofnats.com/riemann.ps}.
\bibitem{Erdos01} P. Erd\H os, \emph{A selection of problems and
results in combinatorics}, Recent trends in combinatorics
(Matrahaza, 1995), Cambridge Univ. Press, Cambridge, 2001, pp. 1--6.
\bibitem{ConcreteMath}
R.L. Graham, D.E. Knuth, and O. Patashnik, \emph{Concrete
mathematics}, Addison-Wesley, Reading, MA, 1989.
\end{thebibliography}
Mani <[email protected]> Thu, Aug 9, 2012 at 1:12 AMTo: usman chaudry <[email protected]>
10/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
%%---------------Appendices--------------------------------
\appendix
\chapter{this is Appendix A}
\section{this is section1}
Start writing here.
\begin{equation}
(a+b)3 = (a+b)2(a+b)
\end{equation}
\section{this is section2}
\begin{equation}
(a+b)3 = (a+b)2(a+b)
\end{equation}
\chapter{this is Appendix B}
\section{this is section1} Start writing here.
\begin{equation}
(a+b)3 = (a+b)2(a+b)
\end{equation}
\subsection{this is subsection}
\begin{equation}
(a+b)3 = (a+b)2(a+b)
\end{equation}
Mani <[email protected]> Thu, Aug 9, 2012 at 3:29 PMTo: usman chaudry <[email protected]>
%%----------Chapter 2------------------------------------------
\chapter{This is second chapter}
\section{Example citation}
%%---------------example citation---------------------
Start writing from here. Here is a citation~\cite{Knuth92}
\section{Example Tables}
\subsection{A table with border} another paragraph and more text
and more and more and more and more and more text
%%------------------example table--------------------
11/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
[Quoted text hidden]
\smallskip
\textbf{Some special characters in TeX:}
\begin{itemize}
\item Accents
\item Braces
\item Dollar signs
\end{itemize}
\subsection{Example numbered list}
%%----------------example numbered list---------------------
\smallskip
\textbf{Some special characters in TeX:}
\begin{enumerate}
\item Accents
\item Braces
\item Dollar signs
\end{enumerate}
\section{Math Example}
\subsection{Inline math mode}
%%-------------------example math equation----------
12/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
Mathematical material to be typeset inline must be surrounded by a
single dollar sign. For example: $a2 + b2 = c2$.
\subsection{Displayed math}
This is a displayed math example without numbering.
\[
\lim_{x \to a}f(x)
\]
\[
\left|\sum_{i=1}n a_ib_i\right| \le \left(\sum_{i=1}n
a_i2\right){1/2} \left(\sum_{i=1}n b_i2\right){1/2}
\]
This is a math equation with numbering.
\begin{equation}
(a+b)3 = (a+b)2(a+b)
\end{equation}
%%-----------------example aligned equation------------------
This is multiline equation example.
\begin{align}
(a+b)3 &= (a+b)2(a+b)\\
13/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
&=(a2+2ab+b2)(a+b)\\
&=(a3+2a2b+ab2) + (a2b+2ab2+b3)\\
&=a3+3a2b+3ab2+b3
\end{align}
%%--------------example matrix-------------------------------
This is a matrix
\[
\begin{matrix}
a+b & uv & x-y & 5\\
a+b+c & u+v &x+y & 10
\end{matrix}
\]
%%------------example cases----------------------------------
This is a case
\[
f(x)=
\begin{cases}
-x{2}, &\text{if $x<0$;}\\
\alpha+x, &\text{if $0 \leq x \leq 1$;}\\
x{2}, &\text{otherwise.}
\end{cases}
\]
%%-----------example theorem, definition, notation and lemma-----------
\subsection{math theorem, definition, notation and lemma}
\begin{theorem} A polynomial $p(z)$ of degree $n$ over $C$ has $n$ roots.
\end{theorem}
\begin{lemma} A polynomial $p(z)$ of degree $n>0$ over $C$ has at least
one root.
\end{lemma}
\begin{definition}
Let $D_{i}$, $i \in I$, be complete distributive
lattices satisfying condition~\textup{(J)}. Their
$\Pi{*}$ product is defined as follows:
\[
\Pi{*} ( D_{i} \mid i \in I ) =
\Pi ( D_{i}{-} \mid i \in I ) + 1;
\]
that is, $\Pi{*} ( D_{i} \mid i \in I )$ is
$\Pi ( D_{i}{-} \mid i \in I )$ with a new unit element.
\end{definition}
14/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
\begin{theorem}
If a lexicographic bottleneck problem can be solved in $O(f(m))$
time, then the type-1 lexicographic balanced optimization problem
can be solved in $O(mf(m))$ time.
\end{theorem}
\begin{theorem}The lexicographic bottleneck problem can be
solved in polynomial time if and only if LBaOP1 can be solved in
polynomial time.
\end{theorem}
\begin{notation}
If $i \in I$ and $d \in D_{i}{-}$, then
\[
\langle \dots, 0, \dots, \overset{i}{d}, \dots, 0,
\dots \rangle
\]
is the element of $\Pi{*} ( D_{i} \mid i \in I )$ whose
$i$th component is $d$ and all the other components
are $0$.
\end{notation}
%%---------------------------example proof---------------------
\subsection{math proof}
\begin{proof}[math theorem proof]
Let the length of every Hamiltonian path in $G$ be $\alpha .$ For
any edge $e=(i,j)\in E(G),$ let $w(e)=c_{ij}.$ Let $H$ be an
arbitrary Hamiltonian cycle in $G$ with
$E(H)=\{e_{1},e_{2},...,e_{n}\}$. For any $i\in \{1,\ldots ,n\},$
$C(H-e_{i})=\alpha .$ Hence $w(e_{i})=\alpha/(n-1)$ for $i=1,\ldots
,n.$ Since $H$ is arbitrary and $G$ is strongly Hamiltonian,
$w(e)=\alpha /(n-1)$ for all $e\in E(G).$
\end{proof}
\section{Graphics example}
\subsection{UNB logo}
%%--------------------example figure-------------------
The ideal graphics format for inclusion in a LaTex document is
"encapsulated postscript" or eps. Here is an example figure.
\begin{figure}[!hbp]
\begin{center}
15/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
Community
AoPSWiki LaTeX Guide TeXeR Videos Articles
Search Wiki
Go Search
Page Tools
Page
Discussion
View source
History
Personal tools
131.202.32.11
Talk for this IP address
Log in
Navigation
Main page
Community portal
Recent changes
Random page
Help
Toolbox
What links here
Related changes
Special pages
Printable version
Permanent link
Bookstore
AoPS Curriculum
Contest Prep
Beast Academy
Recommendations
Apparel/Videos
All Products
Gift Certificates
School
Schedule
WOOT
Recommendations
Classroom
My Classes
Math Jams
FAQ
Alcumus
Instructions
FAQ
FTW!
How to Play
FAQ
Leaderboard
FTW! Forum
Reaper
Videos
Prealgebra
Introduction to Algebra
Counting & Probability
MATHCOUNTS
AMC
More Math Videos
Resources
AoPSWiki
LaTeX Guide
TeXeR
Articles
FAQ
Company
Staff
Blog
History
Contact Us
Mail Lists
Work at AoPS
\includegraphics{unblogo}
\caption{UNB logo}
\end{center}
\end{figure}
Mani <[email protected]>To: usman chaudry <[email protected]>
LOGIN/REGISTER
search
You are here: Resources » LaTeX Guide » Symbols
LaTeX:Symbols
LaTeX
About - LaTeX on AoPS - Downloads - Basics - Math - Examples - Pictures - Layout - Symbols - Commands - Packages - Help
This article will provide a short list of commonly used LaTeX symbols.
Contents [hide]
1 Operators
2 Relations
3 Greek Letters
4 Headline text
5 Arrows
6 Dots
7 Accents
8 Others
9 Command Symbols
10 European Language Symbols
11 Bracketing Symbols
12 Multi-Size Symbols
13 Examples
14 See Also
Operators
SymbolCommand SymbolCommandSymbolCommand
\pm \mp \times\div \cdot \ast\star \dagger \ddagger
\amalg \cap \cup\uplus \sqcap \sqcup\vee \wedge \oplus\ominus \otimes \circ\bullet \diamond \lhd\rhd \unlhd \unrhd
\oslash \odot \bigcirc
\triangleleft \Diamond \bigtriangleup\bigtriangledown \Box \triangleright
\setminus \wr
16/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
\sqrt{x}
Relations
SymbolCommand SymbolCommandSymbolCommand
\le \ge \neq
\sim \ll \gg\doteq \simeq \subset\supset \approx \asymp\subseteq \supseteq \cong\smile \sqsubset \sqsupset\equiv \frown \sqsubseteq\sqsupseteq \propto \bowtie\in \ni \prec
\succ \vdash \dashv\preceq \succeq \models
\perp \parallel \|
\mid
Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an n between the \ and the word. Here
are a few examples, plus a few other negations; it works for many of the others as well.
SymbolCommand SymbolCommandSymbolCommand
\nmid \nleq \ngeq
\nsim \ncong \nparallel
\not< \not> \not=
\not\le \not\ge \not\sim
\not\approx \not\cong \not\equiv
\not\parallel \nless \ngtr
\lneq \gneq \lnsim
\lneqq \gneqq
To use other relations not listed here, such as =, >, and <, in LaTeX, you may just use the symbols on your keyboard.
Greek Letters
Lowercase Letters
SymbolCommandSymbolCommandSymbolCommandSymbolCommand
\alpha \beta \gamma \delta\epsilon \varepsilon \zeta \eta\theta \vartheta \iota \kappa\lambda \mu \nu \xi\pi \varpi \rho \varrho
\sigma \varsigma \tau \upsilon\phi \varphi \chi \psi\omega
Capital Letters
SymbolCommandSymbolCommandSymbolCommandSymbolCommand
\Gamma \Delta \Theta \Lambda\Xi \Pi \Sigma \Upsilon\Phi \Psi \Omega
Headline text
Arrows
SymbolCommand SymbolCommand
\gets \to\leftarrow \Leftarrow\rightarrow \Rightarrow\leftrightarrow \Leftrightarrow\mapsto \hookleftarrow\leftharpoonup \leftharpoondown\rightleftharpoons \longleftarrow\Longleftarrow \longrightarrow\Longrightarrow \longleftrightarrow
\Longleftrightarrow \longmapsto\hookrightarrow \rightharpoonup\rightharpoondown \leadsto\uparrow \Uparrow
\downarrow \Downarrow
\updownarrow \Updownarrow
\nearrow \searrow
\swarrow \nwarrow
Dots
SymbolCommandSymbolCommandSymbolCommandSymbolCommand
\ldots 2 \vdots \cdots 2 \ddots
(The '2's after \ldots and \cdots are only present to make the distinction between the two clear.)
Accents
SymbolCommandSymbolCommandSymbolCommand
17/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
\hat{x} \check{x} \dot{x}
\breve{x} \acute{x} \ddot{x}\grave{x} \tilde{x} \mathring{x}\bar{x} \vec{x}
When applying accents to i and j, you can use \imath and \jmath to keep the dots from interfering with the accents:
SymbolCommand SymbolCommand
\vec{\jmath} \tilde{\imath}
\tilde and \hat have wide versions that allow you to accent an expression:
SymbolCommand SymbolCommand
\widehat{3+x} \widetilde{abc}
Others
SymbolCommandSymbolCommand SymbolCommand
\infty \triangle \angle\aleph \hbar \imath\jmath \ell \wp
\Re \Im \mho\prime \emptyset \nabla\surd \partial \top
\bot \vdash \dashv\forall \exists \neg\flat \natural \sharp
\backslash \Box \Diamond
\clubsuit \diamondsuit \heartsuit\spadesuit \Join \blacksquare
\S \P \copyright
\pounds
Command Symbols
Some symbols are used in commands so they need to be treated in a special way.
SymbolCommandSymbolCommandSymbolCommandSymbolCommand
$$ \$ \& \% \#
\_ \{ \} \backslash
European Language Symbols
SymbolCommandSymbolCommandSymbolCommandSymbolCommand
{\oe} {\ae} {\aa} {\o}{\OE} {\AE} {\AA} {\O}
{\l} {\ss} !{\L} {\SS} ?`
Bracketing Symbols
In mathematics, sometimes we need to enclose expressions in brackets or braces or parentheses. Some of these work just as you'd imagine in
LaTeX; type ( and ) for parentheses, [ and ] for brackets, and | and | for absolute value. However, other symbols have special commands:
SymbolCommandSymbolCommandSymbolCommand
\{ \} \|
\backslash \lfloor \rfloor
\lceil \rceil \langle
\rangle
You might notice that if you use any of these to typeset an expression that is vertically large, like
(\frac{a}{x} )2
the parentheses don't come out the right size:
If we put \left and \right before the relevant parentheses, we get a prettier expression:
\left(\frac{a}{x} \right)2
gives
\left and \right can also be used to resize the following symbols:
SymbolCommandSymbolCommand SymbolCommand
\uparrow \downarrow \updownarrow
\Uparrow \Downarrow \Updownarrow
Multi-Size Symbols
Some symbols render differently in inline math mode and in display mode Display mode occurs when you use \[...\] or $$...$$, or environments like
\begin{equation}...\end{equation}, \begin{align}...\end{align}. Read more in the commands section of the guide about how symbols which take
arguments above and below the symbols, such as a summation symbol, behave in the two modes.
18/18https://mail.google.com/mail/ca/u/0/?ui=2&ik=16153015fb&view=pt&search=inbox&th=1390989558e68d…
In each of the following, the two images show the symbol in display mode, then in inline mode.
SymbolCommandSymbolCommandSymbolCommand
\sum \int \oint
\prod \coprod \bigcap
\bigcup \bigsqcup \bigvee
\bigwedge \bigodot \bigotimes
\bigoplus \biguplus
Examples
x^y is the same as x^{y}, producing .
x_y is the same as x_{y}, producing .
However, x^10 is not the same as x^{10}. The former produces instead of .
See Also
Next: Commands
Previous: Layout
Category: LaTeX
This page was last modified on 9 January 2012, at 19:00. This page has been accessed 2,060,117 times. Privacy policy About AoPSWiki Disclaimers