%%% The first command tells what kind of document we're making. %%% In this case, it is an article in the AMS style (using the %%% name amsart). There are options for font and paper size, %%% among other things. \documentclass[12pt,letterpaper,oneside]{amsart} %%% This part of the file (after the \documentclass command, %%% but before the \begin{document}) is called the ``preamble''. %%% This is where we call packages to be used, and where we put %%% our macro definitions. %%% The following command loads other helpful packages from the AMS \usepackage{amsmath,amsthm,amsfonts,amssymb} \usepackage{mathtools} %extension of amsmath, provides bug fixes and other tools \usepackage{mathrsfs} %Provides a nice \mathscr command %%% Here are a few other useful packages %\usepackage[american]{babel} %language settings (for things other than american english) %\usepackage[mathcal]{euscript} %provides different \mathcal command %\usepackage{ulem} %Package for underlining. \usepackage[active]{srcltx} %creates the .dvi file with links to the source .tex file %\usepackage[notcite,notref]{showkeys} %shows labels in the margins \usepackage[pdftex,bookmarks=true]{hyperref} %adds hypertext links, can't use in ``draft'' mode, and must use in pdf mode %\usepackage{fullpage} %creates smaller margins %%% The following commands allow you to use \Xy-pic to draw %%% commutative diagrams. (You can omit the second line if you want %%% the default style of the nodes to be \textstyle.) %\usepackage[all,cmtip]{xy} %\let\objectstyle=\displaystyle %%% If you'll be importing any graphics, uncomment the following %%% line. (Note: The spelling is correct; the package graphicx.sty is %%% the updated version of the older graphics.sty.) \usepackage{graphicx} %%% The following command loads the amsrefs package, which will be %%% used to create the bibliography: \usepackage[alphabetic]{amsrefs} %%% Here are a few user-defined commands \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\mfr}[1]{\ensuremath \mathfrak{#1}} \newcommand{\mbb}[1]{\ensuremath \mathbb{#1}} \newcommand{\mcl}[1]{\ensuremath \mathcal{#1}} \newcommand{\msc}[1]{\ensuremath \mathscr{#1}} \DeclareMathOperator{\GL}{GL} %%%------------------------------------------------------------------- %%%------------------------------------------------------------------- %%% The Theorem environments: %%% %%% %%% The following commands set it up so that: %%% %%% All Theorems, Corollaries, Lemmas, Propositions, Definitions, %%% Remarks, and Examples will be numbered %%% in a single sequence, and the numbering will be within each %%% section. Displayed equations will be numbered in the same %%% sequence. %%% %%% %%% Theorems, Propositions, Lemmas, and Corollaries will have the most %%% formal typesetting. %%% %%% Definitions will have the next level of formality. %%% %%% Remarks and Examples will be the least formal. %%% % The following causes equations to be numbered within sections \numberwithin{equation}{section} % We'll use the equation counter for all our theorem environments, so % that everything will be numbered in the same sequence. % Theorem environments \theoremstyle{plain} %% This is the default, anyway \newtheorem{thm}[equation]{Theorem} \newtheorem{cor}[equation]{Corollary} \newtheorem{lem}[equation]{Lemma} \newtheorem{prop}[equation]{Proposition} \theoremstyle{definition} \newtheorem{defn}[equation]{Definition} \theoremstyle{remark} \newtheorem{rem}[equation]{Remark} \newtheorem{ex}[equation]{Example} %%%------------------------------------------------------------------- %%%------------------------------------------------------------------- %%%------------------------------------------------------------------- \begin{document} %%% In the title, use a double backslash "\\" to show a linebreak: %%% Use one of the following two forms: %%% \title{Text of the title} %%% or %%% \title[Short form for the running head]{Text of the title} \title[\LaTeX]{Introduction to \LaTeX} %%% If there are multiple authors, they're described one at a time: %%% First author: \author{} \address{} \curraddr{} \email{} \thanks{} %%% Second author: \author{} \address{} \curraddr{} \email{} \thanks{} %%% Third author: \author{} \address{} \curraddr{} \email{} \thanks{} \author{John Q.~Doe} %%% Your address, or department: \address{Department of Mathematics, Eastern Upper Fake University, Nowhereville, SR 99999} %%% Current address is optional. % \curraddr{curraddr} %%% Email address is optional. \email{name@fake.address} %%% Website address is optional. \urladdr{http://name.fake.address/} %%% Thanks acknowledges financial support, e.g., grant money % \thanks{thanks} %%% If there's a second author: % \author{} % \address{} % \curraddr{} % \email{} % \urladdr{website} % \thanks{thanks} %%% AMS subject classification \subjclass[2010]{53C44} %53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) %%% The date, which can also be entered manually: \date{\today} %%% The abstract: \begin{abstract} This paper is a very, very brief introduction to basic \LaTeX usage. Please edit this file however you choose. \end{abstract} %%% This puts the title, author information, and date on the first page. \maketitle %%% To include a table of contents, uncomment the following line: \tableofcontents %%%------------------------------------------------------------------- %%%------------------------------------------------------------------- %%% Start the body of the paper here: \section{Introduction} \label{sec:intro} %it is a good idea to label everything as you go! \noindent What is this all about? \begin{itemize} \item \TeX is typesetting software that is especially useful for typesetting mathematical content. The word \TeX sounds like ``tech.'' \item \LaTeX is an extension of \TeX. \item AMS \LaTeX is a further extension, provided by the American Mathematical Society, geared explicitly towards the mathematical community. \end{itemize} One main philosophy: The author chooses the content and logical structure (chapters, sections, etc.), while \LaTeX takes care of the layout (margins, fonts, spacing, etc.). Therefore, \LaTeX is not WYSIWYG like a normal word processor. \newpage \section{Mathematics} \subsection{Basics} There are two ways to include mathematics in your document. \begin{itemize} \item Inline:~ within a paragraph of text. Type \texttt{\$ your math here \$}. \item Displayed:~on its own line. Type \texttt{\textbackslash [ your math here \textbackslash ]}. \end{itemize} There are many variations on the Displayed type; we'll see some later. Here are some examples that illustrate a few important commands and features. \begin{itemize} \item superscripts: $x^0, {}^0 x$ \item subscripts: $x_0, {}_0 x$ \end{itemize} If the super/subscript is more than one ``symbol'', put it in curly brackets: $x_{0,1}$. Most other typesetting commands come down to a few things. First, simply inserting a symbol, e.g., \texttt{\textbackslash symbol}; second, putting symbols in some sort of construct, e.g., \texttt{\textbackslash command\{argument1\}$\cdots$\{argumentN\}}; third, combining these two ideas. Here are more examples: \begin{itemize} \item greek letters: $\alpha, \beta, \gamma$, etc. \item simple operators: $+, -, \times, \cdot, !, \oplus, \otimes, \wedge, \nabla, \partial$, etc. \item relations: $<, >, \geq, \leq, =, \equiv, \sim, \simeq, \cong, \subset, \subseteq, \in, \notin, \ne$, etc. \item delimiters: $(a), [b], \{c\}, \langle d \rangle, |e|$, etc. \item arrows: $\rightarrow, \leftarrow, \Rightarrow, \Leftrightarrow$, etc. \item dots: $\dots,\cdots,\vdots,\ddots$, etc. \item predefined functions: $\exp, \ln, \log, \sin, \cos, \det$, etc. \item large operators: $\int, \sum, \prod, \cup, \sqcup, \cap,$ etc. \item ...with limits: $\sum_{k=1}^N a_k$. \item roots: $\sqrt[3]{x+y}$ \item fractions: $\frac{x}{y}$ \end{itemize} Certain things show up better in display mode. For example, with the \texttt{\textbackslash left} and \texttt{\textbackslash right} commands, delimiters scale appropriately, and the \texttt{big}/\texttt{long} adjectives can be used for some symbols: \[ \left[ \int_a^b |f(x)|^p \, dx \right]^{1/p}, \quad \left\{ \sum_{k=1}^N \sqrt{\frac{a_k}{k!}} \longrightarrow 1 \right\}, \quad \bigcup_\alpha \left(\bigoplus_{k=1}^\infty U_k \right)^{\otimes \alpha} \] \newpage \subsection{Alignment} A single equation is aligned in the center by default: \[ \int_M d\omega = \int_{\partial M} \omega \] If it is too long, or has many parts, then the \texttt{align} environment is helpful. Use \& to set the alignment and $\backslash\backslash$ to break lines: \begin{align} S &= 1 - 1 + 1 - 1 \cdots \\ &= 1 - ( 1 - 1 + 1 \cdots ) \\ &= 1 - S \\ \Rightarrow S &= \frac{1}{2} \end{align} Use a $\ast$ to make the equation numbers go away (this is true for many other commands as well), and \texttt{tag} to make your own number/text: \begin{align*} S &= 1 - 1 + 1 - 1 \cdots \\ &= 1 - ( 1 - 1 + 1 \cdots ) \\ &= 1 - S \\ \Rightarrow S &= \frac{1}{2} \tag{what?!} \end{align*} You can also have multiple columns: \begin{align*} a_1 &= b_1 & c_1 &= d_1 \\ a_2 &= b_2 & c_2 &= d_2 \end{align*} You could make a matrix this way, but there are \texttt{matrix, pmatrix, bmatrix, vmatrix}, etc. For example: \[ \begin{matrix} a & b \\ c & d \end{matrix}, \quad \begin{pmatrix} a & b \\ c & d \end{pmatrix}, \quad \begin{bmatrix} a & b \\ c & d \end{bmatrix}, \quad \begin{vmatrix} a & b \\ c & d \end{vmatrix} \] Also helpful is \texttt{cases}: \[ |x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases} \] It doesn't require math mode, but the \texttt{tabular} enviroment can make more complicated tables: \begin{center} \begin{tabular}{|l|c|r|} \hline \#1 & \#2 & \#3 \\ \hline \hline a & b & c \\ d & e & f \\ g & h & i \\ \hline \end{tabular} \end{center} \newpage \subsection{Theorem environments} There are built-in enviroments for theorems and theorem-like things. You can also define your own theorem environments. \begin{thm} \label{thm:sample} Here is a sample Theorem. It has an equation: \[ \det : \GL_n \R \longrightarrow \R \setminus \{0\} \] \end{thm} \begin{proof} There is a proof environment that puts an empty square at the end of the proof. \end{proof} \begin{cor} \label{cor:sample} Here is a sample Corollary. \end{cor} \begin{lem} \label{lem:sample} Here is a sample Lemma. \end{lem} \begin{prop} \label{prop:sample} Here is a sample Proposition. \end{prop} \begin{defn} \label{defn:sample} Here is a sample \textit{Definition}. \end{defn} \begin{rem} \label{rem:sample} Here is a sample Remark. \end{rem} \begin{ex} \label{ex:sample} Here is a sample Example. \end{ex} \newpage \section{Other \LaTeX basics} \subsection{Fonts and text} Generally, the font in the document is fixed, but there are a few common fonts used in mathematics. \begin{itemize} \item blackboard: $\mathbb{A}, \mathbb{F}, \mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}$ \item fraktur: $\mathfrak{g}, \mathfrak{h}, \mathfrak{k}, \mathfrak{m}, \mathfrak{n}$ \item script: $\mathscr{A}, \mathscr{B}, \mathscr{C}, \mathscr{D}, \dots$ \item caligraphic: $\mathcal{A}, \mathcal{B}, \mathcal{C}, \mathcal{D}, \dots$ \item roman (upright): $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \dots$ \end{itemize} There are standard alterations for ordinary text as well, although these should be used sparingly. \begin{itemize} \item \textit{italics} \item \textbf{boldface} \item \textsc{small caps} \item \texttt{teletype} \end{itemize} You can use normal text inside of the math environment with the \texttt{text} command: \[ a = b \text{ and } b = c \text{ implies } a = c. \] A few other tips: \begin{itemize} \item You can make lists with the \texttt{itemize} or \texttt{enumerate} environments \item quotation marks are NOT made with shift+apostrophe; open with \texttt{``}, close with \texttt{''} \item all white space greater than one space or one line break is ignored \item there are ``special characters'' that must be preceded by a backslash \[ \text{\#, \$, \%, etc.} \] \end{itemize} \newpage \subsection{Defining your own commands} One great feature of \TeX is its high degree of customizabity. For example, almost no one types \texttt{\textbackslash mathbb\{R\}} every time they want to produce the symbol $\R$. In the preamble, you can add \[ \texttt{ \textbackslash newcommand\{\textbackslash R\}\{\textbackslash mathbb\{R\}\}} \] and then just use \texttt{\textbackslash R} to produce $\R$. You can also define ``functions'' that take certain arguments. If we wanted to make a function that renders given text in the mathbb font, then we could define \[ \texttt{\textbackslash newcommand\{\textbackslash mbb\}[1]\{\textbackslash ensuremath\textbackslash mathbb\{\#1\}\}} \] which is a function taking 1 argument. Another nice thing is the ability to define new symbols representing mathematical operators. It is a general philosophy (not held by everyone!) that things with fixed names (like $\sin$ or $\det$) should be typeset in upright letters and not italicized. For example, if you wanted to talk about the general linear group, you'll notice that there is nothing ``built in'' like there is for $\det$. We can do it with \[ \texttt{\textbackslash DeclareMathOperator\{\textbackslash GL\}\{GL\}}, \] which allow us to produce \[ \GL_n(\R) \quad \text{instead of} \quad GL_n(\R). \] Along these lines, there are a huge number of packages that contain other symbols, environments, and commands. Load them in the preamble. \newpage \subsection{Graphics} %%% To import a graphics file, you must have said %%% \usepackage{graphicx} %%% in the preamble (i.e., before the \begin{document}). %%% Putting it into a figure environment enables it to float to the %%% next page if there isn't enough room for it on the current page. %%% The \label command must come after the \caption command. \begin{figure}[h] \includegraphics[scale=0.7]{ball1} %using an image from a pdf file \includegraphics{balls2} %using a jpg image \caption{Two images (hopefully).} \label{fig:images} \end{figure} It is relatively easy to include graphics in your document. If your output is a \texttt{pdf}, your graphics must be in one of the following formats: \texttt{jpg, png, pdf}. Mathematica and Matlab can output images in these formats. Note that different output formats generally accept different image formats. Here is a nice reference: \[ \texttt{\url{http://en.wikibooks.org/wiki/LaTeX/Importing\_Graphics}} \] \newpage \subsection{Labels, references, citations} In a formal paper, it is a good idea to label things like equations, figures, and (sub)sections so that they can be easily referenced at other points in the paper. Lables are easy, just put \texttt{\textbackslash label\{label\_name\}} after the item. Note that labeling an equation requires the \texttt{equation} environment: \begin{equation}\label{eq:pythag} a^2 + b^2 = c^2 \end{equation} One references a label with \texttt{\textbackslash ref} command. Similarly, one can cite sources from the References section of the paper. For our purposes, reference entries are handled in a separate file, which is called \[ \texttt{refs\_template.bib} \] It is handled at the very end of the document. To create an entry, it is easy to simply go to \[ \texttt{\url{http://www.ams.org/mathscinet/}} \] to search for your reference, click on its listing, then select the ``BiBTeX'' output. Copy this into the references file, change the label, and cite it using your new label. Here's an example: \begin{quotation} Equation (\ref{eq:pythag}) follows from \cite{chow04}*{Theorem 3.141592}. \end{quotation} \newpage \section{Where to learn more} Here are a few links to helpful internet references. \begin{itemize} \item Google! Just about any question you will have has been answered somewhere already. \item Detexify allows you to draw a symbol, and it tries to figure out what the \TeX command is. \[ \texttt{\url{http://detexify.kirelabs.org/classify.html}} \] \item If that doesn't work, try The Comprehensive LaTeX Symbol List. \[ \texttt{\url{http://www.math.dartmouth.edu/~rweber/latex/tex\_symbols.pdf}} \] \item Everything from this document is found in more detail here: \[ \texttt{\url{ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf}} \] \item Here is furter documentation for AMS-LaTeX \[ \texttt{\url{http://ams.org/publications/authors/tex/amslatex.html}} \] \end{itemize} Finally, here's a nice reference card that you should print: \[ \texttt{\url{www.math.brown.edu/~jhs/ReferenceCards/LaTeXRefCard.v2.0.pdf}} \] %%% ------------------------------------------------------------------- %%% ------------------------------------------------------------------- %%% This is where we create the bibliography. \bibliography{refs_template} \end{document}