L A TEX and Basic Text Editing

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1 L A TEX and Basic Text Editing 1 Basics L A TEXis a mathematical typesetting word processing tool. You need a compiler to display L A TEX, and you can dowload the open-source freeware at MikTex.org. We have two input modes: text and math. We transition into math mode with dollar signs or a function call. The \symbol signals a L A TEX command is beginning. My favorite equation is $xˆ2-1=0$ My favorite equation is x 2 1 = 0 2 Algebra Object Polynomial 2xˆ{12}+xˆ6-xˆ2+12 2x 12 + x 6 x x Rational Expression \frac{x}{1-x} 1 x Subscripts 3x 1+x 2 \leq 2y 3x 1 + x 2 2y Radical Expression \sqrt{7x-1} 7x 1 Higher Order Roots \sqrt[3]{64} 3 64 Not Equal To 3\neq Note that ˆ produces superscripts and produces subscripts. L A TEXneeds to be told to re-size brackets, braces, parentheses and other encolsures using the \left and \right commands as follows: \left(\frac{x}{x+1}\right) \left \frac{x}{x+\frac{1}{x}}\right ( x ) x+1 x x+ 1 x

2 3 Trignometry For the degree symbol, we superscript the \circ symbol. \sin(\frac{\pi}{2}) sin( π) 2 \ln{x} ln x \cosˆ2(2\theta) cos 2 (2θ) \tan45ˆ{\circ} \cotˆ{-1}\left(\frac{\sqrt{3}}{2}\right) tan 45 ( 3 ) cot 1 2 For uppercase Greek letters, we capitalize: The text $\Sigma$ produces Σ, where $\sigma$ produces σ. 4 Summations, Integrals and Limits \sum{\frac{1}{n}} \sum k 2kxˆ2 \displaystyle\sum {k=0}ˆ{3}4xˆ9 1 n k 2kx2 3 4x 9 x=0 The \displaystyle command places the limits above/below the symbol and a larger, bolder version of the summation. Note that L A TEXonly requires brackets around the limits if they are two characters or longer. \int xˆ2 dx \int 0ˆ1 4tˆ3 dt x 2 dx 1 0 4t3 dt We can list the limits in either order. Specifically, the text \intˆ1 0 4tˆ3 dt would also produce the exact same expression in the last line of the table above.

3 \lim {t\rightarrow -\infty}eˆ{2t} \displaystyle \lim {x \rightarrow 0}\frac{x-4}{3xˆ2} lim t e 2t x 4 lim x 0 3x 2 The \displaystyle command inside the equation produces the familiar typesetting. 5 Probability We can use \binom to display binomial coefficients, or choose notation. standard deck of playing cards are also coded in. The suits for a \binom{8}{3}\geq\{7\choose 3} A\clubsuit K\heartsuit ) ( 7 3) ( 8 3 A K P(A\cup B\cap\barC)\leq 1 P (A B C) 1 6 Matrices, Arrays and Tables For all matrices, tables and arrays, we use the ampersand & to split cells and a double backslash \\to start a new line. \begin{matrix}x&y\\w&z\end{matrix} \begin{pmatrix}1&2\\0&3\end{pmatrix} \begin{vmatrix}k&0\\0&k\end{vmatrix}=kˆ2 x y w z ( ) k 0 0 k = k2 Bmatrix creates a bracketed matrix. The function cdots makes continued dots ; vdots makes vertical dots ; and ddots makes diagonal dots (other types of dots exist).

4 \begin{bmatrix} \\ 0&\cdots&0\\ \vdots&\ddots&\vdots\\ 0&\cdots&0 \end{bmatrix} Since L A TEXdoes NOT recognize spaces or returns in math input mode, we can use spacing, tabs and hard returns to organize our code for easier scripting and debugging. Above, each row of the matrix is typed on a separate line Tables The tabular environment works much the same as the matrix environment, but with a different input mode default. Matrix expects mathematical expressions in its cells. Tabular expects text entries. In text mode, we can use dollar signs $ to switch to math input mode. Consider the following table: \begin{center}\begin{table}{ lr } Planet&Diameter(km)\\[5pt] Mercury&4878\\ Venus&12104\\ Earth&12756\\ Mars&6794 \end{table}\end{center} The code { lr } specifies the first column is to be left justified, the second right justified. A lowercase C would center the text in that column. The vertical lines in this statement give us the left and right borders of the box drawn around the table. The statements create horizontal lines, in this case the top and bottom borders.

5 Planet Diameter(km) Mercury 4878 Venus Earth Mars 6794 The command [5pt] adds extra spacing between the title line and the rest of the table. 6.2 Matrix Games Array is another matrix/table environment that uses mathematics input mode as its default. Often, this is the easiest way to display matrix games, as shown below: The result is shown below. \{center}$\begin{array}{c ccc}\\ A&1&0&0 \\ B&0&2&0 \\ C&0&0&-1 \end{array}$\end{center} A B C A B C Array is essentially the matrix environment but allows for tabular style controls of the interior and exterior borders. Consider trying to display a game matrix with labels for the players Rose and Colin. The simplest solution is a 2x2 table, with an array in the bottom right cell for the matrix game, the top left cell blank, and the player labels in the other two cells. The player labels are produced in text style as table cells, while everything inside the array is displayed in math input style - exactly what we want. This is how it would look with a title centered above it: Example Game 3.2 Rose Colin A B C A B C 0 0 1

6 Here is the L A TEXthat will produce it: \begin{center}\begin{tabular}{cc} \multicolumn{2}{c}{example Game 3.2}\\[5pt] &Colin\\ Rose&$\begin{array}{c ccc} &A&B&C\\ A&1&0&0\\ B&0&2&0\\ C&0&0&-1\\ \endarray$\\ \end{tabular}\end{center} Note that the array is bracketed with $ s. In a table cell, we re in text input mode. The $ s switch us to math input mode. The final row of a table, matrix or array does not need the \\to conclude it, but sometimes leaving them helps with scripting and debugging. 7 Equations If we type \begin{equation}y=3x\end{equation}, the result is a numbered equation centered in between the lines of text: y = 3x (1) We can add an asterisk to produce an equation without the numbering, as in \begin{equation*}y=3x\end{equation*}: y = 3x For groups of equations, we can use Gather or Align environments: The code \begin{gather*}2x+2y=1\\12y=-3\end{gather*} produces: 2x + 2y = 1 12y = 3 Sometimes, we prefer to group the equations with the equal signs aligned. Note the positioning of the & s in the following equations: \begin{align}2x+2y&=1\\12y&=-3\end{align}. This produces:

7 2x + 2y = 1 (2) 12y = 3 (3) The asterisk functions as before, disallowing the numbering of the equations. Without it, the equations are numbered consecutively throughout the document. 8 Documents Most L A TEXusers create template documents with a basic header. About the simplest way to start TEX-ing up a document is like this: \documentclass{article} \usepackage{amsmath} \begin{document} We type our document here... \end{document} The \usepackage{amsmath} allows common mathematics expressions to display properly, and is almost always worthwhile. The following will work for most purposes and includes a tile, author and date heading like the L A TEXproduced document you re reading. \documentclass{article} \usepackage{amsmath} \title{type Title Here} \author{firstname LastName} \begin{document} \maketitle We type our document here... \end{document}

8 The article document class will work for any undergraduate need. Using the package AMS Math allows several common commands to function properly, such as \binom, and we bracket the body of the article with \begin{document} and \{document} statements as shown.

Introduction to Math in LaTeX

Robert Andersen University of Oxford and University of Western Ontario ICPSR Summer Program, July 2002 Introduction to Math in LaTeX LaTeX has three basic modes: 1. Text mode 2. Inline math mode (allows