Seminar Sam Panzer

Good Evening, and Welcome First, an overview of what these seminars will cover Topics: – What you need to get started – What LaTeX is (and what it isn’t) – A bit of history (if you’re interested) – Basic concepts – Writing simple documents With a special addendum for the CIS 160 proof tree templates

Start Your Browsers LaTeX is a fairly large system (a few hundred MB) First, download and install TeX Live from tl.zip (unless you’re on Linux) tl.zip Windows users, install the TeXNic Center from nicCenter/1.0%20Stable%20RC1/TXCSetup_1StableRC1.exe/download nicCenter/1.0%20Stable%20RC1/TXCSetup_1StableRC1.exe/download Mac users, install the TeXShop IDE from Linux users, install the texlive package

About LaTeX LaTeX is a document markup language – According to Wikipedia LaTeX documents describe the layout and content for the typesetting program TeX You describe the presentation of a document, and LaTeX makes it look pretty

A Bit of History LaTeX is a high-level front-end to the TeX typesetting system It was originally written in the early 1980s Many contemporary academic papers are typeset in LaTeX

LaTeX Input Three common types of input: – Commands Start with a backslash – Text Just typed! – Math Enclosed in dollar signs All LaTeX will be displayed in this font for this presentation

On Structure Each LaTeX document begins by stating which type of output it generates – Article, report, book, letter, slides Usually use article \documentclass{article} The contents of the document reside between \begin{document} and \end{document} All other examples are assumed to be between \begin{document} and \end{document}

A Simple Sample Latex Document \documentclass{article} \title{Evil Plans} \author{Sam Panzer} \begin{document} \maketitle Tonight, we take over the world! \end{document}

Commands As before, they start with backslashes – \noindent – Two backslashes start a new line Required arguments are placed in braces \textbf{Bold Text} – \emph{Italicized Text} – \hspace{3mm} Optional arguments go in brackets – \documentclass[twoside,10pt]{article} There is a command for just about anything! Check

Example, with commands \noindent \textbf{Homework 5} \\\noindent CIS 260 \hspace{5mm} Pf. Gallier Intuitionistic logic differs from classical logic in that proof-by-contradiction (\emph{RAA}) is disallowed.

Math Inline expressions are enclosed in dollar signs $f(x_1,x_2) = x_1^2 + 2x_2$ Results in Use double dollar signs to place an equation on its own line Carets (^) are used for superscripts, and underscores (_) for subscripts

Math II Common Commands – \frac{numerator}{denominator} – \sqrt{inside} – \sum_{subscript}^{superscript} – \int_{lower bound}^{upper bound}{integral} – \infty – \cdot – \leq and \geq – \( and \) – \Rightarrow – Any Greek letter is \lettername E.g. \pi, \Gamma For uppercase, capitalize the first letter – Unless the uppercase looks like English…

Math example \section{The Algebraic-Geometric Infinite Series} We often see series in the form $S = a+ ar + ar^2 +...,$ and are familiar with the formula for evaluating them, given that $|r| < 1.$ In this case, the series is slightly different - the numerators follow an algebraic series, and the denominators a geometric series. $$S = \frac{1}{1} + \frac{2}{4} + \frac{3}{16} + \frac{4}{64} +... = \sum_{k=0}^\infty{\frac{k + 1}{4^k}}$$ The trick used to solve a geometric series was to multiply the entire series by the common ratio, then subtract the result from the original series. Here, $$4S = 4 + \frac{2}{1} + \frac{3}{4} + \frac{4}{16} +... $$ Subtracting the original, we have reduced the original problem to a geometric series, $$4S - S = 4 + \frac{1}{1} + \frac{1}{4} + \frac{1}{16} +....$$ Finally, $$3S = 4 + \sum_{k=0}^\infty{\frac{1}{4^k}} = 4 + \frac{4}{3},$$ so $S = \frac{16}{9}$

Output

Setting up your math homework \documentclass{article} \usepackage{amsmath} \begin{document} \section{Problem 1} From Theorem 7.2, we know that $| |^2 \leq ||v||\cdot ||w||.$ \end{document}

Example math-heavy excerpt (Copied from an old homework) \section{The Fibonacci Numbers} $F_0 = 1, F_1 = 1, F_{n+2} = F_{n+1} + F_{n}$ if $n \geq 0.$ \vspace{3mm} \\\textbf{Base case for induction}: $n = 0$ Then $F_{n+2} = \binom{2}{0} + \binom{1}{1} + \binom{0}{2} = 2.$ According to the recursive definition, $F_2 = F_1 + F_0 = = 2.$ Inductive case: Assume the (complete) induction hypothesis, for all $n \geq m \geq 2,$ $$F_m = \sum_{k=0}^m \binom{m-k}{k},$$ we try to show that $$F_{n+1} = \sum_{k=0}^{n+1} \binom{n + 1 -k}{k}.$$ Consider $F_{n+1}.$ By the recursive definition of $F,$ we have $F_{n+1} = F_n + F_{n-1}.$ By the inductive hypothesis, we have that $$F_{n+1} = \sum_{k=0}^n\binom{n-k}{k} + \sum_{k=0}^{n-1}\binom{n-1-k}{k}.$$ Now recall that $\binom{-1}{n+1} = \binom{-1}{n} = 0,$ so we can add these into the summations. $$F_{n+1} = \sum_{k=0}^{n + 1}\binom{n - k}{k} + \sum_{k=0}^{n}\binom{n -1 -k}{k}.$$ To combine the summations, we remove the first item from the first summation then adjust the indices. $$F_{n+1} = \binom{n}{0} + \sum_{k=1}^{n + 1}\binom{n -k}{k} + \sum_{k=0}^{n}\binom{n - 1 -k}{k} = \binom{n}{0} + \sum_{k=1}^{n+1}\binom{n -k}{k} + \sum_{k=1}^{n + 1}\binom{n -k}{k - 1}.$$ Combining the summations and applying $\binom{k-1}{p} + \binom{k-1}{p-1} = \binom{k}{p},$ $$F_{n+1} = \binom{n}{0}+\sum_{k=1}^{n + 1} \binom{n - k + 1}{k} = \sum_{k=0}^{n + 1} \binom{n - k + 1}{k}$$ as desired.

Example Output

Some useful LaTeX tidbits LaTeX ignores single line breaks – You need a blank line to start a new paragraph LaTeX collapses whitespace – Multiple consecutive blank lines are treated exactly as a single blank line – Multiple spaces between words are handled as if they were a single space LaTeX ignores all characters on a line after it sees a % – This is called commenting – Useful for removing bits of work you don’t want to be shown but don’t want to delete Underscores (_) and carets (^) only affect the next character – Place everything that needs to be affected within braces E.g. $x^{-1} = a_1b_1$ results in

That’s all for now! This session covered the basics – Though some of the example code might be complicated I included extra slides for the CIS 160 people