1. Seminar Sam Panzer

2. 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

3. Start Your Browsers LaTeX is a fairly large system (a few hundred MB) First, download and install TeX Live from http://mirror.ctan.org/systems/texlive/tlnet/install- tl.zip (unless you’re on Linux) http://mirror.ctan.org/systems/texlive/tlnet/install- tl.zip Windows users, install the TeXNic Center from http://sourceforge.net/projects/texniccenter/files/TeX nicCenter/1.0%20Stable%20RC1/TXCSetup_1StableRC1.exe/download http://sourceforge.net/projects/texniccenter/files/TeX nicCenter/1.0%20Stable%20RC1/TXCSetup_1StableRC1.exe/download Mac users, install the TeXShop IDE from http://www.uoregon.edu/~koch/texshop/texshop.zip http://www.uoregon.edu/~koch/texshop/texshop.zip Linux users, install the texlive package

4. 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

5. 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

6. 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

7. 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}

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

9. 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 http://detexify.kirelabs.org/classify.html http://detexify.kirelabs.org/classify.html

10. 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.

11. 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

12. 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…

13. 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 $S = \frac{16}{9}$

14. Output

15. 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}

16. 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, $F_2 = F_1 + F_0 = 1 + 1 = 2.$ 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.

17. Example Output

18. 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

19. 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