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CS109 LaTeX Cheat Sheet
Created by Derek Chong for CS109 during Spring 2020.
This cheat sheet assumes you have done an introductory tutorial and have a basic level of
general knowledge. It focuses on giving you a quick reference for language features you will
encounter in CS109, in order to make your life easier when working on problem sets.
Frequently-Used Markup
Building Blocks
\geq \leq \neq \approx \sim \Rightarrow \sqrt{42} \infty \lambda \mu, \sigma \Phi(0) \Sigma \theta \bar{X}, \hat{X} A,B,\dots,Z 1,2,\cdots,n \verb|my_function() | \frac{42 \textrm{ units} \times 42 \textrm{ units}}{ \textrm{ units} \times 42 \textrm{ units}} \sum_{i=0}^{n} \frac{a}{b} \prod_{i=0}^{n} \frac{a}{b}
Probability
P(A \cap B) P(A \cup B) \binom{n}{k} P(A_1|B^C)
P(\textrm{text } | \textrm{ text}) P(\textrm{cond} \leq 5.0) \frac{P(\textrm{a } | \textrm{ b}) \times P(\textrm{b})}{P(\t extrm{a})} \frac{P(\textrm{a } | \textrm{ b}) \times P(\textrm{b})}{P(\t extrm{a } | \textrm{ b})P(\textrm{b}) + P(\textrm{a } | \textrm{ b}^C)P(\textrm{b}^C )}
Random Variables
X \sim \textrm{Ber}(p) X \sim \textrm{Bin}(n,p) X \sim \textrm{Poi}(\lambd a=0) X \sim \textrm{Exp}(\lambd a=0) X \sim \mathcal{N}(\mu = 0, \sigma^2 = 1) \theta \sim \textrm{Beta}(a,b)
Calculus
\int_{-1}^{1} x^2 - 2x + 1 dx \left[ x - \frac{1}{2}x^ \right]{-1}^ \iint{0<y<x<1} \frac{x}{y} dy dx \left. \frac{2}{3}y
- \frac{3}{4}y^ \right|_{-1}^{x}
Variance and Covariance
\textrm{Var}(X) \textrm{Cov}(X,Y) \begin{bmatrix} a & b \ c & d \end{bmatrix} \rho
Useful Structures Groups of Equations
\begin{align*} chunks can be used to organise multiple lines of equations.
\begin{align} P(X=x|Y=1,W=P_1) &= \frac{P(X=x,Y=1 | W=P_1)}{P(Y=1|W=P_1)} \ &= P(X=x|W=P_1) \ &= \binom{5}{x}(0.1)^x(0.9)^{5-x} \ P(X=x|Y=1,W=P_2) &= \frac{P(X=x,Y=1 | W=P_2)}{P(Y=1|W=P_2)} \ &= P(X=x|W=P_2) \ &= \binom{5}{x}(0.1)^x(0.9)^{5-x} \end{align} Venn Diagrams You may have to install the venndiagram package (and include \usepackage{venndiagram}) \begin{venndiagram3sets}[labelA={Foo},labelB={Bar},labelC ={Baz}, labelOnlyA={1},labelOnlyB={2},labelOnlyC={3}, labelOnlyAB={4},labelOnlyAC={5},labelOnlyBC={6},labelABC= {7}, labelNotABC={8}] \begin{center} \begin{venndiagram3sets}[labelA={Foo},labelB={Bar},labelC ={Baz}, labelOnlyA={1},labelOnlyB={2},labelOnlyC={3}, labelOnlyAB={4},labelOnlyAC={5},labelOnlyBC={6},labelABC= {7},labelNotABC={8},shade={yellow}] \fillOnlyB\end{venndiagram3sets} \end{center}
\begin{center} \begin{venndiagram2sets}[labelA={Foo},labelB={Bar}, labelOnlyA={$x$},labelOnlyB={$z$}, labelAB={$y$}, shade={white}] \fillAll \end{venndiagram2sets} \end{center} Full package documentation is available here: https://ctan.math.illinois.edu/macros/latex/contrib/venndiagram/venndiagram.pdf Plotting Graphs \begin{tikzpicture} \begin{axis}[ axis lines = center, xlabel = {$p$}, ] \addplot [domain=-0.05:1.5, samples=100, color=blue]{x}; \addlegendentry{$p$} \addplot [domain=-0.05:1.5, samples=100, color=red]{x*x}; \addlegendentry{$q = p^2$} \end{axis} \end{tikzpicture} Probability Trees \tikzstyle{level 1}=[level distance=3.5cm, sibling distance=3cm] \tikzstyle{level 2}=[level distance=3.5cm, sibling distance=3.3cm] \tikzstyle{bag} = [text width=4em, text centered] \tikzstyle{end} = [circle, minimum width=3pt,fill, inner sep=0pt] \begin{tikzpicture}[grow=right] \node[bag] {Foo} child { node[bag] {Bar} child { node[end, label=right:{Baz}] {} edge from parent node[above] {$X$} node[below] {$x$} } child { node[end, label=right:{Xyzzy}] {} edge from parent node[above] {$X$} node[below] {$x$} }
General Tips
● Local LaTeX : Running LaTeX locally can help you learn faster than Overleaf - a shorter
feedback loop is really helpful!
● Wolfram Alpha : You can paste LaTeX snippets directly into Wolfram Alpha and most of
the time it'll understand them correctly and do something useful.
○ You can even add Wolfram Alpha as a custom search engine in Chrome. This
lets you type "w [your LaTeX equation]" into your location bar, and it'll take you
straight to the answer in Wolfram. Just go to this link, and add this as an entry.
● Half-LaTeX environments : Using a half-LaTeX environment like MS Word, Powerpoint,
or Google Docs with the Auto-LaTeX Equations Addon is super useful while you’re doing
your rough work.
○ Save up snippets for typesetting and test them in Wolfram Alpha as you go!
○ Auto-LaTeX may throw an error if you’re signed into >1 Google Account at once
○ MS Office LaTeX support was added in 2016, is not yet available on macOS
● Keyboard shortcuts :
○ On TeXShop, you can type \bali and press Esc twice, and it'll set up a
\begin{align*} block. Or \b[xyz] for any \begin{xyz} block.
○ It can be nice to define custom shortcuts for things you find yourself typing
frequently, such as \textrm{} or Bayes’ Theorem.
● Expectations : You don’t have to use any of the above structures if you don’t want to!
The teaching team will accept and grade PSets in any format you submit.
● Motivation : Strong LaTeX skills will make you more effective in all future courses. Goals
