\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{SirUmbreon77} \pdfinfo{ /Title (math-1901-final.pdf) /Creator (Cheatography) /Author (SirUmbreon77) /Subject (Math 1901 Final Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{1510A3} \definecolor{LightBackground}{HTML}{F0F0F9} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Math 1901 Final Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{SirUmbreon77} via \textcolor{DarkBackground}{\uline{cheatography.com/50420/cs/13917/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}SirUmbreon77 \\ \uline{cheatography.com/sirumbreon77} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 12th December, 2017.\\ Updated 12th December, 2017.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{x{1.64241 cm} x{3.33459 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Sets}} \tn % Row 0 \SetRowColor{LightBackground} ∈ & "Is an element of..." \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} ∪ & {\bf{Union:}} combine elements of A and B \tn % Row Count 3 (+ 2) % Row 2 \SetRowColor{LightBackground} ∩ & {\bf{Intersection:}} elements that appear in both sets \tn % Row Count 5 (+ 2) % Row 3 \SetRowColor{white} ⊄ & Is not a subset of \tn % Row Count 6 (+ 1) % Row 4 \SetRowColor{LightBackground} ⊆ & {\bf{Subset:}} all elements in A are in B \tn % Row Count 8 (+ 2) % Row 5 \SetRowColor{white} ⊂ & {\bf{Proper Subset:}} A is a proper subset of B iff A is a subset of B and B is not equal to A \tn % Row Count 12 (+ 4) % Row 6 \SetRowColor{LightBackground} ∅ & Empty set \tn % Row Count 13 (+ 1) % Row 7 \SetRowColor{white} \{ \} & Empty set \tn % Row Count 14 (+ 1) % Row 8 \SetRowColor{LightBackground} \textasciitilde{}\textasciitilde{} \{∅\} \textasciitilde{}\textasciitilde{} & Not an empty set \tn % Row Count 15 (+ 1) % Row 9 \SetRowColor{white} A̅ & {\bf{Compliment:}} the set consisting of all element in U that are not in A \tn % Row Count 18 (+ 3) % Row 10 \SetRowColor{LightBackground} Set builder notation & \{formula for elements| restrictions\} \tn % Row Count 20 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Venn Diagrams}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/sirumbreon77_1513046345_Alltheminone.jpg}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{1.14425 cm} p{1.14425 cm} x{2.2885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Conjunction}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{p}} & {\bf{q}} & {\bf{p∧ q}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} T & T & T \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} T & F & F \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} F & T & F \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} F & F & F \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{1.32733 cm} p{1.32733 cm} x{1.92234 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Disjunction}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{p}} & {\bf{q}} & {\bf{pVq}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} T & T & T \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} T & F & T \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} F & T & T \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} F & F & F \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{2.23965 cm} p{2.73735 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Negation}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{p}} & {\bf{\textasciitilde{}p}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} T & F \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} F & T \tn % Row Count 3 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.9908 cm} x{2.9862 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Other Statements}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{NAND}} & {\bf{Not And:}} Negation of And \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} {\bf{NOR}} & {\bf{Not Or:}} Negation of OR \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} {\bf{EOR}} & {\bf{Exclusive Or:}} exactly one of p and q is true \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} Conditional Statement → & If p then q \tn % Row Count 8 (+ 2) % Row 4 \SetRowColor{LightBackground} Biconditional Statement ↔ & p iff (if and only if) q \tn % Row Count 10 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{p{0.75186 cm} p{0.75186 cm} x{1.33664 cm} x{1.33664 cm} } \SetRowColor{DarkBackground} \mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Boolean Tables}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{A}} & {\bf{B}} & {\bf{A + B}} & {\bf{A x B}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} 1 & 1 & 1 & 1 \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} 1 & 0 & 1 & 0 \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} 0 & 1 & 1 & 0 \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} 0 & 0 & 0 & 0 \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}----} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Circuits}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/sirumbreon77_1513048769_Circuits.jpg}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Logic Circuits}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/sirumbreon77_1513052919_logic circuits.jpg}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability/Stats}} \tn % Row 0 \SetRowColor{LightBackground} Perms & P(n,r) = n!/((n−r)!) \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} Combs & C(n,r) = n!/(n−r)!r! \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} Sample Space & Set of all possible outcomes \tn % Row Count 4 (+ 2) % Row 3 \SetRowColor{white} Mean & Sum of set divided by length of set \tn % Row Count 6 (+ 2) % Row 4 \SetRowColor{LightBackground} Median & Middle term of an organized \tn % Row Count 8 (+ 2) % Row 5 \SetRowColor{white} & Take the average of two terms if there is more than one middle term \tn % Row Count 11 (+ 3) % Row 6 \SetRowColor{LightBackground} Mode & The number that occurs most in a set \tn % Row Count 13 (+ 2) % Row 7 \SetRowColor{white} σ$^{\textrm{2}}$ (Variance) & Calculate the mean For each number, subtract the mean and square the result Calculate the average of the squared differences, or sum up the squared differences and divide by N, the number of values. \tn % Row Count 21 (+ 8) % Row 8 \SetRowColor{LightBackground} σ (Standard Deviation) & Square Root of Variance (σ$^{\textrm{2}}$) \tn % Row Count 23 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability Formulas}} \tn % Row 0 \SetRowColor{LightBackground} b= Binomial Probability & b(x; n, P) = nCx Px (1 - P) \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{n= number of trials} \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{x= number of successes} \tn % Row Count 4 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{P= probability of success} \tn % Row Count 5 (+ 1) % Row 4 \SetRowColor{LightBackground} Binomial Distribution & μ = n·P \tn % Row Count 7 (+ 2) % Row 5 \SetRowColor{white} & σ$^{\textrm{2}}$ = n · P · (1-P) \tn % Row Count 9 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}