\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{Steler} \pdfinfo{ /Title (mathematics-in-our-world-prelim-01.pdf) /Creator (Cheatography) /Author (Steler) /Subject (Mathematics in our World Prelim 01 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}{A3A3A3} \definecolor{LightBackground}{HTML}{F3F3F3} \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{Mathematics in our World Prelim 01 Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Steler} via \textcolor{DarkBackground}{\uline{cheatography.com/193298/cs/40504/}}} \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}Steler \\ \uline{cheatography.com/steler} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Not Yet Published.\\ Updated 28th September, 2023.\\ 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{1.54287 cm} x{3.43413 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{What are Patterns?}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{Patterns are sequences or designs that are orderly or that repeats} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{{\bf{Types of Patterns:}}} \tn % Row Count 3 (+ 1) % Row 2 \SetRowColor{LightBackground} Symmetry & It is when different sides are alike. A reflection of a mirror is one of symmetry. \tn % Row Count 7 (+ 4) % Row 3 \SetRowColor{white} Fractals & These are 'never-ending' patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale. \tn % Row Count 12 (+ 5) % Row 4 \SetRowColor{LightBackground} Spirals & A pattern that spirals, examples are seashells, hurricanes, and galaxies. \tn % Row Count 15 (+ 3) % Row 5 \SetRowColor{white} Fibonacci Patterns & The least understood pattern in nature, it is a pattern that increases its sequence exponentially. (i.e. 1,2,4,8,16,32,etc.) \tn % Row Count 20 (+ 5) % Row 6 \SetRowColor{LightBackground} \seqsplit{Tesselations} & A pattern formed of cubes or tiles, can occur in both living and non-living things. \tn % Row Count 24 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.64241 cm} x{3.33459 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{The Use of Mathematics}} \tn % Row 0 \SetRowColor{LightBackground} Technology & This aspect depends on basic research to advance. Its value is determined on by math and experimentation using statistics \tn % Row Count 5 (+ 5) % Row 1 \SetRowColor{white} & Examples: Predicting the Weather, Navigation, Computer Circuits. \tn % Row Count 8 (+ 3) % Row 2 \SetRowColor{LightBackground} Engineering & Math is used to design components and products, maintain operating components, model real-life situations for testing and learning purposes as well build and maintain structures. \tn % Row Count 15 (+ 7) % Row 3 \SetRowColor{white} & Examples: Robotics, Construction, Microwaves, Rockets and Satellites, Automotive Design. \tn % Row Count 19 (+ 4) % Row 4 \SetRowColor{LightBackground} Media & Math can be found in Media. Using camera lens or convincing nature of numbers for advertising. \tn % Row Count 23 (+ 4) % Row 5 \SetRowColor{white} & Examples: Digital Music, Movie Graphics, Polling and Voting. \tn % Row Count 26 (+ 3) % Row 6 \SetRowColor{LightBackground} Medicine and Health & Advanced medical studies rely on statistics . \tn % Row Count 28 (+ 2) % Row 7 \SetRowColor{white} & Examples: Crowd People: Population Dynamics, Pharmacy and Medicine, MRI and Tomography. \tn % Row Count 32 (+ 4) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{5.377cm}{x{1.64241 cm} x{3.33459 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{The Use of Mathematics (cont)}} \tn % Row 8 \SetRowColor{LightBackground} Finance and Business & Businesses require skill in product making and providing service. Overseeing finances is key to survival and success. \tn % Row Count 5 (+ 5) % Row 9 \SetRowColor{white} & Examples: Insurance, Loans and Mortgages, Fraud Detection, Pricing Strategies, Game Theory. \tn % Row Count 9 (+ 4) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{0.84609 cm} x{4.13091 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Language of Mathematics}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{What is Language?}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{2}{x{5.377cm}}{It is a complex system of words and symbols, either spoken or written, used by a particular community as a means of communication.} \tn % Row Count 4 (+ 3) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\bf{Characteristics of Language}}} \tn % Row Count 5 (+ 1) % Row 3 \SetRowColor{white} \seqsplit{Precise} & Able to make very fine distinctions. \tn % Row Count 7 (+ 2) % Row 4 \SetRowColor{LightBackground} \seqsplit{Concise} & Able to say things briefly. \tn % Row Count 9 (+ 2) % Row 5 \SetRowColor{white} \seqsplit{Powerful} & Able to express complex thoughts with relative ease. \tn % Row Count 11 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.8308 cm} x{1.64772 cm} x{1.09848 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{English Language of Mathematics}} \tn % Row 0 \SetRowColor{LightBackground} & English & \seqsplit{Mathematics} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Name given to an object of interest: & Noun. & \seqsplit{Expression}. \tn % Row Count 5 (+ 3) % Row 2 \SetRowColor{LightBackground} & Example: Carol, Manila, book & Example: 5, 2+3, 1/2 \tn % Row Count 8 (+ 3) % Row 3 \SetRowColor{white} A complete thought: & Sentence. & \seqsplit{Sentence.} \tn % Row Count 10 (+ 2) % Row 4 \SetRowColor{LightBackground} & Example: Dash likes guinea pigs. & Example: 3+4=7, 3+4=8 \tn % Row Count 13 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Sets, Functions, and Relations}} \tn % Row 0 \SetRowColor{LightBackground} The word "is" has three distinct meanings. & Example: "5 is the square root of 25." "5 is less than 10." "5 is a prime number." \tn % Row Count 5 (+ 5) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{1.74195 cm} x{3.23505 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Elementary Logic}} \tn % Row 0 \SetRowColor{LightBackground} {\bf{Logical Connective}} & It is a symbol or a word used to connect 2 or more sentences. Each logical connective can be expressed as a truth function. \tn % Row Count 5 (+ 5) % Row 1 \SetRowColor{white} {\bf{Negation "\textasciitilde{}"}} & Opposite of the statement, usually employing the word {\emph{not}}. \tn % Row Count 8 (+ 3) % Row 2 \SetRowColor{LightBackground} Original Statement: & Negation of Statement: \tn % Row Count 10 (+ 2) % Row 3 \SetRowColor{white} "p" Today is Monday & "\textasciitilde{}p" Today is not monday. \tn % Row Count 12 (+ 2) % Row 4 \SetRowColor{LightBackground} {\bf{Conjunction "∧"}} & It is formed by using the word "and" to join two sentences. \tn % Row Count 15 (+ 3) % Row 5 \SetRowColor{white} & "p∧q" Sister likes dogs and Mother likes cats. \tn % Row Count 17 (+ 2) % Row 6 \SetRowColor{LightBackground} {\bf{Disjunction "∨"}} & It is formed by using the word "or" to join two simple sentences. \tn % Row Count 20 (+ 3) % Row 7 \SetRowColor{white} & "p∨q" The clock is slow or the time is correct. \tn % Row Count 22 (+ 2) % Row 8 \SetRowColor{LightBackground} {\bf{Implication "⇒"}} & It is a type of relationship between 2 statements or sentences. It is formed using the word "if" to create implication. \tn % Row Count 27 (+ 5) % Row 9 \SetRowColor{white} & "p⇒q" If my heart stops, then I will die. \tn % Row Count 29 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}