96 lines
3.4 KiB
TeX
96 lines
3.4 KiB
TeX
\documentclass[11pt]{book}
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\usepackage[paperwidth=90mm,paperheight=140mm,margin=5mm,bottom=6mm,footskip=4mm]{geometry} % https://mirrors.ctan.org/macros/latex/contrib/geometry/geometry.pdf
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\usepackage[hidelinks]{hyperref} % http://mirrors.ctan.org/macros/latex/contrib/hyperref/doc/hyperref-doc.pdf
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\usepackage{amsfonts} % http://mirrors.ctan.org/fonts/amsfonts/doc/amsfndoc.pdf
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\usepackage{amsmath} % http://mirrors.ctan.org/macros/latex/required/amsmath/amsldoc.pdf
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\usepackage{catchfile} % https://mirrors.ctan.org/macros/latex/contrib/catchfile/catchfile.pdf
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\usepackage{enumitem} % http://mirrors.ctan.org/macros/latex/contrib/enumitem/enumitem.pdf
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\usepackage{fontawesome} % http://mirrors.ctan.org/fonts/fontawesome/doc/fontawesome.pdf
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\usepackage{kotex} %
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\usepackage{paracol} % https://mirrors.ctan.org/macros/latex/contrib/paracol/paracol-man.pdf
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\usepackage{qrcode} % http://mirrors.ctan.org/macros/latex/contrib/qrcode/qrcode.pdf
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\usepackage{titlesec} % https://mirrors.ctan.org/macros/latex/contrib/titlesec/titlesec.pdf
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\usepackage{xcolor} % http://mirrors.ctan.org/macros/latex/contrib/xcolor/xcolor.pdf
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\usepackage{xstring} % https://mirrors.ctan.org/macros/generic/xstring/xstring-en.pdf
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\titleformat{\chapter}[block]{\huge\bfseries}{}{0pt}{}{}
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\titlespacing{\chapter}{0pt}{-20pt}{0pt}
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\setlist[description]{leftmargin=15pt,labelindent=0pt}
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\CatchFileDef{\HEAD}{../../.git/refs/heads/master}{}
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\newcommand{\gitrevision}{\StrLeft{\HEAD}{7}}
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\newcommand{\gh}{
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https://github.com/pompydev/cheatsheets/tree/\HEAD
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}
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\newcommand{\cc}[1]{
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$\vcenter{\hbox{#1}}$
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}
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\begin{document}
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\pagenumbering{gobble}
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\centerline{\large pomp's}
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\null
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\centerline{\LARGE \textbf{Mathematics}}
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\null
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\centerline{\large Cheat Sheet}
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\vspace{236.5pt}
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\columnratio{0.63}
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\begin{paracol}{2}
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\vspace{21pt}
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\href{\gh}{\cc{\large\faGithub} pompydev/cheatsheets}
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git reversion:\gitrevision
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made with \LaTeX
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\switchcolumn
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\fbox{\qrcode[hyperlink,height=20mm]{\gh}}
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\end{paracol}
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\newpage
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\tableofcontents
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\newpage
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\pagenumbering{arabic}
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\chapter{Algebra}
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\section{Types of Numbers}
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\begin{description}
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\item[$\mathbb{C}$] - Complex / 복소수 ($\pmb{a+bi}$)
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\begin{description}
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\item[$\mathbb{R}$] - Real / 실수 ($\pmb{a}+bi$)
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\begin{description}
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\item[$\mathbb{Q}$] - Rational / 유리수 ($\frac{p}{q} | p,q \in \mathbb{Z}, q \ne 0$)
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\begin{description}
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\item[$\mathbb{Z}$] - Integer / 정수 ($..., -1, 0, 1, ...$)
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\begin{description}
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\item[$\mathbb{N}$] - Natural / 자연수 ($1, 2, 3, ...$)
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\item[$\mathbb{W}$] - Whole ($0, 1, 2, ...$)
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\end{description}
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\end{description}
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\item Irrational / 무리수
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\end{description}
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\item[$\mathbb{I}$] - Imaginary / 허수 ($a+\pmb{bi}$)
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\end{description}
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\end{description}
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\newpage
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\section{Rational decimal numbers}
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\subsection{Termination test}
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Given simplified fraction of rational number $x = \frac{p}{q}$, if $q = 2^m \cdot 5^n | m, n \in \mathbb{Z}$,
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then decimal form of $x$ is terminating.
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\subsection{Decimal-fraction conversion}
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To convert non-terminating repeating decimal number to fraction, use the following formula:
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$$
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a.\textcolor{red}{b}\overline{\textcolor{blue}{cd}}=\frac{abcd-ab}{\textcolor{blue}{99}\textcolor{red}{0}}
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$$
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\newpage
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\end{document}
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