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Add latex_template
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24
latex_template/README.md
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24
latex_template/README.md
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# Latex Template
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A personal template I have copied from [Charlie's Math Template](https://github.com/SeniorMars/dotfiles/tree/master/latex_template).
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To use:
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1. Copy this directory to the same directory as your LaTeX file.
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```bash
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$ cp ./letterfonts.tex ./macros.tex ./preamble.tex ./template.tex [some_dir]
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or
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$ ltcp
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```
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ltcp if alias, embedded into my `.zshrc`
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2. Edit the file "template.tex" to your liking.
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## Note
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I'm using texlive with it.
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178
latex_template/letterfonts.tex
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178
latex_template/letterfonts.tex
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% Things Lie
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\newcommand{\kb}{\mathfrak b}
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\newcommand{\kg}{\mathfrak g}
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\newcommand{\kh}{\mathfrak h}
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\newcommand{\kn}{\mathfrak n}
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\newcommand{\ku}{\mathfrak u}
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\newcommand{\kz}{\mathfrak z}
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\DeclareMathOperator{\Ext}{Ext} % Ext functor
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\DeclareMathOperator{\Tor}{Tor} % Tor functor
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\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group
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\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6
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% More script letters etc.
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\newcommand{\SA}{\mathcal A}
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\newcommand{\SB}{\mathcal B}
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\newcommand{\SC}{\mathcal C}
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\newcommand{\SF}{\mathcal F}
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\newcommand{\SG}{\mathcal G}
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\newcommand{\SH}{\mathcal H}
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\newcommand{\OO}{\mathcal O}
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\newcommand{\SCA}{\mathscr A}
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\newcommand{\SCB}{\mathscr B}
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\newcommand{\SCC}{\mathscr C}
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\newcommand{\SCD}{\mathscr D}
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\newcommand{\SCE}{\mathscr E}
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\newcommand{\SCF}{\mathscr F}
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\newcommand{\SCG}{\mathscr G}
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\newcommand{\SCH}{\mathscr H}
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% Mathfrak primes
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\newcommand{\km}{\mathfrak m}
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\newcommand{\kp}{\mathfrak p}
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\newcommand{\kq}{\mathfrak q}
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% number sets
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\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}}
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\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}}
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\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}}
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\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}}
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\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}}
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\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}}
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\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}}
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\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}}
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% expected value
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\newcommand{\EE}{\ensuremath{\mathbb{E}}}
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\newcommand{\charin}{\text{ char }}
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\DeclareMathOperator{\sign}{sign}
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\DeclareMathOperator{\Aut}{Aut}
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\DeclareMathOperator{\Inn}{Inn}
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\DeclareMathOperator{\Syl}{Syl}
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\DeclareMathOperator{\Gal}{Gal}
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\DeclareMathOperator{\GL}{GL} % General linear group
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\DeclareMathOperator{\SL}{SL} % Special linear group
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%---------------------------------------
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% BlackBoard Math Fonts :-
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%---------------------------------------
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%Captital Letters
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\newcommand{\bbA}{\mathbb{A}} \newcommand{\bbB}{\mathbb{B}}
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\newcommand{\bbC}{\mathbb{C}} \newcommand{\bbD}{\mathbb{D}}
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\newcommand{\bbE}{\mathbb{E}} \newcommand{\bbF}{\mathbb{F}}
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\newcommand{\bbG}{\mathbb{G}} \newcommand{\bbH}{\mathbb{H}}
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\newcommand{\bbI}{\mathbb{I}} \newcommand{\bbJ}{\mathbb{J}}
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\newcommand{\bbK}{\mathbb{K}} \newcommand{\bbL}{\mathbb{L}}
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\newcommand{\bbM}{\mathbb{M}} \newcommand{\bbN}{\mathbb{N}}
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\newcommand{\bbO}{\mathbb{O}} \newcommand{\bbP}{\mathbb{P}}
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\newcommand{\bbQ}{\mathbb{Q}} \newcommand{\bbR}{\mathbb{R}}
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\newcommand{\bbS}{\mathbb{S}} \newcommand{\bbT}{\mathbb{T}}
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\newcommand{\bbU}{\mathbb{U}} \newcommand{\bbV}{\mathbb{V}}
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\newcommand{\bbW}{\mathbb{W}} \newcommand{\bbX}{\mathbb{X}}
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\newcommand{\bbY}{\mathbb{Y}} \newcommand{\bbZ}{\mathbb{Z}}
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%---------------------------------------
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% MathCal Fonts :-
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%---------------------------------------
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%Captital Letters
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\newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}}
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\newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}}
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\newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}}
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\newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}}
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\newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}}
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\newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}}
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\newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}}
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\newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}}
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\newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}}
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\newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}}
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\newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}}
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\newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}}
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\newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}}
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%---------------------------------------
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% Bold Math Fonts :-
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%---------------------------------------
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%Captital Letters
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\newcommand{\bmA}{\boldsymbol{A}} \newcommand{\bmB}{\boldsymbol{B}}
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\newcommand{\bmC}{\boldsymbol{C}} \newcommand{\bmD}{\boldsymbol{D}}
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\newcommand{\bmE}{\boldsymbol{E}} \newcommand{\bmF}{\boldsymbol{F}}
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\newcommand{\bmG}{\boldsymbol{G}} \newcommand{\bmH}{\boldsymbol{H}}
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\newcommand{\bmI}{\boldsymbol{I}} \newcommand{\bmJ}{\boldsymbol{J}}
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\newcommand{\bmK}{\boldsymbol{K}} \newcommand{\bmL}{\boldsymbol{L}}
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\newcommand{\bmM}{\boldsymbol{M}} \newcommand{\bmN}{\boldsymbol{N}}
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\newcommand{\bmO}{\boldsymbol{O}} \newcommand{\bmP}{\boldsymbol{P}}
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\newcommand{\bmQ}{\boldsymbol{Q}} \newcommand{\bmR}{\boldsymbol{R}}
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\newcommand{\bmS}{\boldsymbol{S}} \newcommand{\bmT}{\boldsymbol{T}}
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\newcommand{\bmU}{\boldsymbol{U}} \newcommand{\bmV}{\boldsymbol{V}}
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\newcommand{\bmW}{\boldsymbol{W}} \newcommand{\bmX}{\boldsymbol{X}}
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\newcommand{\bmY}{\boldsymbol{Y}} \newcommand{\bmZ}{\boldsymbol{Z}}
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%Small Letters
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\newcommand{\bma}{\boldsymbol{a}} \newcommand{\bmb}{\boldsymbol{b}}
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\newcommand{\bmc}{\boldsymbol{c}} \newcommand{\bmd}{\boldsymbol{d}}
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\newcommand{\bme}{\boldsymbol{e}} \newcommand{\bmf}{\boldsymbol{f}}
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\newcommand{\bmg}{\boldsymbol{g}} \newcommand{\bmh}{\boldsymbol{h}}
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\newcommand{\bmi}{\boldsymbol{i}} \newcommand{\bmj}{\boldsymbol{j}}
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\newcommand{\bmk}{\boldsymbol{k}} \newcommand{\bml}{\boldsymbol{l}}
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\newcommand{\bmm}{\boldsymbol{m}} \newcommand{\bmn}{\boldsymbol{n}}
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\newcommand{\bmo}{\boldsymbol{o}} \newcommand{\bmp}{\boldsymbol{p}}
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\newcommand{\bmq}{\boldsymbol{q}} \newcommand{\bmr}{\boldsymbol{r}}
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\newcommand{\bms}{\boldsymbol{s}} \newcommand{\bmt}{\boldsymbol{t}}
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\newcommand{\bmu}{\boldsymbol{u}} \newcommand{\bmv}{\boldsymbol{v}}
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\newcommand{\bmw}{\boldsymbol{w}} \newcommand{\bmx}{\boldsymbol{x}}
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\newcommand{\bmy}{\boldsymbol{y}} \newcommand{\bmz}{\boldsymbol{z}}
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%---------------------------------------
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% Scr Math Fonts :-
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%---------------------------------------
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\newcommand{\sA}{{\mathscr{A}}} \newcommand{\sB}{{\mathscr{B}}}
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\newcommand{\sC}{{\mathscr{C}}} \newcommand{\sD}{{\mathscr{D}}}
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\newcommand{\sE}{{\mathscr{E}}} \newcommand{\sF}{{\mathscr{F}}}
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\newcommand{\sG}{{\mathscr{G}}} \newcommand{\sH}{{\mathscr{H}}}
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\newcommand{\sI}{{\mathscr{I}}} \newcommand{\sJ}{{\mathscr{J}}}
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\newcommand{\sK}{{\mathscr{K}}} \newcommand{\sL}{{\mathscr{L}}}
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\newcommand{\sM}{{\mathscr{M}}} \newcommand{\sN}{{\mathscr{N}}}
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\newcommand{\sO}{{\mathscr{O}}} \newcommand{\sP}{{\mathscr{P}}}
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\newcommand{\sQ}{{\mathscr{Q}}} \newcommand{\sR}{{\mathscr{R}}}
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\newcommand{\sS}{{\mathscr{S}}} \newcommand{\sT}{{\mathscr{T}}}
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\newcommand{\sU}{{\mathscr{U}}} \newcommand{\sV}{{\mathscr{V}}}
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\newcommand{\sW}{{\mathscr{W}}} \newcommand{\sX}{{\mathscr{X}}}
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\newcommand{\sY}{{\mathscr{Y}}} \newcommand{\sZ}{{\mathscr{Z}}}
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%---------------------------------------
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% Math Fraktur Font
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%---------------------------------------
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%Captital Letters
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\newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}}
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\newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}}
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\newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}}
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\newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}}
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\newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}}
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\newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}}
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\newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}}
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\newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}}
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\newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}}
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\newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}}
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\newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}}
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\newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}}
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\newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}}
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%Small Letters
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\newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}}
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\newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}}
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\newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}}
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\newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}}
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\newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}}
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\newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}}
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\newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}}
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\newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}}
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\newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}}
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\newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}}
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\newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}}
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\newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}}
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\newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}}
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88
latex_template/macros.tex
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latex_template/macros.tex
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%From M275 "Topology" at SJSU
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\newcommand{\id}{\mathrm{id}}
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\newcommand{\taking}[1]{\xrightarrow{#1}}
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\newcommand{\inv}{^{-1}}
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%From M170 "Introduction to Graph Theory" at SJSU
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\DeclareMathOperator{\diam}{diam}
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\DeclareMathOperator{\ord}{ord}
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\newcommand{\defeq}{\overset{\mathrm{def}}{=}}
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%From the USAMO .tex files
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\newcommand{\ts}{\textsuperscript}
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\newcommand{\dg}{^\circ}
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\newcommand{\ii}{\item}
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% % From Math 55 and Math 145 at Harvard
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% \newenvironment{subproof}[1][Proof]{%
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% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}%
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% {\end{proof}}
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\newcommand{\liff}{\leftrightarrow}
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\newcommand{\lthen}{\rightarrow}
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\newcommand{\opname}{\operatorname}
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\newcommand{\surjto}{\twoheadrightarrow}
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\newcommand{\injto}{\hookrightarrow}
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\newcommand{\On}{\mathrm{On}} % ordinals
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\DeclareMathOperator{\img}{im} % Image
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\DeclareMathOperator{\Img}{Im} % Image
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\DeclareMathOperator{\coker}{coker} % Cokernel
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\DeclareMathOperator{\Coker}{Coker} % Cokernel
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\DeclareMathOperator{\Ker}{Ker} % Kernel
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\DeclareMathOperator{\rank}{rank}
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\DeclareMathOperator{\Spec}{Spec} % spectrum
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\DeclareMathOperator{\Tr}{Tr} % trace
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\DeclareMathOperator{\pr}{pr} % projection
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\DeclareMathOperator{\ext}{ext} % extension
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\DeclareMathOperator{\pred}{pred} % predecessor
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\DeclareMathOperator{\dom}{dom} % domain
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\DeclareMathOperator{\ran}{ran} % range
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\DeclareMathOperator{\Hom}{Hom} % homomorphism
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\DeclareMathOperator{\Mor}{Mor} % morphisms
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\DeclareMathOperator{\End}{End} % endomorphism
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\newcommand{\eps}{\epsilon}
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\newcommand{\veps}{\varepsilon}
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\newcommand{\ol}{\overline}
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\newcommand{\ul}{\underline}
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\newcommand{\wt}{\widetilde}
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\newcommand{\wh}{\widehat}
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\newcommand{\vocab}[1]{\textbf{\color{blue} #1}}
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\providecommand{\half}{\frac{1}{2}}
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\newcommand{\dang}{\measuredangle} %% Directed angle
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\newcommand{\ray}[1]{\overrightarrow{#1}}
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\newcommand{\seg}[1]{\overline{#1}}
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\newcommand{\arc}[1]{\wideparen{#1}}
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\DeclareMathOperator{\cis}{cis}
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\DeclareMathOperator*{\lcm}{lcm}
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\DeclareMathOperator*{\argmin}{arg min}
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\DeclareMathOperator*{\argmax}{arg max}
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\newcommand{\cycsum}{\sum_{\mathrm{cyc}}}
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\newcommand{\symsum}{\sum_{\mathrm{sym}}}
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\newcommand{\cycprod}{\prod_{\mathrm{cyc}}}
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\newcommand{\symprod}{\prod_{\mathrm{sym}}}
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\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}}
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\newcommand{\parinn}{\setlength{\parindent}{1cm}}
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\newcommand{\parinf}{\setlength{\parindent}{0cm}}
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% \newcommand{\norm}{\|\cdot\|}
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\newcommand{\inorm}{\norm_{\infty}}
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\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}}
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\newcommand{\oset}{V_{\alpha}}
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\newcommand{\opset}[1]{V_{\alpha_{#1}}}
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\newcommand{\lub}{\text{lub}}
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\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}}
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\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}}
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\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}}
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\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}}
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\newcommand{\lm}{\lambda}
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\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}}
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\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}}
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\newcommand{\lt}{\left}
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\newcommand{\rt}{\right}
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\newcommand{\bs}[1]{\boldsymbol{#1}}
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\newcommand{\exs}{\exists}
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\newcommand{\st}{\strut}
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\newcommand{\dps}[1]{\displaystyle{#1}}
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\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} }
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\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed}
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773
latex_template/preamble.tex
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773
latex_template/preamble.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% PACKAGE IMPORTS
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry}
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\usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools}
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\usepackage[utf8]{inputenc}
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\usepackage[T2A]{fontenc}
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\usepackage[varbb]{newpxmath}
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\usepackage{xfrac}
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\usepackage[makeroom]{cancel}
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\usepackage{mathtools}
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\usepackage{bookmark}
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\usepackage{enumitem}
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\usepackage{hyperref,theoremref}
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\hypersetup{
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pdftitle={Assignment},
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colorlinks=true, linkcolor=doc!90,
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bookmarksnumbered=true,
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bookmarksopen=true
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}
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\usepackage[most,many,breakable]{tcolorbox}
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\usepackage{xcolor}
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\usepackage{varwidth}
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\usepackage{varwidth}
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\usepackage{etoolbox}
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%\usepackage{authblk}
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\usepackage{nameref}
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\usepackage{multicol,array}
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\usepackage{tikz-cd}
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\usepackage[ruled,vlined,linesnumbered]{algorithm2e}
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\usepackage{comment} % enables the use of multi-line comments (\ifx \fi)
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\usepackage{import}
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\usepackage{xifthen}
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\usepackage{pdfpages}
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\usepackage{transparent}
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\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}}
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\SetCommentSty{mycommfont}
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\newcommand{\incfig}[1]{%
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\def\svgwidth{\columnwidth}
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\import{./figures/}{#1.pdf_tex}
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}
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\usepackage{tikzsymbols}
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\renewcommand\qedsymbol{$\Laughey$}
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%\usepackage{import}
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%\usepackage{xifthen}
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%\usepackage{pdfpages}
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%\usepackage{transparent}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% SELF MADE COLORS
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\definecolor{myg}{RGB}{56, 140, 70}
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\definecolor{myb}{RGB}{45, 111, 177}
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\definecolor{myr}{RGB}{199, 68, 64}
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\definecolor{mytheorembg}{HTML}{F2F2F9}
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\definecolor{mytheoremfr}{HTML}{00007B}
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\definecolor{mylenmabg}{HTML}{FFFAF8}
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\definecolor{mylenmafr}{HTML}{983b0f}
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\definecolor{mypropbg}{HTML}{f2fbfc}
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\definecolor{mypropfr}{HTML}{191971}
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\definecolor{myexamplebg}{HTML}{F2FBF8}
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\definecolor{myexamplefr}{HTML}{88D6D1}
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\definecolor{myexampleti}{HTML}{2A7F7F}
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\definecolor{mydefinitbg}{HTML}{E5E5FF}
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\definecolor{mydefinitfr}{HTML}{3F3FA3}
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\definecolor{notesgreen}{RGB}{0,162,0}
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\definecolor{myp}{RGB}{197, 92, 212}
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\definecolor{mygr}{HTML}{2C3338}
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\definecolor{myred}{RGB}{127,0,0}
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\definecolor{myyellow}{RGB}{169,121,69}
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\definecolor{myexercisebg}{HTML}{F2FBF8}
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\definecolor{myexercisefg}{HTML}{88D6D1}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% TCOLORBOX SETUPS
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\setlength{\parindent}{1cm}
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%================================
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% THEOREM BOX
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%================================
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\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Theorem}{Theorem}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mytheorembg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mytheoremfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mytheoremfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mytheoremfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{theorem}{Theorem}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mytheorembg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mytheoremfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mytheoremfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mytheoremfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcolorbox{Theoremcon}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = mytheorembg
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{mytheoremfr}
|
||||
,sharp corners
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
}
|
||||
|
||||
%================================
|
||||
% Corollery
|
||||
%================================
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Corollary}{Corollary}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = myp!10
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{myp!85!black}
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper = \tcbtitle\par\smallskip
|
||||
,coltitle = myp!85!black
|
||||
,fonttitle = \bfseries\sffamily
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,segmentation style={solid, myp!85!black}
|
||||
}
|
||||
{th}
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{corollary}{Corollary}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = myp!10
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{myp!85!black}
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper = \tcbtitle\par\smallskip
|
||||
,coltitle = myp!85!black
|
||||
,fonttitle = \bfseries\sffamily
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,segmentation style={solid, myp!85!black}
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
%================================
|
||||
% LENMA
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Lenma}{Lenma}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mylenmabg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mylenmafr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mylenmafr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mylenmafr},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{lenma}{Lenma}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mylenmabg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mylenmafr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mylenmafr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mylenmafr},
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
%================================
|
||||
% PROPOSITION
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Prop}{Proposition}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mypropbg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mypropfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mypropfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mypropfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{prop}{Proposition}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = mypropbg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{mypropfr},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = mypropfr,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, mypropfr},
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
%================================
|
||||
% CLAIM
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{claim}{Claim}
|
||||
{%
|
||||
enhanced
|
||||
,breakable
|
||||
,colback = myg!10
|
||||
,frame hidden
|
||||
,boxrule = 0sp
|
||||
,borderline west = {2pt}{0pt}{myg}
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper = \tcbtitle\par\smallskip
|
||||
,coltitle = myg!85!black
|
||||
,fonttitle = \bfseries\sffamily
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,segmentation style={solid, myg!85!black}
|
||||
}
|
||||
{th}
|
||||
|
||||
|
||||
|
||||
%================================
|
||||
% Exercise
|
||||
%================================
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=section]{Exercise}{Exercise}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = myexercisebg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{myexercisefg},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = myexercisefg,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, myexercisefg},
|
||||
}
|
||||
{th}
|
||||
|
||||
\tcbuselibrary{theorems,skins,hooks}
|
||||
\newtcbtheorem[number within=chapter]{exercise}{Exercise}
|
||||
{%
|
||||
enhanced,
|
||||
breakable,
|
||||
colback = myexercisebg,
|
||||
frame hidden,
|
||||
boxrule = 0sp,
|
||||
borderline west = {2pt}{0pt}{myexercisefg},
|
||||
sharp corners,
|
||||
detach title,
|
||||
before upper = \tcbtitle\par\smallskip,
|
||||
coltitle = myexercisefg,
|
||||
fonttitle = \bfseries\sffamily,
|
||||
description font = \mdseries,
|
||||
separator sign none,
|
||||
segmentation style={solid, myexercisefg},
|
||||
}
|
||||
{th}
|
||||
|
||||
%================================
|
||||
% EXAMPLE BOX
|
||||
%================================
|
||||
|
||||
\newtcbtheorem[number within=section]{Example}{Example}
|
||||
{%
|
||||
colback = myexamplebg
|
||||
,breakable
|
||||
,colframe = myexamplefr
|
||||
,coltitle = myexampleti
|
||||
,boxrule = 1pt
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper=\tcbtitle\par\smallskip
|
||||
,fonttitle = \bfseries
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,description delimiters parenthesis
|
||||
}
|
||||
{ex}
|
||||
|
||||
\newtcbtheorem[number within=chapter]{example}{Example}
|
||||
{%
|
||||
colback = myexamplebg
|
||||
,breakable
|
||||
,colframe = myexamplefr
|
||||
,coltitle = myexampleti
|
||||
,boxrule = 1pt
|
||||
,sharp corners
|
||||
,detach title
|
||||
,before upper=\tcbtitle\par\smallskip
|
||||
,fonttitle = \bfseries
|
||||
,description font = \mdseries
|
||||
,separator sign none
|
||||
,description delimiters parenthesis
|
||||
}
|
||||
{ex}
|
||||
|
||||
%================================
|
||||
% DEFINITION BOX
|
||||
%================================
|
||||
|
||||
\newtcbtheorem[number within=section]{Definition}{Definition}{enhanced,
|
||||
before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm,
|
||||
attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm,
|
||||
boxed title style={frame code={
|
||||
\path[fill=tcbcolback]
|
||||
([yshift=-1mm,xshift=-1mm]frame.north west)
|
||||
arc[start angle=0,end angle=180,radius=1mm]
|
||||
([yshift=-1mm,xshift=1mm]frame.north east)
|
||||
arc[start angle=180,end angle=0,radius=1mm];
|
||||
\path[left color=tcbcolback!60!black,right color=tcbcolback!60!black,
|
||||
middle color=tcbcolback!80!black]
|
||||
([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east)
|
||||
[rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east)
|
||||
-- (frame.south east) -- (frame.south west)
|
||||
-- ([xshift=-1mm,yshift=-1mm]frame.north west)
|
||||
[sharp corners]-- cycle;
|
||||
},interior engine=empty,
|
||||
},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},#1}{def}
|
||||
\newtcbtheorem[number within=chapter]{definition}{Definition}{enhanced,
|
||||
before skip=2mm,after skip=2mm, colback=red!5,colframe=red!80!black,boxrule=0.5mm,
|
||||
attach boxed title to top left={xshift=1cm,yshift*=1mm-\tcboxedtitleheight}, varwidth boxed title*=-3cm,
|
||||
boxed title style={frame code={
|
||||
\path[fill=tcbcolback]
|
||||
([yshift=-1mm,xshift=-1mm]frame.north west)
|
||||
arc[start angle=0,end angle=180,radius=1mm]
|
||||
([yshift=-1mm,xshift=1mm]frame.north east)
|
||||
arc[start angle=180,end angle=0,radius=1mm];
|
||||
\path[left color=tcbcolback!60!black,right color=tcbcolback!60!black,
|
||||
middle color=tcbcolback!80!black]
|
||||
([xshift=-2mm]frame.north west) -- ([xshift=2mm]frame.north east)
|
||||
[rounded corners=1mm]-- ([xshift=1mm,yshift=-1mm]frame.north east)
|
||||
-- (frame.south east) -- (frame.south west)
|
||||
-- ([xshift=-1mm,yshift=-1mm]frame.north west)
|
||||
[sharp corners]-- cycle;
|
||||
},interior engine=empty,
|
||||
},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},#1}{def}
|
||||
|
||||
|
||||
|
||||
%================================
|
||||
% Solution BOX
|
||||
%================================
|
||||
|
||||
\makeatletter
|
||||
\newtcbtheorem{question}{Question}{enhanced,
|
||||
breakable,
|
||||
colback=white,
|
||||
colframe=myb!80!black,
|
||||
attach boxed title to top left={yshift*=-\tcboxedtitleheight},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},
|
||||
boxed title size=title,
|
||||
boxed title style={%
|
||||
sharp corners,
|
||||
rounded corners=northwest,
|
||||
colback=tcbcolframe,
|
||||
boxrule=0pt,
|
||||
},
|
||||
underlay boxed title={%
|
||||
\path[fill=tcbcolframe] (title.south west)--(title.south east)
|
||||
to[out=0, in=180] ([xshift=5mm]title.east)--
|
||||
(title.center-|frame.east)
|
||||
[rounded corners=\kvtcb@arc] |-
|
||||
(frame.north) -| cycle;
|
||||
},
|
||||
#1
|
||||
}{def}
|
||||
\makeatother
|
||||
|
||||
%================================
|
||||
% SOLUTION BOX
|
||||
%================================
|
||||
|
||||
\makeatletter
|
||||
\newtcolorbox{solution}{enhanced,
|
||||
breakable,
|
||||
colback=white,
|
||||
colframe=myg!80!black,
|
||||
attach boxed title to top left={yshift*=-\tcboxedtitleheight},
|
||||
title=Solution,
|
||||
boxed title size=title,
|
||||
boxed title style={%
|
||||
sharp corners,
|
||||
rounded corners=northwest,
|
||||
colback=tcbcolframe,
|
||||
boxrule=0pt,
|
||||
},
|
||||
underlay boxed title={%
|
||||
\path[fill=tcbcolframe] (title.south west)--(title.south east)
|
||||
to[out=0, in=180] ([xshift=5mm]title.east)--
|
||||
(title.center-|frame.east)
|
||||
[rounded corners=\kvtcb@arc] |-
|
||||
(frame.north) -| cycle;
|
||||
},
|
||||
}
|
||||
\makeatother
|
||||
|
||||
%================================
|
||||
% Question BOX
|
||||
%================================
|
||||
|
||||
\makeatletter
|
||||
\newtcbtheorem{qstion}{Question}{enhanced,
|
||||
breakable,
|
||||
colback=white,
|
||||
colframe=mygr,
|
||||
attach boxed title to top left={yshift*=-\tcboxedtitleheight},
|
||||
fonttitle=\bfseries,
|
||||
title={#2},
|
||||
boxed title size=title,
|
||||
boxed title style={%
|
||||
sharp corners,
|
||||
rounded corners=northwest,
|
||||
colback=tcbcolframe,
|
||||
boxrule=0pt,
|
||||
},
|
||||
underlay boxed title={%
|
||||
\path[fill=tcbcolframe] (title.south west)--(title.south east)
|
||||
to[out=0, in=180] ([xshift=5mm]title.east)--
|
||||
(title.center-|frame.east)
|
||||
[rounded corners=\kvtcb@arc] |-
|
||||
(frame.north) -| cycle;
|
||||
},
|
||||
#1
|
||||
}{def}
|
||||
\makeatother
|
||||
|
||||
\newtcbtheorem[number within=chapter]{wconc}{Wrong Concept}{
|
||||
breakable,
|
||||
enhanced,
|
||||
colback=white,
|
||||
colframe=myr,
|
||||
arc=0pt,
|
||||
outer arc=0pt,
|
||||
fonttitle=\bfseries\sffamily\large,
|
||||
colbacktitle=myr,
|
||||
attach boxed title to top left={},
|
||||
boxed title style={
|
||||
enhanced,
|
||||
skin=enhancedfirst jigsaw,
|
||||
arc=3pt,
|
||||
bottom=0pt,
|
||||
interior style={fill=myr}
|
||||
},
|
||||
#1
|
||||
}{def}
|
||||
|
||||
|
||||
|
||||
%================================
|
||||
% NOTE BOX
|
||||
%================================
|
||||
|
||||
\usetikzlibrary{arrows,calc,shadows.blur}
|
||||
\tcbuselibrary{skins}
|
||||
\newtcolorbox{note}[1][]{%
|
||||
enhanced jigsaw,
|
||||
colback=gray!20!white,%
|
||||
colframe=gray!80!black,
|
||||
size=small,
|
||||
boxrule=1pt,
|
||||
title=\textbf{Note:-},
|
||||
halign title=flush center,
|
||||
coltitle=black,
|
||||
breakable,
|
||||
drop shadow=black!50!white,
|
||||
attach boxed title to top left={xshift=1cm,yshift=-\tcboxedtitleheight/2,yshifttext=-\tcboxedtitleheight/2},
|
||||
minipage boxed title=1.5cm,
|
||||
boxed title style={%
|
||||
colback=white,
|
||||
size=fbox,
|
||||
boxrule=1pt,
|
||||
boxsep=2pt,
|
||||
underlay={%
|
||||
\coordinate (dotA) at ($(interior.west) + (-0.5pt,0)$);
|
||||
\coordinate (dotB) at ($(interior.east) + (0.5pt,0)$);
|
||||
\begin{scope}
|
||||
\clip (interior.north west) rectangle ([xshift=3ex]interior.east);
|
||||
\filldraw [white, blur shadow={shadow opacity=60, shadow yshift=-.75ex}, rounded corners=2pt] (interior.north west) rectangle (interior.south east);
|
||||
\end{scope}
|
||||
\begin{scope}[gray!80!black]
|
||||
\fill (dotA) circle (2pt);
|
||||
\fill (dotB) circle (2pt);
|
||||
\end{scope}
|
||||
},
|
||||
},
|
||||
#1,
|
||||
}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% SELF MADE COMMANDS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
|
||||
\newcommand{\thm}[2]{\begin{Theorem}{#1}{}#2\end{Theorem}}
|
||||
\newcommand{\cor}[2]{\begin{Corollary}{#1}{}#2\end{Corollary}}
|
||||
\newcommand{\mlenma}[2]{\begin{Lenma}{#1}{}#2\end{Lenma}}
|
||||
\newcommand{\mprop}[2]{\begin{Prop}{#1}{}#2\end{Prop}}
|
||||
\newcommand{\clm}[3]{\begin{claim}{#1}{#2}#3\end{claim}}
|
||||
\newcommand{\wc}[2]{\begin{wconc}{#1}{}\setlength{\parindent}{1cm}#2\end{wconc}}
|
||||
\newcommand{\thmcon}[1]{\begin{Theoremcon}{#1}\end{Theoremcon}}
|
||||
\newcommand{\ex}[2]{\begin{Example}{#1}{}#2\end{Example}}
|
||||
\newcommand{\dfn}[2]{\begin{Definition}[colbacktitle=red!75!black]{#1}{}#2\end{Definition}}
|
||||
\newcommand{\dfnc}[2]{\begin{definition}[colbacktitle=red!75!black]{#1}{}#2\end{definition}}
|
||||
\newcommand{\qs}[2]{\begin{question}{#1}{}#2\end{question}}
|
||||
\newcommand{\pf}[2]{\begin{myproof}[#1]#2\end{myproof}}
|
||||
\newcommand{\nt}[1]{\begin{note}#1\end{note}}
|
||||
|
||||
\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
|
||||
\node[shape=circle,draw,inner sep=1pt] (char) {#1};}}
|
||||
\newcommand\getcurrentref[1]{%
|
||||
\ifnumequal{\value{#1}}{0}
|
||||
{??}
|
||||
{\the\value{#1}}%
|
||||
}
|
||||
\newcommand{\getCurrentSectionNumber}{\getcurrentref{section}}
|
||||
\newenvironment{myproof}[1][\proofname]{%
|
||||
\proof[\bfseries #1: ]%
|
||||
}{\endproof}
|
||||
|
||||
\newcommand{\mclm}[2]{\begin{myclaim}[#1]#2\end{myclaim}}
|
||||
\newenvironment{myclaim}[1][\claimname]{\proof[\bfseries #1: ]}{}
|
||||
|
||||
\newcounter{mylabelcounter}
|
||||
|
||||
\makeatletter
|
||||
\newcommand{\setword}[2]{%
|
||||
\phantomsection
|
||||
#1\def\@currentlabel{\unexpanded{#1}}\label{#2}%
|
||||
}
|
||||
\makeatother
|
||||
|
||||
|
||||
|
||||
|
||||
\tikzset{
|
||||
symbol/.style={
|
||||
draw=none,
|
||||
every to/.append style={
|
||||
edge node={node [sloped, allow upside down, auto=false]{$#1$}}}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
% deliminators
|
||||
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
|
||||
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
|
||||
|
||||
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
|
||||
\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
|
||||
\DeclarePairedDelimiter{\round}{\lfloor}{\rceil}
|
||||
|
||||
\newsavebox\diffdbox
|
||||
\newcommand{\slantedromand}{{\mathpalette\makesl{d}}}
|
||||
\newcommand{\makesl}[2]{%
|
||||
\begingroup
|
||||
\sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}%
|
||||
\pdfsave
|
||||
\pdfsetmatrix{1 0 0.2 1}%
|
||||
\rlap{\usebox{\diffdbox}}%
|
||||
\pdfrestore
|
||||
\hskip\wd\diffdbox
|
||||
\endgroup
|
||||
}
|
||||
\newcommand{\dd}[1][]{\ensuremath{\mathop{}\!\ifstrempty{#1}{%
|
||||
\slantedromand\@ifnextchar^{\hspace{0.2ex}}{\hspace{0.1ex}}}%
|
||||
{\slantedromand\hspace{0.2ex}^{#1}}}}
|
||||
\ProvideDocumentCommand\dv{o m g}{%
|
||||
\ensuremath{%
|
||||
\IfValueTF{#3}{%
|
||||
\IfNoValueTF{#1}{%
|
||||
\frac{\dd #2}{\dd #3}%
|
||||
}{%
|
||||
\frac{\dd^{#1} #2}{\dd #3^{#1}}%
|
||||
}%
|
||||
}{%
|
||||
\IfNoValueTF{#1}{%
|
||||
\frac{\dd}{\dd #2}%
|
||||
}{%
|
||||
\frac{\dd^{#1}}{\dd #2^{#1}}%
|
||||
}%
|
||||
}%
|
||||
}%
|
||||
}
|
||||
\providecommand*{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial#3^{#1}}}
|
||||
% - others
|
||||
\DeclareMathOperator{\Lap}{\mathcal{L}}
|
||||
\DeclareMathOperator{\Var}{Var} % varience
|
||||
\DeclareMathOperator{\Cov}{Cov} % covarience
|
||||
\DeclareMathOperator{\E}{E} % expected
|
||||
|
||||
% Since the amsthm package isn't loaded
|
||||
|
||||
% I prefer the slanted \leq
|
||||
\let\oldleq\leq % save them in case they're every wanted
|
||||
\let\oldgeq\geq
|
||||
\renewcommand{\leq}{\leqslant}
|
||||
\renewcommand{\geq}{\geqslant}
|
||||
|
||||
% % redefine matrix env to allow for alignment, use r as default
|
||||
% \renewcommand*\env@matrix[1][r]{\hskip -\arraycolsep
|
||||
% \let\@ifnextchar\new@ifnextchar
|
||||
% \array{*\c@MaxMatrixCols #1}}
|
||||
|
||||
|
||||
%\usepackage{framed}
|
||||
%\usepackage{titletoc}
|
||||
%\usepackage{etoolbox}
|
||||
%\usepackage{lmodern}
|
||||
|
||||
|
||||
%\patchcmd{\tableofcontents}{\contentsname}{\sffamily\contentsname}{}{}
|
||||
|
||||
%\renewenvironment{leftbar}
|
||||
%{\def\FrameCommand{\hspace{6em}%
|
||||
% {\color{myyellow}\vrule width 2pt depth 6pt}\hspace{1em}}%
|
||||
% \MakeFramed{\parshape 1 0cm \dimexpr\textwidth-6em\relax\FrameRestore}\vskip2pt%
|
||||
%}
|
||||
%{\endMakeFramed}
|
||||
|
||||
%\titlecontents{chapter}
|
||||
%[0em]{\vspace*{2\baselineskip}}
|
||||
%{\parbox{4.5em}{%
|
||||
% \hfill\Huge\sffamily\bfseries\color{myred}\thecontentspage}%
|
||||
% \vspace*{-2.3\baselineskip}\leftbar\textsc{\small\chaptername~\thecontentslabel}\\\sffamily}
|
||||
%{}{\endleftbar}
|
||||
%\titlecontents{section}
|
||||
%[8.4em]
|
||||
%{\sffamily\contentslabel{3em}}{}{}
|
||||
%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage}
|
||||
%\titlecontents{subsection}
|
||||
%[8.4em]
|
||||
%{\sffamily\contentslabel{3em}}{}{}
|
||||
%{\hspace{0.5em}\nobreak\itshape\color{myred}\contentspage}
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% TABLE OF CONTENTS
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
\usepackage{tikz}
|
||||
\definecolor{doc}{RGB}{0,0,0}
|
||||
\usepackage{titletoc}
|
||||
\contentsmargin{0cm}
|
||||
\titlecontents{chapter}[3.7pc]
|
||||
{\addvspace{30pt}%
|
||||
\begin{tikzpicture}[remember picture, overlay]%
|
||||
\draw[fill=black,draw=black] (-7,-.1) rectangle (-0.9,.5);%
|
||||
\pgftext[left,x=-3.5cm,y=0.2cm]{\color{white}\Large\sc\bfseries Chapter\ \thecontentslabel};%
|
||||
\end{tikzpicture}\color{black}\large\sc\bfseries}%
|
||||
{}
|
||||
{}
|
||||
{\;\titlerule\;\large\sc\bfseries Page \thecontentspage
|
||||
\begin{tikzpicture}[remember picture, overlay]
|
||||
\draw[fill=black,draw=black] (2pt,0) rectangle (4,0.1pt);
|
||||
\end{tikzpicture}}%
|
||||
\titlecontents{section}[3.7pc]
|
||||
{\addvspace{2pt}}
|
||||
{\contentslabel[\thecontentslabel]{2pc}}
|
||||
{}
|
||||
{\hfill\small \thecontentspage}
|
||||
[]
|
||||
\titlecontents*{subsection}[3.7pc]
|
||||
{\addvspace{-1pt}\small}
|
||||
{}
|
||||
{}
|
||||
{\ --- \small\thecontentspage}
|
||||
[ \textbullet\ ][]
|
||||
|
||||
\makeatletter
|
||||
\renewcommand{\tableofcontents}{%
|
||||
\center{\Huge{\sc\bfseries Contents}}
|
||||
\@starttoc{toc}}
|
||||
\makeatother
|
||||
|
||||
128
latex_template/template.tex
Normal file
128
latex_template/template.tex
Normal file
|
|
@ -0,0 +1,128 @@
|
|||
\documentclass{report}
|
||||
|
||||
\input{preamble}
|
||||
\input{macros}
|
||||
\input{letterfonts}
|
||||
|
||||
\title{\Huge{Some Class}\\Random Examples}
|
||||
\author{\huge{Тест}}
|
||||
\date{}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\maketitle
|
||||
\newpage% or \cleardoublepage
|
||||
% \pdfbookmark[<level>]{<title>}{<dest>}
|
||||
\pdfbookmark[section]{\contentsname}{toc}
|
||||
\tableofcontents
|
||||
\pagebreak
|
||||
|
||||
\chapter{}
|
||||
\section{Random Examples}
|
||||
\dfn{Limit of Sequence in $\bs{\bbR}$}{Let $\{s_n\}$ be a sequence in $\bbR$. We say $$\lim_{n\to\infty}s_n=s$$ where $s\in\bbR$ if $\forall$ real numbers $\eps>0$ $\exists$ natural number $N$ such that for $n>N$ $$s-\eps<s_n<s+\eps\text{ i.e. }|s-s_n|<\eps$$}
|
||||
\qs{}{Is the set ${x-}$axis${\setminus\{\text{Origin}\}}$ a closed set}
|
||||
\sol We have to take its complement and check whether that set is a open set i.e. if it is a union of open balls
|
||||
\nt{We will do topology in Normed Linear Space (Mainly $\bbR^n$ and occasionally $\bbC^n$)using the language of Metric Space}
|
||||
\clm{Topology}{}{Topology is cool}
|
||||
\ex{Open Set and Close Set}{
|
||||
\begin{tabular}{rl}
|
||||
Open Set: & $\bullet$ $\phi$ \\
|
||||
& $\bullet$ $\bigcup\limits_{x\in X}B_r(x)$ (Any $r>0$ will do) \\[3mm]
|
||||
& $\bullet$ $B_r(x)$ is open \\
|
||||
Closed Set: & $\bullet$ $X,\ \phi$ \\
|
||||
& $\bullet$ $\overline{B_r(x)}$ \\
|
||||
& $x-$axis $\cup$ $y-$axis
|
||||
\end{tabular}}
|
||||
\thm{}{If $x\in$ open set $V$ then $\exists$ $\delta>0$ such that $B_{\delta}(x)\subset V$}
|
||||
\begin{myproof}By openness of $V$, $x\in B_r(u)\subset V$
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
\draw[red] (0,0) circle [x radius=3.5cm, y radius=2cm] ;
|
||||
\draw (3,1.6) node[red]{$V$};
|
||||
\draw [blue] (1,0) circle (1.45cm) ;
|
||||
\filldraw[blue] (1,0) circle (1pt) node[anchor=north]{$u$};
|
||||
\draw (2.9,0.4) node[blue]{$B_r(u)$};
|
||||
\draw [green!40!black] (1.7,0) circle (0.5cm) node [yshift=0.7cm]{$B_{\delta}(x)$} ;
|
||||
\filldraw[green!40!black] (1.7,0) circle (1pt) node[anchor=west]{$x$};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
|
||||
Given $x\in B_r(u)\subset V$, we want $\delta>0$ such that $x\in B_{\delta} (x)\subset B_r(u)\subset V$. Let $d=d(u,x)$. Choose $\delta $ such that $d+\delta<r$ (e.g. $\delta<\frac{r-d}{2}$)
|
||||
|
||||
If $y\in B_{\delta}(x)$ we will be done by showing that $d(u,y)<r$ but $$d(u,y)\leq d(u,x)+d(x,y)<d+\delta<r$$
|
||||
\end{myproof}
|
||||
|
||||
\cor{}{By the result of the proof, we can then show...}
|
||||
\mlenma{}{Suppose $\vec{v_1}, \dots, \vec{v_n} \in \RR[n]$ is subspace of $\RR^n$.}
|
||||
\mprop{}{$1 + 1 = 2$.}
|
||||
|
||||
\section{Random}
|
||||
\dfn{Normed Linear Space and Norm $\boldsymbol{\|\cdot\|}$}{Let $V$ be a vector space over $\bbR$ (or $\bbC$). A norm on $V$ is function $\|\cdot\|\ V\to \bbR_{\geq 0}$ satisfying \begin{enumerate}[label=\bfseries\tiny\protect\circled{\small\arabic*}]
|
||||
\item \label{n:1}$\|x\|=0 \iff x=0$ $\forall$ $x\in V$
|
||||
\item \label{n:2} $\|\lambda x\|=|\lambda|\|x\|$ $\forall$ $\lambda\in\bbR$(or $\bbC$), $x\in V$
|
||||
\item \label{n:3} $\|x+y\| \leq \|x\|+\|y\|$ $\forall$ $x,y\in V$ (Triangle Inequality/Subadditivity)
|
||||
\end{enumerate}And $V$ is called a normed linear space.
|
||||
|
||||
$\bullet $ Same definition works with $V$ a vector space over $\bbC$ (again $\|\cdot\|\to\bbR_{\geq 0}$) where \ref{n:2} becomes $\|\lambda x\|=|\lambda|\|x\|$ $\forall$ $\lambda\in\bbC$, $x\in V$, where for $\lambda=a+ib$, $|\lambda|=\sqrt{a^2+b^2}$ }
|
||||
|
||||
|
||||
\ex{$\bs{p-}$Norm}{\label{pnorm}$V={\bbR}^m$, $p\in\bbR_{\geq 0}$. Define for $x=(x_1,x_2,\cdots,x_m)\in\bbR^m$ $$\|x\|_p=\Big(|x_1|^p+|x_2|^p+\cdots+|x_m|^p\Big)^{\frac1p}$$(In school $p=2$)}
|
||||
\textbf{Special Case $\bs{p=1}$}: $\|x\|_1=|x_1|+|x_2|+\cdots+|x_m|$ is clearly a norm by usual triangle inequality. \par
|
||||
\textbf{Special Case $\bs{p\to\infty\ (\bbR^m$ with $\|\cdot\|_{\infty})}$}: $\|x\|_{\infty}=\max\{|x_1|,|x_2|,\cdots,|x_m|\}$\\
|
||||
For $m=1$ these $p-$norms are nothing but $|x|$.
|
||||
Now exercise
|
||||
\qs{}{\label{exs1}Prove that triangle inequality is true if $p\geq 1$ for $p-$norms. (What goes wrong for $p<1$ ?)}
|
||||
\sol{\textbf{For Property \ref{n:3} for norm-2} \subsubsection*{\textbf{When field is $\bbR:$}} We have to show\begin{align*}
|
||||
& \sum_i(x_i+y_i)^2\leq \left(\sqrt{\sum_ix_i^2} +\sqrt{\sum_iy_i^2}\right)^2 \\
|
||||
\implies & \sum_i (x_i^2+2x_iy_i+y_i^2)\leq \sum_ix_i^2+2\sqrt{\left[\sum_ix_i^2\right]\left[\sum_iy_i^2\right]}+\sum_iy_i^2 \\
|
||||
\implies & \left[\sum_ix_iy_i\right]^2\leq \left[\sum_ix_i^2\right]\left[\sum_iy_i^2\right]
|
||||
\end{align*}So in other words prove $\langle x,y\rangle^2 \leq \langle x,x\rangle\langle y,y\rangle$ where
|
||||
$$\langle x,y\rangle =\sum\limits_i x_iy_i$$
|
||||
|
||||
\begin{note}
|
||||
\begin{itemize}
|
||||
\item $\|x\|^2=\langle x,x\rangle$
|
||||
\item $\langle x,y\rangle=\langle y,x\rangle$
|
||||
\item $\langle \cdot,\cdot\rangle$ is $\bbR-$linear in each slot i.e. \begin{align*}
|
||||
\langle rx+x',y\rangle=r\langle x,y\rangle+\langle x',y\rangle \text{ and similarly for second slot}
|
||||
\end{align*}Here in $\langle x,y\rangle$ $x$ is in first slot and $y$ is in second slot.
|
||||
\end{itemize}
|
||||
\end{note}Now the statement is just the Cauchy-Schwartz Inequality. For proof $$\langle x,y\rangle^2\leq \langle x,x\rangle\langle y,y\rangle $$ expand everything of $\langle x-\lambda y,x-\lambda y\rangle$ which is going to give a quadratic equation in variable $\lambda $ \begin{align*}
|
||||
\langle x-\lambda y,x-\lambda y\rangle & =\langle x,x-\lambda y\rangle-\lambda\langle y,x-\lambda y\rangle \\
|
||||
& =\langle x ,x\rangle -\lambda\langle x,y\rangle -\lambda\langle y,x\rangle +\lambda^2\langle y,y\rangle \\
|
||||
& =\langle x,x\rangle -2\lambda\langle x,y\rangle+\lambda^2\langle y,y\rangle
|
||||
\end{align*}Now unless $x=\lambda y$ we have $\langle x-\lambda y,x-\lambda y\rangle>0$ Hence the quadratic equation has no root therefore the discriminant is greater than zero.
|
||||
|
||||
\subsubsection*{\textbf{When field is $\bbC:$}}Modify the definition by $$\langle x,y\rangle=\sum_i\overline{x_i}y_i$$Then we still have $\langle x,x\rangle\geq 0$}
|
||||
|
||||
\section{Algorithms}
|
||||
\begin{algorithm}[H]
|
||||
\KwIn{This is some input}
|
||||
\KwOut{This is some output}
|
||||
\SetAlgoLined
|
||||
\SetNoFillComment
|
||||
\tcc{This is a comment}
|
||||
\vspace{3mm}
|
||||
some code here\;
|
||||
$x \leftarrow 0$\;
|
||||
$y \leftarrow 0$\;
|
||||
\uIf{$ x > 5$} {
|
||||
x is greater than 5 \tcp*{This is also a comment}
|
||||
}
|
||||
\Else {
|
||||
x is less than or equal to 5\;
|
||||
}
|
||||
\ForEach{y in 0..5} {
|
||||
$y \leftarrow y + 1$\;
|
||||
}
|
||||
\For{$y$ in $0..5$} {
|
||||
$y \leftarrow y - 1$\;
|
||||
}
|
||||
\While{$x > 5$} {
|
||||
$x \leftarrow x - 1$\;
|
||||
}
|
||||
\Return Return something here\;
|
||||
\caption{what}
|
||||
\end{algorithm}
|
||||
|
||||
\end{document}
|
||||
Loading…
Reference in a new issue