%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % PACKAGE IMPORTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[tmargin=2cm,rmargin=1in,lmargin=1in,margin=0.85in,bmargin=2cm,footskip=.2in]{geometry} \usepackage{amsmath,amsfonts,amsthm,amssymb,mathtools} \usepackage[utf8]{inputenc} \usepackage[T2A]{fontenc} \usepackage[varbb]{newpxmath} \usepackage{xfrac} \usepackage[makeroom]{cancel} \usepackage{mathtools} \usepackage{bookmark} \usepackage{enumitem} \usepackage{hyperref,theoremref} \hypersetup{ pdftitle={Assignment}, colorlinks=true, linkcolor=doc!90, bookmarksnumbered=true, bookmarksopen=true } \usepackage[most,many,breakable]{tcolorbox} \usepackage{xcolor} \usepackage{varwidth} \usepackage{varwidth} \usepackage{etoolbox} %\usepackage{authblk} \usepackage{nameref} \usepackage{multicol,array} \usepackage{tikz-cd} \usepackage[ruled,vlined,linesnumbered]{algorithm2e} \usepackage{comment} % enables the use of multi-line comments (\ifx \fi) \usepackage{import} \usepackage{xifthen} \usepackage{pdfpages} \usepackage{transparent} \newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}} \SetCommentSty{mycommfont} \newcommand{\incfig}[1]{% \def\svgwidth{\columnwidth} \import{./figures/}{#1.pdf_tex} } \usepackage{tikzsymbols} \renewcommand\qedsymbol{$\Laughey$} %\usepackage{import} %\usepackage{xifthen} %\usepackage{pdfpages} %\usepackage{transparent} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % SELF MADE COLORS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \definecolor{myg}{RGB}{56, 140, 70} \definecolor{myb}{RGB}{45, 111, 177} \definecolor{myr}{RGB}{199, 68, 64} \definecolor{mytheorembg}{HTML}{F2F2F9} \definecolor{mytheoremfr}{HTML}{00007B} \definecolor{mylenmabg}{HTML}{FFFAF8} \definecolor{mylenmafr}{HTML}{983b0f} \definecolor{mypropbg}{HTML}{f2fbfc} \definecolor{mypropfr}{HTML}{191971} \definecolor{myexamplebg}{HTML}{F2FBF8} \definecolor{myexamplefr}{HTML}{88D6D1} \definecolor{myexampleti}{HTML}{2A7F7F} \definecolor{mydefinitbg}{HTML}{E5E5FF} \definecolor{mydefinitfr}{HTML}{3F3FA3} \definecolor{notesgreen}{RGB}{0,162,0} \definecolor{myp}{RGB}{197, 92, 212} \definecolor{mygr}{HTML}{2C3338} \definecolor{myred}{RGB}{127,0,0} \definecolor{myyellow}{RGB}{169,121,69} \definecolor{myexercisebg}{HTML}{F2FBF8} \definecolor{myexercisefg}{HTML}{88D6D1} %%%%%%%%%%%%%%%%%%%%%%%%%%%% % TCOLORBOX SETUPS %%%%%%%%%%%%%%%%%%%%%%%%%%%% \setlength{\parindent}{1cm} %================================ % THEOREM BOX %================================ \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