Add latex_template

latex_template/README.md

@@ -0,0 +1,24 @@
+# Latex Template
+
+A personal template I have copied from [Charlie's Math Template](https://github.com/SeniorMars/dotfiles/tree/master/latex_template).
+
+To use:
+1. Copy this directory to the same directory as your LaTeX file.
+
+```bash
+$ cp ./letterfonts.tex ./macros.tex ./preamble.tex ./template.tex [some_dir]
+
+or
+
+$ ltcp
+```
+
+ltcp if alias, embedded into my `.zshrc`
+
+	
+2. Edit the file "template.tex" to your liking.
+
+
+## Note
+
+I'm using texlive with it.

latex_template/letterfonts.tex

@@ -0,0 +1,178 @@
+% Things Lie
+\newcommand{\kb}{\mathfrak b}
+\newcommand{\kg}{\mathfrak g}
+\newcommand{\kh}{\mathfrak h}
+\newcommand{\kn}{\mathfrak n}
+\newcommand{\ku}{\mathfrak u}
+\newcommand{\kz}{\mathfrak z}
+\DeclareMathOperator{\Ext}{Ext} % Ext functor
+\DeclareMathOperator{\Tor}{Tor} % Tor functor
+\newcommand{\gl}{\opname{\mathfrak{gl}}} % frak gl group
+\renewcommand{\sl}{\opname{\mathfrak{sl}}} % frak sl group chktex 6
+
+% More script letters etc.
+\newcommand{\SA}{\mathcal A}
+\newcommand{\SB}{\mathcal B}
+\newcommand{\SC}{\mathcal C}
+\newcommand{\SF}{\mathcal F}
+\newcommand{\SG}{\mathcal G}
+\newcommand{\SH}{\mathcal H}
+\newcommand{\OO}{\mathcal O}
+
+\newcommand{\SCA}{\mathscr A}
+\newcommand{\SCB}{\mathscr B}
+\newcommand{\SCC}{\mathscr C}
+\newcommand{\SCD}{\mathscr D}
+\newcommand{\SCE}{\mathscr E}
+\newcommand{\SCF}{\mathscr F}
+\newcommand{\SCG}{\mathscr G}
+\newcommand{\SCH}{\mathscr H}
+
+% Mathfrak primes
+\newcommand{\km}{\mathfrak m}
+\newcommand{\kp}{\mathfrak p}
+\newcommand{\kq}{\mathfrak q}
+
+% number sets
+\newcommand{\RR}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{R}}{\mathbb{R}^{#1}}}}
+\newcommand{\NN}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{N}}{\mathbb{N}^{#1}}}}
+\newcommand{\ZZ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Z}}{\mathbb{Z}^{#1}}}}
+\newcommand{\QQ}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{Q}}{\mathbb{Q}^{#1}}}}
+\newcommand{\CC}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{C}}{\mathbb{C}^{#1}}}}
+\newcommand{\PP}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{P}}{\mathbb{P}^{#1}}}}
+\newcommand{\HH}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{H}}{\mathbb{H}^{#1}}}}
+\newcommand{\FF}[1][]{\ensuremath{\ifstrempty{#1}{\mathbb{F}}{\mathbb{F}^{#1}}}}
+% expected value
+\newcommand{\EE}{\ensuremath{\mathbb{E}}}
+\newcommand{\charin}{\text{ char }}
+\DeclareMathOperator{\sign}{sign}
+\DeclareMathOperator{\Aut}{Aut}
+\DeclareMathOperator{\Inn}{Inn}
+\DeclareMathOperator{\Syl}{Syl}
+\DeclareMathOperator{\Gal}{Gal}
+\DeclareMathOperator{\GL}{GL} % General linear group
+\DeclareMathOperator{\SL}{SL} % Special linear group
+
+%---------------------------------------
+% BlackBoard Math Fonts :-
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\bbA}{\mathbb{A}}	\newcommand{\bbB}{\mathbb{B}}
+\newcommand{\bbC}{\mathbb{C}}	\newcommand{\bbD}{\mathbb{D}}
+\newcommand{\bbE}{\mathbb{E}}	\newcommand{\bbF}{\mathbb{F}}
+\newcommand{\bbG}{\mathbb{G}}	\newcommand{\bbH}{\mathbb{H}}
+\newcommand{\bbI}{\mathbb{I}}	\newcommand{\bbJ}{\mathbb{J}}
+\newcommand{\bbK}{\mathbb{K}}	\newcommand{\bbL}{\mathbb{L}}
+\newcommand{\bbM}{\mathbb{M}}	\newcommand{\bbN}{\mathbb{N}}
+\newcommand{\bbO}{\mathbb{O}}	\newcommand{\bbP}{\mathbb{P}}
+\newcommand{\bbQ}{\mathbb{Q}}	\newcommand{\bbR}{\mathbb{R}}
+\newcommand{\bbS}{\mathbb{S}}	\newcommand{\bbT}{\mathbb{T}}
+\newcommand{\bbU}{\mathbb{U}}	\newcommand{\bbV}{\mathbb{V}}
+\newcommand{\bbW}{\mathbb{W}}	\newcommand{\bbX}{\mathbb{X}}
+\newcommand{\bbY}{\mathbb{Y}}	\newcommand{\bbZ}{\mathbb{Z}}
+
+%---------------------------------------
+% MathCal Fonts :-
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\mcA}{\mathcal{A}}	\newcommand{\mcB}{\mathcal{B}}
+\newcommand{\mcC}{\mathcal{C}}	\newcommand{\mcD}{\mathcal{D}}
+\newcommand{\mcE}{\mathcal{E}}	\newcommand{\mcF}{\mathcal{F}}
+\newcommand{\mcG}{\mathcal{G}}	\newcommand{\mcH}{\mathcal{H}}
+\newcommand{\mcI}{\mathcal{I}}	\newcommand{\mcJ}{\mathcal{J}}
+\newcommand{\mcK}{\mathcal{K}}	\newcommand{\mcL}{\mathcal{L}}
+\newcommand{\mcM}{\mathcal{M}}	\newcommand{\mcN}{\mathcal{N}}
+\newcommand{\mcO}{\mathcal{O}}	\newcommand{\mcP}{\mathcal{P}}
+\newcommand{\mcQ}{\mathcal{Q}}	\newcommand{\mcR}{\mathcal{R}}
+\newcommand{\mcS}{\mathcal{S}}	\newcommand{\mcT}{\mathcal{T}}
+\newcommand{\mcU}{\mathcal{U}}	\newcommand{\mcV}{\mathcal{V}}
+\newcommand{\mcW}{\mathcal{W}}	\newcommand{\mcX}{\mathcal{X}}
+\newcommand{\mcY}{\mathcal{Y}}	\newcommand{\mcZ}{\mathcal{Z}}
+
+
+%---------------------------------------
+% Bold Math Fonts :-
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\bmA}{\boldsymbol{A}}	\newcommand{\bmB}{\boldsymbol{B}}
+\newcommand{\bmC}{\boldsymbol{C}}	\newcommand{\bmD}{\boldsymbol{D}}
+\newcommand{\bmE}{\boldsymbol{E}}	\newcommand{\bmF}{\boldsymbol{F}}
+\newcommand{\bmG}{\boldsymbol{G}}	\newcommand{\bmH}{\boldsymbol{H}}
+\newcommand{\bmI}{\boldsymbol{I}}	\newcommand{\bmJ}{\boldsymbol{J}}
+\newcommand{\bmK}{\boldsymbol{K}}	\newcommand{\bmL}{\boldsymbol{L}}
+\newcommand{\bmM}{\boldsymbol{M}}	\newcommand{\bmN}{\boldsymbol{N}}
+\newcommand{\bmO}{\boldsymbol{O}}	\newcommand{\bmP}{\boldsymbol{P}}
+\newcommand{\bmQ}{\boldsymbol{Q}}	\newcommand{\bmR}{\boldsymbol{R}}
+\newcommand{\bmS}{\boldsymbol{S}}	\newcommand{\bmT}{\boldsymbol{T}}
+\newcommand{\bmU}{\boldsymbol{U}}	\newcommand{\bmV}{\boldsymbol{V}}
+\newcommand{\bmW}{\boldsymbol{W}}	\newcommand{\bmX}{\boldsymbol{X}}
+\newcommand{\bmY}{\boldsymbol{Y}}	\newcommand{\bmZ}{\boldsymbol{Z}}
+%Small Letters
+\newcommand{\bma}{\boldsymbol{a}}	\newcommand{\bmb}{\boldsymbol{b}}
+\newcommand{\bmc}{\boldsymbol{c}}	\newcommand{\bmd}{\boldsymbol{d}}
+\newcommand{\bme}{\boldsymbol{e}}	\newcommand{\bmf}{\boldsymbol{f}}
+\newcommand{\bmg}{\boldsymbol{g}}	\newcommand{\bmh}{\boldsymbol{h}}
+\newcommand{\bmi}{\boldsymbol{i}}	\newcommand{\bmj}{\boldsymbol{j}}
+\newcommand{\bmk}{\boldsymbol{k}}	\newcommand{\bml}{\boldsymbol{l}}
+\newcommand{\bmm}{\boldsymbol{m}}	\newcommand{\bmn}{\boldsymbol{n}}
+\newcommand{\bmo}{\boldsymbol{o}}	\newcommand{\bmp}{\boldsymbol{p}}
+\newcommand{\bmq}{\boldsymbol{q}}	\newcommand{\bmr}{\boldsymbol{r}}
+\newcommand{\bms}{\boldsymbol{s}}	\newcommand{\bmt}{\boldsymbol{t}}
+\newcommand{\bmu}{\boldsymbol{u}}	\newcommand{\bmv}{\boldsymbol{v}}
+\newcommand{\bmw}{\boldsymbol{w}}	\newcommand{\bmx}{\boldsymbol{x}}
+\newcommand{\bmy}{\boldsymbol{y}}	\newcommand{\bmz}{\boldsymbol{z}}
+
+%---------------------------------------
+% Scr Math Fonts :-
+%---------------------------------------
+
+\newcommand{\sA}{{\mathscr{A}}}   \newcommand{\sB}{{\mathscr{B}}}
+\newcommand{\sC}{{\mathscr{C}}}   \newcommand{\sD}{{\mathscr{D}}}
+\newcommand{\sE}{{\mathscr{E}}}   \newcommand{\sF}{{\mathscr{F}}}
+\newcommand{\sG}{{\mathscr{G}}}   \newcommand{\sH}{{\mathscr{H}}}
+\newcommand{\sI}{{\mathscr{I}}}   \newcommand{\sJ}{{\mathscr{J}}}
+\newcommand{\sK}{{\mathscr{K}}}   \newcommand{\sL}{{\mathscr{L}}}
+\newcommand{\sM}{{\mathscr{M}}}   \newcommand{\sN}{{\mathscr{N}}}
+\newcommand{\sO}{{\mathscr{O}}}   \newcommand{\sP}{{\mathscr{P}}}
+\newcommand{\sQ}{{\mathscr{Q}}}   \newcommand{\sR}{{\mathscr{R}}}
+\newcommand{\sS}{{\mathscr{S}}}   \newcommand{\sT}{{\mathscr{T}}}
+\newcommand{\sU}{{\mathscr{U}}}   \newcommand{\sV}{{\mathscr{V}}}
+\newcommand{\sW}{{\mathscr{W}}}   \newcommand{\sX}{{\mathscr{X}}}
+\newcommand{\sY}{{\mathscr{Y}}}   \newcommand{\sZ}{{\mathscr{Z}}}
+
+
+%---------------------------------------
+% Math Fraktur Font
+%---------------------------------------
+
+%Captital Letters
+\newcommand{\mfA}{\mathfrak{A}}	\newcommand{\mfB}{\mathfrak{B}}
+\newcommand{\mfC}{\mathfrak{C}}	\newcommand{\mfD}{\mathfrak{D}}
+\newcommand{\mfE}{\mathfrak{E}}	\newcommand{\mfF}{\mathfrak{F}}
+\newcommand{\mfG}{\mathfrak{G}}	\newcommand{\mfH}{\mathfrak{H}}
+\newcommand{\mfI}{\mathfrak{I}}	\newcommand{\mfJ}{\mathfrak{J}}
+\newcommand{\mfK}{\mathfrak{K}}	\newcommand{\mfL}{\mathfrak{L}}
+\newcommand{\mfM}{\mathfrak{M}}	\newcommand{\mfN}{\mathfrak{N}}
+\newcommand{\mfO}{\mathfrak{O}}	\newcommand{\mfP}{\mathfrak{P}}
+\newcommand{\mfQ}{\mathfrak{Q}}	\newcommand{\mfR}{\mathfrak{R}}
+\newcommand{\mfS}{\mathfrak{S}}	\newcommand{\mfT}{\mathfrak{T}}
+\newcommand{\mfU}{\mathfrak{U}}	\newcommand{\mfV}{\mathfrak{V}}
+\newcommand{\mfW}{\mathfrak{W}}	\newcommand{\mfX}{\mathfrak{X}}
+\newcommand{\mfY}{\mathfrak{Y}}	\newcommand{\mfZ}{\mathfrak{Z}}
+%Small Letters
+\newcommand{\mfa}{\mathfrak{a}}	\newcommand{\mfb}{\mathfrak{b}}
+\newcommand{\mfc}{\mathfrak{c}}	\newcommand{\mfd}{\mathfrak{d}}
+\newcommand{\mfe}{\mathfrak{e}}	\newcommand{\mff}{\mathfrak{f}}
+\newcommand{\mfg}{\mathfrak{g}}	\newcommand{\mfh}{\mathfrak{h}}
+\newcommand{\mfi}{\mathfrak{i}}	\newcommand{\mfj}{\mathfrak{j}}
+\newcommand{\mfk}{\mathfrak{k}}	\newcommand{\mfl}{\mathfrak{l}}
+\newcommand{\mfm}{\mathfrak{m}}	\newcommand{\mfn}{\mathfrak{n}}
+\newcommand{\mfo}{\mathfrak{o}}	\newcommand{\mfp}{\mathfrak{p}}
+\newcommand{\mfq}{\mathfrak{q}}	\newcommand{\mfr}{\mathfrak{r}}
+\newcommand{\mfs}{\mathfrak{s}}	\newcommand{\mft}{\mathfrak{t}}
+\newcommand{\mfu}{\mathfrak{u}}	\newcommand{\mfv}{\mathfrak{v}}
+\newcommand{\mfw}{\mathfrak{w}}	\newcommand{\mfx}{\mathfrak{x}}
+\newcommand{\mfy}{\mathfrak{y}}	\newcommand{\mfz}{\mathfrak{z}}

latex_template/macros.tex

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+%From M275 "Topology" at SJSU
+\newcommand{\id}{\mathrm{id}}
+\newcommand{\taking}[1]{\xrightarrow{#1}}
+\newcommand{\inv}{^{-1}}
+
+%From M170 "Introduction to Graph Theory" at SJSU
+\DeclareMathOperator{\diam}{diam}
+\DeclareMathOperator{\ord}{ord}
+\newcommand{\defeq}{\overset{\mathrm{def}}{=}}
+
+%From the USAMO .tex files
+\newcommand{\ts}{\textsuperscript}
+\newcommand{\dg}{^\circ}
+\newcommand{\ii}{\item}
+
+% % From Math 55 and Math 145 at Harvard
+% \newenvironment{subproof}[1][Proof]{%
+% \begin{proof}[#1] \renewcommand{\qedsymbol}{$\blacksquare$}}%
+% {\end{proof}}
+
+\newcommand{\liff}{\leftrightarrow}
+\newcommand{\lthen}{\rightarrow}
+\newcommand{\opname}{\operatorname}
+\newcommand{\surjto}{\twoheadrightarrow}
+\newcommand{\injto}{\hookrightarrow}
+\newcommand{\On}{\mathrm{On}} % ordinals
+\DeclareMathOperator{\img}{im} % Image
+\DeclareMathOperator{\Img}{Im} % Image
+\DeclareMathOperator{\coker}{coker} % Cokernel
+\DeclareMathOperator{\Coker}{Coker} % Cokernel
+\DeclareMathOperator{\Ker}{Ker} % Kernel
+\DeclareMathOperator{\rank}{rank}
+\DeclareMathOperator{\Spec}{Spec} % spectrum
+\DeclareMathOperator{\Tr}{Tr} % trace
+\DeclareMathOperator{\pr}{pr} % projection
+\DeclareMathOperator{\ext}{ext} % extension
+\DeclareMathOperator{\pred}{pred} % predecessor
+\DeclareMathOperator{\dom}{dom} % domain
+\DeclareMathOperator{\ran}{ran} % range
+\DeclareMathOperator{\Hom}{Hom} % homomorphism
+\DeclareMathOperator{\Mor}{Mor} % morphisms
+\DeclareMathOperator{\End}{End} % endomorphism
+
+\newcommand{\eps}{\epsilon}
+\newcommand{\veps}{\varepsilon}
+\newcommand{\ol}{\overline}
+\newcommand{\ul}{\underline}
+\newcommand{\wt}{\widetilde}
+\newcommand{\wh}{\widehat}
+\newcommand{\vocab}[1]{\textbf{\color{blue} #1}}
+\providecommand{\half}{\frac{1}{2}}
+\newcommand{\dang}{\measuredangle} %% Directed angle
+\newcommand{\ray}[1]{\overrightarrow{#1}}
+\newcommand{\seg}[1]{\overline{#1}}
+\newcommand{\arc}[1]{\wideparen{#1}}
+\DeclareMathOperator{\cis}{cis}
+\DeclareMathOperator*{\lcm}{lcm}
+\DeclareMathOperator*{\argmin}{arg min}
+\DeclareMathOperator*{\argmax}{arg max}
+\newcommand{\cycsum}{\sum_{\mathrm{cyc}}}
+\newcommand{\symsum}{\sum_{\mathrm{sym}}}
+\newcommand{\cycprod}{\prod_{\mathrm{cyc}}}
+\newcommand{\symprod}{\prod_{\mathrm{sym}}}
+\newcommand{\Qed}{\begin{flushright}\qed\end{flushright}}
+\newcommand{\parinn}{\setlength{\parindent}{1cm}}
+\newcommand{\parinf}{\setlength{\parindent}{0cm}}
+% \newcommand{\norm}{\|\cdot\|}
+\newcommand{\inorm}{\norm_{\infty}}
+\newcommand{\opensets}{\{V_{\alpha}\}_{\alpha\in I}}
+\newcommand{\oset}{V_{\alpha}}
+\newcommand{\opset}[1]{V_{\alpha_{#1}}}
+\newcommand{\lub}{\text{lub}}
+\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}}
+\newcommand{\Del}[3]{\frac{\partial^{#1} #2}{\partial^{#1} #3}}
+\newcommand{\deld}[2]{\dfrac{\partial #1}{\partial #2}}
+\newcommand{\Deld}[3]{\dfrac{\partial^{#1} #2}{\partial^{#1} #3}}
+\newcommand{\lm}{\lambda}
+\newcommand{\uin}{\mathbin{\rotatebox[origin=c]{90}{$\in$}}}
+\newcommand{\usubset}{\mathbin{\rotatebox[origin=c]{90}{$\subset$}}}
+\newcommand{\lt}{\left}
+\newcommand{\rt}{\right}
+\newcommand{\bs}[1]{\boldsymbol{#1}}
+\newcommand{\exs}{\exists}
+\newcommand{\st}{\strut}
+\newcommand{\dps}[1]{\displaystyle{#1}}
+
+\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} }
+\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed}

latex_template/preamble.tex

@@ -0,0 +1,773 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 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
+

latex_template/template.tex

@@ -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}