\documentclass[11pt]{article}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   % ... or a4paper or a5paper or ... 
%\geometry{landscape}                % Activate for for rotated page geometry
%\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{amsfonts, amscd, amssymb, amsthm, amsmath}
\usepackage{pdfsync}%leaves makers for tex searching
\usepackage{enumerate}


%%%%% Margins %%%%% 
\setlength{\topmargin}{1in} %top/bot margins
\setlength{\oddsidemargin}{\topmargin} %sidemargins

\setlength{\textheight}{11in} \setlength{\textwidth}{8.5in}
\setlength{\hoffset}{-1in} \setlength{\voffset}{-1in} \setlength{\evensidemargin}{\oddsidemargin} \addtolength{\textheight}{-2 \topmargin}\addtolength{\textwidth}{-2\oddsidemargin}
\setlength{\headheight}{0pt} \setlength{\headsep}{20pt} \setlength{\footskip}{20pt}
\addtolength{\textheight}{-\footskip} \addtolength{\textheight}{-\headheight} \addtolength{\textheight}{-\headsep}


%%%%% Headers %%%%% 
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf[rh]{\thepage}% right header
\fancyhf[lh]{}% left header
\fancyhf[ch]{}% centre header
\fancyhf[lf]{}% left footer
\fancyhf[cf]{}% centre
\fancyhf[rf]{}% right
\renewcommand\headrulewidth{0pt}% remove if you want a rule beneath the header



%%%%% Theorems %%%%% 
\theoremstyle{plain}
	\newtheorem{thm}{Theorem}[section]
	\newtheorem{lemma}[thm]{Lemma}
	\newtheorem{prop}[thm]{Proposition}
	\newtheorem{cor}[thm]{Corollary}
\theoremstyle{definition}
	\newtheorem*{defn}{Definition}
	\newtheorem{remark}[thm]{Remark}
\theoremstyle{example}
	\newtheorem*{example}{Example}


%%%%% Pictures %%%%% 
%\usepackage{etex} %fixes the fight that pictex has with every other drawing package
%\usepackage{pictexwd}
\usepackage{tikz}
%\usepackage{graphicx}
\usepackage{epstopdf}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}
\usepackage[pdftex,bookmarks]{hyperref}

\usepgflibrary{shapes.geometric}
\tikzstyle{V}=[draw, fill =black, circle, inner sep=0pt, minimum size=1.5pt]
\tikzstyle{over}=[draw=white,double=black,line width=2pt, double distance=.5pt]


\newcommand\TikZ[1]{\begin{matrix}\begin{tikzpicture}#1\end{tikzpicture}\end{matrix}}


%PARTITIONS
\newcounter{r}
\newcommand\Part[1]{
        \setcounter{r}{1}
	 \foreach \x in {#1}{
 	{\ifnum\value{r}=1
		\draw (0,\value{r}-1)--(\x,\value{r}-1); 
		\fi}
	\draw (0,\value{r}) to (\x,\value{r});
   	\foreach \y in {0, ..., \x} {\draw (\y,\value{r})--(\y,\value{r}-1);}
	\addtocounter{r}{1}
 }}
 \def\PartUNIT{.175}
%Self-contained tikz images for \Part above. 
\newcommand{\PART}[1]{
\begin{matrix}
\begin{tikzpicture}[xscale=\PartUNIT, yscale=-\PartUNIT] 
	\Part{#1}
\end{tikzpicture}
\end{matrix}
}


%BRAIDS:
\def\Over[#1,#2][#3,#4]{ %1,2=start position; 3,4=end position
	\draw[style=over]   (#1,#2) .. controls ++(0,#4*.5-#2*.5) and ++(0,-#4*.5+#2*.5) .. (#3,#4);}
\def\Under[#1,#2][#3,#4]{ %1,2=start position; 3,4=end position
	\draw  (#1,#2) .. controls ++(0,#4*.5-#2*.5) and ++(0,-#4*.5+#2*.5) .. (#3,#4);}
\def\Cross[#1,#2][#3,#4]{%Mimic over, under follows
	\Under[#3,#2][#1,#4]\Over[#1,#2][#3,#4]}
\def\Tops[#1][#2][#3]{%1=pole locations, 2=top, 3=k 
	\foreach\x in {#1}{
		\draw (\x+.1,#2) -- (\x+.1,#2+.15) (\x-.1,#2) -- (\x-.1,#2+.15) ;
		\draw (\x+.1,#2+.15) arc (0:360:1mm and .5mm);}
	%Nodes 
	\foreach \x in {1,...,#3} {\draw (\x,#2)  to (\x,#2+.05) node[V]{};}
	}
\def\Bottoms[#1][#2][#3]{%1=pole locations, 2 = bottom, 3=top 
	\foreach\x in {#1}{
		\draw (\x+.1,#2) -- (\x+.1,#2-.1) (\x-.1,#2) -- (\x-.1,#2-.1) ;
		\draw (\x+.1,#2-.1) arc (0:-180:1mm and .5mm);}
	%Nodes 
	\foreach \x in {1,...,#3} {\draw (\x,#2)  to (\x,#2-.05) node[V]{};}
	}
\def\Caps[#1][#2,#3][#4]{%1=pole locations, 2 = bottom, 3=top, 4=k 
	\Tops[#1][#3][#4]
	\Bottoms[#1][#2][#4]
	}
\def\Pole[#1][#2,#3]{%1=horizontal location, 2 = bottom, 3=top
	\shade[left color=white,right color=white] (#1+.1,#2) rectangle (#1-.1,#3);
	\draw[over] (#1+.1,#2) to (#1+.1,#3) (#1-.1,#2) to (#1-.1,#3) ;}
\def\Label[#1,#2][#3][#4]{%1,2 = top/bot position, 3=i, 4=label
	\node[above] at (#3,#2+.1) {#4};
	\node[below] at (#3,#1-.1) {#4};		}
	
	
%%%%% Color  %%%%% 
\usepackage{color}
\definecolor{dred}{rgb}{.65, 0, 0.15}
\newcommand{\NOTE}[1]{{\color{blue}#1}}
\newcommand{\MOVED}[1]{{\color{gray}#1}}
\newcommand{\blue}[1]{{\color{blue} #1 }}


%%%%% Alphabets %%%%% 
\def\cA{\mathcal{A}}\def\cB{\mathcal{B}}\def\cC{\mathcal{C}}\def\cD{\mathcal{D}}\def\cE{\mathcal{E}}\def\cF{\mathcal{F}}\def\cG{\mathcal{G}}\def\cH{\mathcal{H}}\def\cI{\mathcal{I}}\def\cJ{\mathcal{J}}\def\cK{\mathcal{K}}\def\cL{\mathcal{L}}\def\cM{\mathcal{M}}\def\cN{\mathcal{N}}\def\cO{\mathcal{O}}\def\cP{\mathcal{P}}\def\cQ{\mathcal{Q}}\def\cR{\mathcal{R}}\def\cS{\mathcal{S}}\def\cT{\mathcal{T}}\def\cU{\mathcal{U}}\def\cV{\mathcal{V}}\def\cW{\mathcal{W}}\def\cX{\mathcal{X}}\def\cY{\mathcal{Y}}\def\cZ{\mathcal{Z}}

\def\AA{\mathbb{A}} \def\BB{\mathbb{B}} \def\CC{\mathbb{C}} \def\DD{\mathbb{D}} \def\EE{\mathbb{E}} \def\FF{\mathbb{F}} \def\GG{\mathbb{G}} \def\HH{\mathbb{H}} \def\II{\mathbb{I}} \def\JJ{\mathbb{J}} \def\KK{\mathbb{K}} \def\LL{\mathbb{L}} \def\MM{\mathbb{M}} \def\NN{\mathbb{N}} \def\OO{\mathbb{O}} \def\PP{\mathbb{P}} \def\QQ{\mathbb{Q}} \def\RR{\mathbb{R}} \def\SS{\mathbb{S}} \def\TT{\mathbb{T}} \def\UU{\mathbb{U}} \def\VV{\mathbb{V}} \def\WW{\mathbb{W}} \def\XX{\mathbb{X}} \def\YY{\mathbb{Y}} \def\ZZ{\mathbb{Z}}  

\def\fa{\mathfrak{a}} \def\fb{\mathfrak{b}} \def\fc{\mathfrak{c}} \def\fd{\mathfrak{d}} \def\fe{\mathfrak{e}} \def\ff{\mathfrak{f}} \def\fg{\mathfrak{g}} \def\fh{\mathfrak{h}} \def\fj{\mathfrak{j}} \def\fk{\mathfrak{k}} \def\fl{\mathfrak{l}} \def\fm{\mathfrak{m}} \def\fn{\mathfrak{n}} \def\fo{\mathfrak{o}} \def\fp{\mathfrak{p}} \def\fq{\mathfrak{q}} \def\fr{\mathfrak{r}} \def\fs{\mathfrak{s}} \def\ft{\mathfrak{t}} \def\fu{\mathfrak{u}} \def\fv{\mathfrak{v}} \def\fw{\mathfrak{w}} \def\fx{\mathfrak{x}} \def\fy{\mathfrak{y}} \def\fz{\mathfrak{z}}
\def\fgl{\mathfrak{gl}}  \def\fsl{\mathfrak{sl}}  \def\fso{\mathfrak{so}}  \def\fsp{\mathfrak{sp}}  
\def\GL{\mathrm{GL}} \def\SL{\mathrm{SL}}  \def\SP{\mathrm{SL}}

\def\<{\langle} \def\>{\rangle}
\def\ad{\mathrm{ad}} 
\def\Alg{\mathrm{Alg}}
\def\Aut{\mathrm{Aut}}
\def\dim{\mathrm{dim}} 
\def\End{\mathrm{End}} 
\def\ev{\mathrm{ev}} 
\def\half{\hbox{$\frac12$}}
\def\Hom{\mathrm{Hom}} 
\def\id{\mathrm{id}}
\def\img{\mathrm{img}}
\def\Ind{\mathrm{Ind}}
\def\Irr{\mathrm{Irr}} 
\def\ker{\mathrm{ker}}
\def\Lie{\mathrm{Lie}}
\def\normeq{\unlhd}
\def\qtr{\mathrm{qtr}} 
\def\rad{\mathrm{rad}} 
\def\Res{\mathrm{Res}} 
\def\tr{\mathrm{tr}} 
\def\Tr{\mathrm{Tr}} 
\def\vep{\varepsilon}
\def\wt{\mathrm{wt}}

\newcommand{\Rubric}[1]{~\\\vfill \hfill{\def\arraystretch{1.75}\begin{tabular} {|c|c|} \hline
#1 & Points Possible  \\ \hline \hline
complete & \hspace{3mm} 0 \hspace{3mm} 1 \hspace{3mm} 2 \hspace{3mm} 
			3 \hspace{3mm} 4 \hspace{3mm} \\ \hline
mathematically valid & \hspace{3mm} 0 \hspace{3mm} 1 \hspace{3mm} 2 \hspace{3mm} 
			3 \hspace{3mm} 4 \hspace{3mm} \\ \hline
readable & \hspace{3mm} 0 \hspace{3mm} 1 \hspace{3mm} 2 \hspace{3mm} 
			3 \hspace{3mm} 4 \hspace{3mm} \\ \hline
mathematically fluent & \hspace{3mm} 0 \hspace{3mm} 1 \hspace{3mm} 2 \hspace{3mm} 
			3 \hspace{3mm}  4 \hspace{3mm}  \\ \hline
Total:& \qquad\qquad\qquad(out of 16)\\
\hline
\end{tabular}}\pagebreak}

\def\Grade{
	\hfill{\def\arraystretch{1.5}
		\begin{tabular}{|c@{\qquad}|c@{\qquad}|}
			\multicolumn{2}{l}{\bf Labs:}\\\hline
			&\\\hline&\\\hline&\\\hline&\\\hline&\\\hline&\\\hline
		\end{tabular}\qquad
		\begin{tabular}{|c|c|@{\qquad\qquad}|}
			\multicolumn{2}{l}{\bf Overall:}\\\hline
			Intro & \bf 8 \\\hline Words & \bf 16  \\\hline
			E1 & \bf 16  \\\hline Labs & \bf 64 \\\hline
			Refl & \bf 16 \\\hline\hline Total & \bf 120 \\\hline
\end{tabular}
}}

\def\Score{~\\\vfill \hfill
	$\TikZ{\draw (0,0) rectangle (1.5,1.5); \node[above right] at (0,1.5) {\bf Score:};}$}

\def\ReflOne{\label{revised1}~\smallskip \textbf{Note:} A self-reflection on the revision process for this proof is given in Section \ref{reflection1}. \hfill $\TikZ{\draw[thick] (0,0) rectangle (1,1);}$}


\def\ReflTwo{\label{revised2}~\smallskip \textbf{Note:} A self-reflection on the revision process for this proof is given in Section \ref{reflection2}. \hfill $\TikZ{\draw[thick] (0,0) rectangle (1,1);}$}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\title{Math 308 Final Portfolio}
\author{YOUR NAME}
\date{December 18, 2018}                                           % Activate to display a given date or no date

\begin{document}
	\maketitle
	\tableofcontents
	\Grade
	\thispagestyle{empty}
\pagebreak


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}


%%% YOUR INTRODUCTION GOES HERE



\Score\pagebreak
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Proof without words}

\paragraph{\bf Statement:} 
%%% PUT STATEMENT HERE, with no line break in between.


\paragraph{\bf Original proof without words:} 

%%% UNCOMMENT THE FOLLOWING, replacing "FILENAME" with the relevant filename (minus the .pdf).  This is not YOUR original draft; this is the picture that you wrote your proof from.
%	\centerline{\includegraphics{FILENAME}} 

\begin{proof}[Proof with words]
%%% YOUR PROOF GOES HERE
\end{proof}


\Rubric{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Proof from Exam 1}

\paragraph{\bf Statement:} 
%%% PUT STATEMENT HERE, with no line break in between.


\begin{proof}
%%% YOUR PROOF GOES HERE
\end{proof}


\Rubric{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Proofs from Proof Lab 1: Direct Proofs}

%%% INCLUDE one subsection for each problem, labeled by "Problem NUMBER, STARS" where "NUMBER" should be replaced by I, II, III, IV, etc. as relevant, and STARS should be the relevant number of stars.
\subsection{Problem NUMBER, $\star\star\star\star\star$}

\paragraph{\bf Statement:} 
%%% PUT STATEMENT HERE, with no line break in between.

\begin{proof}
%%% YOUR PROOF GOES HERE



\end{proof}

\Rubric{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Proofs from Proof Lab 2: Proof by Induction}

%%% INCLUDE one subsection for each problem, labeled by "Problem NUMBER, STARS" where "NUMBER" should be replaced by I, II, III, IV, etc. as relevant, and STARS should be the relevant number of stars.
\subsection{Problem NUMBER, $\star\star\star\star\star$}

\paragraph{\bf Statement:} 
%%% PUT STATEMENT HERE, with no line break in between.

\begin{proof}
%%% YOUR PROOF GOES HERE



\end{proof}


\Rubric{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Proofs from Proof Lab 3: Proof by Contradiction}

%%% INCLUDE one subsection for each problem, labeled by "Problem NUMBER, STARS" where "NUMBER" should be replaced by I, II, III, IV, etc. as relevant, and STARS should be the relevant number of stars.
\subsection{Problem NUMBER, $\star\star\star\star\star$}

\paragraph{\bf Statement:} 
%%% PUT STATEMENT HERE, with no line break in between.

\begin{proof}
%%% YOUR PROOF GOES HERE



\end{proof}

\Rubric{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendix
\section{Self-reflections}

\subsection{First reflection}\label{reflection1}
This is a reflection on the proof of PROBLEM, whose final draft is in Section \ref{revised1}. 

%%% INSTRUCTIONS: 
%%% REPLACE "PROBLEM" with something like Proof lab 2, Problem V, and
%%% PUT \ReflOne right after the relevant \section{} or \subsection{}.
%%% FOR EXAMPLE, \subsection{Problem V, $\star \star$}\ReflOne
%%% THEN DELETE THIS CODE


%%% YOUR REFLECTION GOES HERE. 




\Score

\subsection{Second reflection}
This is a reflection on the proof of PROBLEM, whose final draft is in Section \ref{revised2}. 

%%% INSTRUCTIONS: 
%%% REPLACE "PROBLEM" with something like Proof lab 2, Problem V, and
%%% PUT \ReflTwo right after the relevant \section{} or \subsection{}.
%%% FOR EXAMPLE, \subsection{Problem V, $\star \star$}\ReflTwo
%%% THEN DELETE THIS CODE


%%% YOUR REFLECTION GOES HERE. 



\Score


\vfill

%\pagebreak 		%% <-- UNCOMMENT IF YOU \includegraphics BELOW.
\section{First drafts and peer-edits}

%%%YOU CAN either place a 
%		\centerline{(See attached)}
%%% HERE; OR make a pdf of each page you want to include and put
%		\centerline{\includegraphics[width=6.5]{FILENAME}} \pagebreak
%%% ONE FOR EACH PAGE. 


\end{document}  