\ProvidesPackage{preamble}
%Macros
\newcommand{\eps}{\varepsilon}
\newcommand{\Z}{\mathbb{Z}}
\renewcommand{\P}{\mathbb{P}}
\newcommand{\one}{\mathbf{1}}
\newcommand{\X}{\mathbf{X}}
\newcommand{\F}{\mathcal{D}}
\newcommand{\cF}{\mathcal{F}}
\newcommand{\D}{\mathcal{D}}
\newcommand{\Df}{\mathcal{D}f}
\newcommand{\A}{\mathbf{A}}
\newcommand{\G}{\mathcal{G}}
\newcommand{\B}{\mathbf{B}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\V}{\mathbf{V}}
\newcommand{\Y}{\mathbf{Y}}
\newcommand{\x}{\mathbf{x}}
\newcommand{\y}{\mathbf{y}}
\newcommand{\W}{\mathcal{W}}
\newcommand{\N}{\mathbb{N}}
\renewcommand{\L}{\mathcal{L}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Q}{\mathbb{Q}}
\renewcommand{\phi}{\varphi}
\DeclareMathOperator{\Lip}{Lip}
\newcommand{\vb}[1]{\mathbf{#1}}
\newcommand{\bphi}{\boldsymbol{\varphi}}
\renewcommand{\bar}[1]{\overline{#1}}
\renewcommand{\tilde}[1]{\widetilde{#1}}
\newcommand{\proj}{\text{Proj}}
\newcommand{\remph}[1]{{\color{red}#1}}
\renewcommand{\l}{L^2}
\newcommand{\lz}{{\l(\Z_n)}}
\newcommand{\lzr}{{\l(\Z_n;\R)}}
\newcommand{\lzd}{{\l(\Z_n^d)}}
\newcommand{\zd}{{\Z_n^d}}
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\Re}{\text{Re}}
\newcommand{\rx}{{\color{red} \mathbf{x}}}
\newcommand{\bo}{{\color{blue} \mathbf{\circ}}}
\newcommand{\Lw}[1]{\frac{\partial \L}{\partial W_{#1}}}
\newcommand{\Lb}[1]{\frac{\partial \L}{\partial b_{#1}}}
\newcommand{\Lz}[1]{\frac{\partial \L}{\partial z_{#1}}}

\newenvironment{bp}{\color{blue}\begin{proof}}{\end{proof}}
\newenvironment{bs}{\color{blue}\begin{proof}[Solution]}{\end{proof}}
\DeclareMathOperator*{\tr}{Trace}
\DeclareMathOperator*{\sinc}{sinc}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\def\Xint#1{\mathchoice
{\XXint\displaystyle\textstyle{#1}}%
{\XXint\textstyle\scriptstyle{#1}}%
{\XXint\scriptstyle\scriptscriptstyle{#1}}%
{\XXint\scriptscriptstyle\scriptscriptstyle{#1}}%
\!\int}
\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$ }
\vcenter{\hbox{$#2#3$ }}\kern-.6\wd0}}
\def\ddashint{\Xint=}
\def\dashint{\Xint-}

\newcommand{\Log}{\text{Log}}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\theoremstyle{definition}
%\newtheorem{example}{Example}
\newtheorem{examplex}{Example}
\newenvironment{example}{\pushQED{\qed}\renewcommand{\qedsymbol}{$\triangle$}\examplex}{\popQED\endexamplex} 
\newtheorem{remark}[theorem]{Remark}
%\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{exercisex}[theorem]{Exercise}
\newenvironment{exercise}{\pushQED{\qed}\renewcommand{\qedsymbol}{$\triangle$}\exercisex}{\popQED\endexercisex} 
\newtheorem{projectx}{Project}
\newenvironment{project}{\pushQED{\qed}\renewcommand{\qedsymbol}{$\triangle$}\projectx}{\popQED\endprojectx} 
\newtheorem{definition}[theorem]{Definition}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{conjecture}[theorem]{Conjecture}

\renewcommand{\frame}[1]{\clearpage\section*{#1}}
\graphicspath{{./images/}}
