% Template based on:
% https://www.cs.columbia.edu/~djhsu/coms4774-s21/scribe.html

\documentclass[12pt]{article}

\usepackage{amscd}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amstext}
\usepackage{amsthm}
\usepackage{bbold}
\usepackage{bm}
\usepackage{colonequals}
\usepackage[dvips,letterpaper,margin=1in]{geometry}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{xcolor}

\usepackage{csquotes}
\MakeOuterQuote{"}

\definecolor{cblack}{rgb}{0,0,0}
\definecolor{cblue}{rgb}{0.121569,0.466667,0.705882}
\definecolor{corange}{rgb}{1.000000,0.498039,0.054902}
\definecolor{cgreen}{rgb}{0.172549,0.627451,0.172549}
\definecolor{cred}{rgb}{0.839216,0.152941,0.156863}
\definecolor{cpurple}{rgb}{0.580392,0.403922,0.741176}
\definecolor{cbrown}{rgb}{0.549020,0.337255,0.294118}
\definecolor{cpink}{rgb}{0.890196,0.466667,0.760784}
\definecolor{cgray}{rgb}{0.498039,0.498039,0.498039}

\usepackage{hyperref}
\hypersetup{
  linkcolor  = cblue,
  citecolor  = cgreen,
  urlcolor   = corange,
  colorlinks = true,
}

% Lecture information
\newcommand\coursename{CPSC 664, Spring 2023}
\newcommand\scribe{YOUR NAME HERE}
\newcommand\lecturer{Tim Kunisky}
\newcommand\lecturedate{LECTURE DATE HERE}
\newcommand\lecturetitle{LECTURE \#: TITLE HERE}

% Define theorem environments here.
\newtheorem{claim}{Claim}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{remark}[theorem]{Remark}
\newtheorem{assumption}[theorem]{Assumption}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{question}[theorem]{Question}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{conjecture}[theorem]{Conjecture}

% Some of my macros
\renewcommand{\AA}{\mathbb{A}}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\DD}{\mathbb{D}}
\newcommand{\EE}{\mathbb{E}}
\newcommand{\FF}{\mathbb{F}}
\newcommand{\HH}{\mathbb{H}}
\newcommand{\NN}{\mathbb{N}}
\newcommand{\PP}{\mathbb{P}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\RR}{\mathbb{R}}
\renewcommand{\SS}{\mathbb{S}}
\newcommand{\ZZ}{\mathbb{Z}}
\DeclareSymbolFont{bbold}{U}{bbold}{m}{n}
\DeclareSymbolFontAlphabet{\mathbbold}{bbold}
\newcommand{\One}{\mathbbold{1}}

\newcommand{\ba}{\bm a}
\newcommand{\bb}{\bm b}
\newcommand{\bc}{\bm c}
\newcommand{\bd}{\bm d}
\newcommand{\be}{\bm e}
\newcommand{\bg}{\bm g}
\newcommand{\bh}{\bm h}
\newcommand{\bi}{\bm i}
\newcommand{\bj}{\bm j}
\newcommand{\bk}{\bm k}
\newcommand{\bbm}{\bm m}
\newcommand{\bp}{\bm p}
\newcommand{\bq}{\bm q}
\newcommand{\br}{\bm r}
\newcommand{\bs}{\bm s}
\newcommand{\bt}{\bm t}
\newcommand{\bu}{\bm u}
\newcommand{\bv}{\bm v}
\newcommand{\bw}{\bm w}
\newcommand{\bx}{\bm x}
\newcommand{\by}{\bm y}
\newcommand{\bz}{\bm z}

\newcommand{\bA}{\bm A}
\newcommand{\bB}{\bm B}
\newcommand{\bC}{\bm C}
\newcommand{\bD}{\bm D}
\newcommand{\bE}{\bm E}
\newcommand{\bF}{\bm F}
\newcommand{\bG}{\bm G}
\newcommand{\bH}{\bm H}
\newcommand{\bI}{\bm I}
\newcommand{\bL}{\bm L}
\newcommand{\bM}{\bm M}
\newcommand{\bN}{\bm N}
\newcommand{\bP}{\bm P}
\newcommand{\bQ}{\bm Q}
\newcommand{\bR}{\bm R}
\newcommand{\bS}{\bm S}
\newcommand{\bT}{\bm T}
\newcommand{\bU}{\bm U}
\newcommand{\bV}{\bm V}
\newcommand{\bW}{\bm W}
\newcommand{\bX}{\bm X}
\newcommand{\bY}{\bm Y}
\newcommand{\bZ}{\bm Z}

\newcommand{\zero}{\bm{0}}
\newcommand{\one}{\bm{1}}

\newcommand{\sA}{\mathcal{A}}
\newcommand{\sB}{\mathcal{B}}
\newcommand{\sC}{\mathcal{C}}
\newcommand{\sD}{\mathcal{D}}
\newcommand{\sE}{\mathcal{E}}
\newcommand{\sF}{\mathcal{F}}
\newcommand{\sG}{\mathcal{G}}
\newcommand{\sH}{\mathcal{H}}
\newcommand{\sI}{\mathcal{I}}
\newcommand{\sJ}{\mathcal{J}}
\newcommand{\sK}{\mathcal{K}}
\newcommand{\sL}{\mathcal{L}}
\newcommand{\sM}{\mathcal{M}}
\newcommand{\sN}{\mathcal{N}}
\newcommand{\sO}{\mathcal{O}}
\newcommand{\sP}{\mathcal{P}}
\newcommand{\sQ}{\mathcal{Q}}
\newcommand{\sR}{\mathcal{R}}
\newcommand{\sS}{\mathcal{S}}
\newcommand{\sT}{\mathcal{T}}
\newcommand{\sU}{\mathcal{U}}
\newcommand{\sV}{\mathcal{V}}
\newcommand{\sX}{\mathcal{X}}
\newcommand{\sY}{\mathcal{Y}}

\newcommand{\fB}{\mathscr{B}}
\newcommand{\fC}{\mathscr{C}}
\newcommand{\fE}{\mathscr{E}}
\newcommand{\fH}{\mathscr{H}}
\newcommand{\fI}{\mathscr{I}}
\newcommand{\fP}{\mathscr{P}}
\newcommand{\fV}{\mathscr{V}}

\DeclareSymbolFont{sfoperators}{OT1}{cmss}{m}{n}
% don't waste a math group
\DeclareSymbolFontAlphabet{\mathsf}{sfoperators}
% tell LaTeX to use sfoperators for names of operators
\makeatletter
\renewcommand{\operator@font}{\mathgroup\symsfoperators}
\makeatother

\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator{\GOE}{GOE}
\DeclareMathOperator{\sym}{sym}
\DeclareMathOperator{\Part}{Part}
\DeclareMathOperator{\poly}{poly}
\DeclareMathOperator{\Unif}{Unif}
\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\Cov}{Cov}
\DeclareMathOperator{\Tr}{Tr}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\obj}{obj}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\sgn}{sgn}

\renewcommand\Re{\operatorname{Re}}
\renewcommand\Im{\operatorname{Im}}
% These put symbols below.
\newcommand{\Px}{\mathop{\mathbb{P}}}
\newcommand{\Ex}{\mathop{\mathbb{E}}}
\newcommand{\Varx}{\mathop{\mathsf{Var}}}

\newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}}

%
% Put your custom macros here if you want.
%

\begin{document}

% This creates the header for scribe notes.
\noindent \coursename \hfill Scribe: \scribe \\
\lecturedate \hfill Lecturer: \lecturer
\vspace{1em}

\hrule

\vspace{1.5em}
\begin{center}
  {\Large\lecturetitle}
\end{center}

\section{Section 1}

This is text.
This is an equation:
\begin{equation}
A = B.
\end{equation}

\begin{theorem}[Theorem 1]
    \label{thm:my-theorem}
    This is a claim.
\end{theorem}

This is a reference to the claim in Theorem~\ref{thm:my-theorem}.
This is a longer paragraph elaborating on my Theorem.
This is another sentence.

\begin{remark}[Topic]
    This is a remark on my theorem.
\end{remark}

\section{Section 2}

Here is a demonstration of some useful probability notations:
\begin{align*}
  \Ex_{\text{subscript}}[Z]
  &= \EE\left[ \sum_{i = 1}^N \One\{A_i\} \right] \\
  &= \sum_{i = 1}^N \PP[A_i] \numberthis
\end{align*}
Some more:
\begin{equation}
    \EE Z^2 - (\EE Z)^2 = \Var[Z] = \bx^{\top} \Cov[\by] \bx
\end{equation}
And linear algebra notations:
\begin{equation}
    \bA \one = \bX^{\top} \by = \langle \ba, \bb \rangle \bz \text{ for } \bY \succeq \bm 0
\end{equation}
Some functions:
\begin{align}
  f: \sA &\to \CC \\
  x &\mapsto f(x)
\end{align}
Some optimization:
\begin{equation}
    x = \left\{\begin{array}{ll} \text{maximize} & f(\by) \\ \text{subject to} & \text{conditions on } \by \end{array}\right\} = \argmin_{x \in \sX} \{\obj(x)\}.
\end{equation}

\end{document}
