%
% LaTeX Problem Set Template originally designed
% by former CS103 TA Sachin Padmanabhan.
%
% Updated for Fall 2018 by Michael Zhu
% Updated for Fall 2019 by Joshua Spayd
% Updated for Fall 2020 by Lucy Lu
% Updated for Winter/Spring 2021 by Cynthia Bailey Lee
% Updated for Fall 2021 by Grant McClearn

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{mathdots}
\usepackage[pdftex]{graphicx}
\usepackage{fancyhdr}
\usepackage[margin=1in]{geometry}
\usepackage{multicol}
\usepackage{bm}
\usepackage{listings}
\PassOptionsToPackage{usenames,dvipsnames}{color}  %% Allow color names
\usepackage{pdfpages}
\usepackage{algpseudocode}
\usepackage{tikz}
\usepackage{enumitem}
\usepackage[T1]{fontenc}
\usepackage{inconsolata}
\usepackage{framed}
\usepackage{wasysym}
\usepackage[thinlines]{easytable}
\usepackage{hyperref}
\usepackage{wrapfig}
\hypersetup{
    colorlinks=true,
    linkcolor=blue,
    filecolor=magenta,
    urlcolor=blue,
}

\title{CS 103: Mathematical Foundations of Computing\\Midterm Exam I}
\author{[TODO: Replace this with your name]}
\date{\today}

% Running author based on https://tex.stackexchange.com/questions/68308/how-to-add-running-title-and-author#answer-68310
\makeatletter
\let\runauthor\@author
\makeatother

\lhead{\runauthor}
\chead{Midterm Exam I}
\rhead{\today}
\lfoot{}
\cfoot{CS 103: Mathematical Foundations of Computing --- Fall 2021}
\rfoot{\thepage}

\newcommand{\abs}[1]{\lvert #1 \rvert}
\newcommand{\absfit}[1]{\left\lvert #1 \right\rvert}
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\eval}[3]{\left[#1\right]_{#2}^{#3}}
\renewcommand{\(}{\left(}
\renewcommand{\)}{\right)}
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}
\newcommand{\ceil}[1]{\left\lceil#1\right\rceil}
\newcommand{\pd}[1]{\frac{\partial}{\partial #1}}
\newcommand{\inner}[1]{\langle#1\rangle}
\newcommand{\cond}{\bigg|}
\newcommand{\rank}[1]{\mathbf{rank}(#1)}
\newcommand{\range}[1]{\mathbf{range}(#1)}
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\newcommand{\repr}[1]{\left\langle#1\right\rangle}

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% start MZ
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\renewcommand{\emptyset}{\text{\O}}
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\usepackage{mdframed}
\usepackage{float}

\makeatother
% end MZ

\definecolor{shadecolor}{gray}{0.95}

\theoremstyle{plain}
\newtheorem*{lem}{Lemma}

\theoremstyle{plain}
\newtheorem*{claim}{Claim}

\theoremstyle{definition}
\newtheorem*{answer}{Answer}

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\renewcommand{\footrulewidth}{0.4pt}

\setlength{\parindent}{0pt}

\pagestyle{fancy}

\renewcommand{\thefootnote}{\fnsymbol{footnote}}

% Lucy
\usepackage{boxedminipage}
\newenvironment{blank}[1]{\colorbox{shadecolor}{\strut \underline{\hspace{#1}}}}
% Lucy

\begin{document}

\maketitle

\begin{center}
  \emph{Due Sunday, October 17 at 2:30 pm Pacific}
\end{center}

\vspace{1cm}

Please submit your answers to Problem Two (Translating Into Logic) separately from this PDF.

\section*{Symbols Reference}
Here are some symbols that may be useful for this midterm. 

\begin{itemize}
    \item Floor:   $\floor{x}$
    \item Ceiling: $\ceil{x}$
    \item Less-than-or-equal-to and greater-than-or-equal-to: $x \le y$ and $y \ge x$
    \item Natural numbers: $\mathbb{N}$
    \item Integers: $\mathbb{Z}$
\end{itemize}

\LaTeX typing tips:
\begin{itemize}
    \item Set (curly braces need an escape character backslash): ${1, 2, 3}$ (incorrect), $\{1, 2, 3\}$ (correct)
    \item Exponents (use curly braces if exponent is more than 1 character): $x^2$, $2^{3x}$
    \item Subscripts (use curly braces if subscript is more than 1 character): $x_0$, $x_{10}$
\end{itemize}

\newpage

\section*{Problem One: Quarter-Squares (8 Points)}
    \begin{shaded}
    Write your answer to Problem One here.
    \end{shaded}
    
\newpage

\section*{Problem Three: Tower of Power (4 Points)}
    i.
    \begin{shaded}
    Write your answer to Problem Three, part i. here.
    \end{shaded}
    ii.
    \begin{shaded}
    Write your answer to Problem Three, part ii. here.
    \end{shaded}
    iii.
    \begin{shaded}
    Write your answer to Problem Three, part iii. here.
    \end{shaded}
    iv.
    \begin{shaded}
    Write your answer to Problem Three, part iv. here.
    \end{shaded}
    
\newpage

\section*{Problem Four: A Clever Little Equation (8 Points)}
    i.
    \begin{shaded}
    Write your answer to Problem Four, part i. here.
    \end{shaded}
    
    ii.
    \begin{shaded}
    Write your answer to Problem Four, part ii. here.
    \end{shaded}
    
    iii.
    \begin{shaded}
    Write your answer to Problem Four, part iii. here.
    \end{shaded}
    
\end{document}
