% This is a TeX file
% It is essentially a programming language for mathematics documents
% You can ignore this first portion of the file, as it is essentially a bunch of "include" statements.
\documentclass[10pt]{article}

\usepackage{pictex, latexsym, graphicx,amsmath,amssymb,amsbsy,amsfonts,amsthm,verbatim}
\usepackage{graphics}
\usepackage{fullpage}
\usepackage{fancyhdr}

\usepackage{algorithm,algorithmic}
\usepackage{multirow}

\setlength{\voffset}{-0.25in}
\setlength{\headsep}{0.25in}
\setlength{\parskip}{1em}
\setlength{\parindent}{0em}

% The following denotes a counter for the problems.
\newcounter{problem}
\newcommand{\problem}{\textbf{\refstepcounter{problem}Problem \theproblem.} }

% These are macro shortcuts! Helpful!
\def\vu{\mathbf{u}}
\def\vx{\mathbf{x}}
\def\vb{\mathbf{b}}
\def\vv{\mathbf{v}}
\def\vw{\mathbf{w}}

\renewcommand{\implies}{\rightarrow}
\renewcommand{\lor}{\vee}
\renewcommand{\land}{\wedge}
\newcommand{\xor}{\oplus}
\renewcommand{\iff}{\leftrightarrow}
\newcommand{\TRUE}{\mathbf{T}}
\newcommand{\FALSE}{\mathbf{F}}
\newcommand{\universe}{\mathcal{U}}

\begin{document}
\pagestyle{fancyplain}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% NOW you can start typing your text that will appear in the PDF!!!

% Note that anything after a '%' is a comment!

% Anything immediately after a '\' is a command. 
% Some denote formatting, some are for special characters.
% The '$' symbol starts and ends "math mode". Use this only for mathematical statements
% In math mode, any sequence of letters is meant to be a list of variables, so use "\sin x" for the sine of x, which will look much different from "sin x"
\chead{COM S 330 --- Homework 01 --- INSERT NAME HERE}

\textit{Type your answers to the following questions and submit a PDF file to Blackboard. 
Use only one page per problem.}



\problem [5pts] Describe your previous mathematical experience, including most recent math courses and how you feel you did. 
Include details on how much you remember the material, your mastery during the course, and how much you enjoyed your experiences.


\textit{Solution:} Depends on the student.

% Be sure to use this \clearpage to make sure your problems are on separate pages!
%\clearpage
\problem [5pts] What are your goals for taking this course? 
Is it simply a requirement, or do you want something in particular from this course?

\textit{Solution:} Depends on the student.

% Be sure to use this \clearpage to make sure your problems are on separate pages!
%\clearpage
\problem [5pts] This course is very different from any computer science course you have taken to date. 
How do you plan to change your study habits in order to achieve success?

\textit{Solution:} Depends on the student.

% Be sure to use this \clearpage to make sure your problems are on separate pages!
%\clearpage
\problem [5pts] Visit Prof. Stolee's office (Carver 416) and say ``Hello!'' 
Then, write something here about something you noticed in his office.

\textit{Solution:} Depends on the student. Here are a few popular items: Standing desk, Dachshund chalkboard, Yoda bobblehead, lego Android, oragami Platonic solid/icosahedron/dodecahedron, Nebraska football, sandwich, Discrete Mathematics with Ducks, Rubik's Cubes, Research notebooks, 

% Be sure to use this \clearpage to make sure your problems are on separate pages!

\clearpage
\problem [5pts] Read the syllabus. Then, summarize the following information:
\begin{enumerate}
	\item What is the homework late policy?
	
\textit{Solution:} If you turn in homework within 24 hours late, you receive a 0.75 multiplier. If you turn it in within 24 to 48 hours late, you receive a 0.5 multiplier. Otherwise no credit.
	
	\item What is the exam make-up policy?
	
\textit{Solution:} Since the final exam replaces the lowest mid-term exam grade, there are no make-up exams.
	
	\item How will your grade be calculated at the end of the semester?
	
\textit{Solution:} The weighted total is $0.15$ times the homework score, $0.20$ times each mid-term exam, and $0.25$ times the final exam score, summed together.

	\item What will happen if I am academically dishonest?

\textit{Solution:} You will be reported to the Dean of Students Office.
	
	\item Where can I get support if I need extra help?
	
\textit{Solution:} The instructor, your TAs, or Disability Resources. Also the CS help room! [Not all of these are required for points, and others may be included.]

\end{enumerate}



% Be sure to use this \clearpage to make sure your problems are on separate pages!

\clearpage
\problem [10pts] Let $p$ and $q$ be the propositions\\
\begin{tabular}[h]{c@{ : }l}
$p$ & I bought a lottery ticket this week.\\
$q$ & I won the million dollar jackpot.
\end{tabular}\\
Express each of these propositions as an English sentence.
\begin{enumerate}
\item $\lnot p$

\textit{Solution:} ``I did not buy a lottery ticket this week.''

\item $p \implies q$

\textit{Solution:} ``If I bought a lottery ticket this week, then I won the million dollar jackpot.''

\item $p \land q$ 

\textit{Solution:} ``I bought a lottery ticket this week and won the million dollar jackpot.''

\item $p \iff q$

\textit{Solution:} ``I bought a lottery ticket this week if and only if I won the million dollar jackpot.''

\item $\lnot p \lor (p \land q)$

\textit{Solution:} ``I did not buy a lottery ticket this week or I bought a lottery ticket this week and won the million dollar jackpot.''

\end{enumerate}





\end{document} 