Solutions to the midterm

The solutions to the midterm are here.

LaTeX template for your adopted group paper

\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{graphicx}
\usepackage{amssymb}
\usepackage{epstopdf}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}


\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{propn}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}


\def\defn{\medskip\noindent{\bf Definition. }}
\def\proof{{\it Proof. }}
\def\qed{\hfill$\blacksquare$}



\title{Scintillating Title}
\author{Me, Of Course}
%\date{}                                           % Activate to display a given date or no date

\begin{document}
\maketitle
%\section{}
%\subsection{}

The group $D_3$ is fascinating, and we all should know why.  In Figure~\ref{cayley}, we see a Cayley table for the group.


\begin{table}[htdp]
\begin{center}
\begin{tabular}{c | c c c }  % the c is for 'center'; you could use l (left) or r (right)
% the | makes a vertical line
    $\times$  & $1$  & $R$  & $R^2$     \\
\hline % makes a horizontal line
  1 & $1$  & $R$  & $R^2$  \\
  $R$ & $R$  & $R^2$  & $1$  \\
  $R^2$ & $R^2$  & $1$  & $R$  \\
\end{tabular}
\end{center}
\caption{Cayley table for my fascinating group}
\label{cayley}   % This allows me to refer back to the table by the right number, even if I add more tables.
\end{table}%

\begin{theorem}\label{cyclic}
The group $D_3$ is cyclic\footnote{If you have questions for me as you write your paper, doing so in a footnote is a perfectly fine way of asking me something!}.
\end{theorem}

\proof
Observe that $D_3 =<R>$.
\qed

\end{document}

Aligned equations

Here is how to TeX up an a``aligned equation'':

$$   % this starts the displayed math mode
\begin{array}{rcl}   % r for aligned right, c for center, and l (L) for aligned left
  b & =  &  b(aa^{-1}) \\       % & separates the columns; \\ starts a new line
  & =  & (ba)a^{-1}  \\
  & =  &   (ca)a^{-1} \qquad\hbox{by associativity}  \\
                                % you won't do this much, but here's how to add space and words
& =  &   c(aa^{-1}) \\
& =  &   c. % note the punctuation; we don't need a new line so no \\
\end{array}
$$

Writing resources for algebra

When you're writing up problems that are more computational, you might use this example of a well-written homework as an example.    And you certainly want to avoid writing a poorly-written homework!

If you want to see an old, old Guide to Writing that I wrote for my calculus students back in the 1990's, look here.  The technology parts of this guide are out-dated, but the style parts are timelessly correct.

HW 0 due Wednesday

Homework 0 is due Wednesday.

You MAY work in groups of two people.
You MAY write this first homework by hand (but please be neat).
You MUST staple your pages, if there's more than one.
You must write on only one side of the page.

Even though you're allowed to write this by hand, it might be a good idea to see if you can get 1/2 hour closer to being a TeX master.  Here are some possible steps along the way to this laudatory goal.

• Download TeXshop or some other TeX-ish software.  Here's one possible link:  http://pages.uoregon.edu/koch/texshop/
• Paste the template from the previous blog post into a blank page, save this as "template" or "I-am-so-cool" or some such, and hit "typeset".
• Try typing an actual math equation, or the statement of a theorem, or something like a proof.

If you have any questions as you go along, feel free to send me an email!

LaTex Template for homework write-ups

\documentclass[12pt]{article}
\usepackage{geometry}              
\geometry{letterpaper}                  
\usepackage{amssymb}


% Dear Student,  these commands below define commands that
% you can use later.  Don't type anything until after "Begin document".
% Any math symbol or expression you type should come between
% two dollar signs.  For example, you might say  something like
% "For every $x \in \integers$, there is some . . . ."

\newcommand\exercise[1]{\noindent {\bf Exercise #1:} }
\newcommand\collaborators[1]{\medskip\noindent {\bf Collaborators:} {\em #1}}

\newcommand\proof{\medskip\noindent{\it Proof.  }}
\newcommand\qed{\hfill{$\blacksquare$}}

\newcommand\Z{\ensuremath{\mathbb{Z}}} %  Integers
\newcommand\N{\ensuremath{\mathbb{N}}} %  Natural Numbers
\newcommand\Q{\ensuremath{\mathbb{Q}}} %  Rationals
\newcommand\R{\ensuremath{\mathbb{R}}} %  Real Numbers


\begin{document}

\noindent {YourNameHere} \hfill Mat 330 \hfill {Homework N}
% Change your name and the homework number in the line above
\vspace{5mm}



\exercise {0.0}% {enter the correct number for chapter.exercise}
Replace this line with the complete statement of the exercise.



\collaborators{Type the names of your collaborators here.}\newline\medskip
% Include the name of every person with whom you
% discussed this exercise outside of class, whether
% you gave or received help.

\proof % Keep this and the \qed if your solution is a proof.
% Otherwise, delete it, but still type your solution where the line below is.
Your solution goes here.
\qed



%If you have questions or comments for your professor, feel free to
% include them here; otherwise you can just erase the next line:

\vspace{5mm}\noindent{\bf Questions for Dr.~Crannell:}\newline
Type your question here.

\end{document}

What's due August 30?

Congrats!  You found the algebra blog!

On Friday, we'll have a quiz on the syllabus, which you can find in a link off on that side ---->.

The first question on that quiz will be "How much does this syllabus quiz count toward your final grade?"

We'll continue working on the yellow "0" sheet in class on Friday, so you don't have to finish it outside of class, but you might find it helpful to fill in the multiplication tables for Z_{12} and Z_{11}.

testing, testing

Here's a test post.