% Filename: 420inf_Spring2009.tex
%  Topology out of "Aspects" 
% Written: January 14, 2009
%

\documentclass[12pt]{article}

\usepackage{amsfonts,amsmath,hyperref} % allows internal hyperlinks

\usepackage[usenames]{color}
\usepackage{geometry}
\geometry{paper=letterpaper, 
		  body={7.45in, 9.70in}, 
		  lmargin=0.55in, 
%		  rmargin=0.75in, 
		  vmarginratio={1:1}
		}

\setlength{\parindent}{0pt}
\addtolength{\parskip}{0.2\baselineskip}

\title{MATH 420, Special Topics: Topology  \\
			Spring 2009
}

\date{January 14, 2009}
\author{Bryan Smith}

\pagestyle{headings}
\begin{document}

\maketitle
\thispagestyle{empty}
\tableofcontents
\setcounter{page}{0}
\newpage

%%%%%%%%% Commands and macros
%% Since the skipped day changes from semester to 
%% 	semester, we define \skipday as part of the template.
\newcommand{\skipday}{Wednesday}

\section{Introduction}
	We will be covering the basics of ``Pointset Topology'' in
	this course. Our material will focus on what type of
	structures need to be placed on a set in order to make it a
	``topological space'' and what properties we can deduce from
	these structures. You have already experienced a similar
	situation in linear algebra where the structure of a
	``vector space'' (addition, scalar multiplication and the
	definition with 10 properties) is placed on a set. Similar
	things are done in Math 433 and 434 in defining groups,
	rings, fields, modules, etc.
	
	It is fair to say that pointset topology is a fundamental
	part of mathematics in that almost every other branch makes
	use of it at some level. The disciplines you are most
	familiar with are interested in what topology can tell them
	about ``continuity'' and related properties of functions,
	For example, Physics, Statistics and Analysis require the
	ideas associated with derivatives (which is more stringent
	than continuity), modern Geometry requires continuity (and
	differentiability) in its concepts of transformations,
	curvature, and metrics, and almost every type of
	optimization uses tools that rely on small changes in inputs
	not having catastrophic effects on outputs of functions
	(i.e., continuity). Hence, at an intuitive level, we will be
	studying what structures are needed to make functions
	between sets be ``continuous'' and
	what other properties follow from those structures.
	
% \vspace{.5in}

\section{Course Information}\label{courseinfo}

\subsection{Textbook}\label{textbook}
	The textbook is {\emph{Aspects of Topology}}, 2nd Ed,
    Christenson and Voxman, \copyright1998, BCS Associates.
		  
	I expect that you already feel comfortable with the basic approaches to
	doing a mathematical proof. However, if you would like to have a
	resource at hand, you might consider one of the many books on
	``how to do proofs'' such as \emph{The Nuts and Bolts of Proofs}.
        
\subsection{Basic Information}\label{basicinfo}
    You can find information pertinent to all of my classes at the link
    below and, once there, information specific to this class by
    clicking on the Math 420 link.
  
  \url{http://math.ups.edu/~bryans/} \cite{myweb}
  
\subsubsection{Logistics}\label{logistics}

\begin{tabular}{|l|c|l|l|} \hline
    \textbf{Professor Bryan Smith}& Thompson 390D & 879-3562 & bryans[at]ups.edu \\
	\hline \hline
	Math 420A 	& Thompson 310 & Mon \& Fri & 11:00 - 11:50  A.M. \\ 
				& Thompson 395 & Tue \& Thu & 11:00 - 11:50  A.M. \\ \hline
  																 \hline
    \textbf{Office Hours}& & Tue. 	& 3:00 - 3:50 P.M  \\ \hline
						 & & Wed. 	& 3:00 - 4:30 P.M. \\ \hline
						 & & Thu.	& 1:00 - 1:50 P.M. \\ \hline 
  \end{tabular}

\vspace{3pt}

		If you have trouble meeting during office hours please make an
		appointment for a better time.

%
%\subsection{Day to Day Structure}\label{week}
%	 A typical class day will be lecture based with time set aside at
%	 the beginning for questions.

%  information examination 
\subsection{Examinations}\label{exams}
	Since the homework will be used to facilitate
	deep understanding, tests will be used more as a basic check of your
	knowledge. Hence, there will be three, ``straightforward'', semester
	examinations that will include definitions as well as proofs. 	

   	  \begin{tabular}{ll}
   		Examination One	&	Thursday February 12	\\
   		Examination Two	&	Thursday March 12  \\
		Examination Three & Thursday April 16
      \end{tabular}

\textbf{Study Session} If there is enough interest we can 
 	schedule an evening study session for the Wednesday 
	before an examination. 

\subsection{Final Examination}\label{final}
   	  \begin{tabular}{lll}
   		12:00 - 2:00 P.M.	&	Monday  & May 11 
      \end{tabular}

	The final will also be ``straightforward'' and comprehensive. The
	final cannot be rescheduled so do not plan plane flights (or
	anything else) that will conflict with it.

%  information homework 
\hypertarget{writing}{
\subsection{Homework}\label{projects}
}              	
Each of you will be assigned one or two homework problems from
each section that we cover for an average of about 3 problems
per week. You may submit a solution more than once but for each
problem there will be a due date beyond which I will not accept
submissions.

You are allowed (and encouraged) to work together and
to use me as a resource while figuring out these problems but
there is to be \textbf{no collaboration} when writing up your
solutions. Also, always remember that failure to include
references is intellectual theft! Please see the
\href{http://www.ups.edu/x4718.xml}{``Academic Honesty''}
section of the \emph{Logger} \cite{logger} to see how serious
this issue is to the university community.


You are to use the \LaTeX{} typesetting system to write up your
solutions. For those of you who are unfamiliar with \LaTeX{}, I
will be happy to give a brief workshop on how to install and use
this package. \LaTeX{} is now the expected way to typeset papers
in mathematics and science.
	
Since you will be using \LaTeX{} to submit your papers, it will be 
easy to compile a collection of our solutions. So,
once you have a solution accepted (and if necessary, corrected),
you will submit the \LaTeX{} code to me in electronic form. I will
then collect the solutions into a single file that we can 
``publish'' to the class at the end of the semester. The immediate
benefit to you will be ongoing access to solutions of all homework
solutions (not just the ones you have worked) to use as learning 
aids throughout the semester. 

When working your problems, feel free to use (or not) any
technology that you like (e.g., SAGE, Scientific Notebook,
CABRI, Geometers Sketchpad, calculators, \emph{Mathematica},
MATLAB, etc.).
 		   
\subsection{Reading}\label{reading}
You need to read math to learn math. 

\subsection{Course Information Updates}\label{grades} If you
  wish, I will post (and update) a grade report on your current
  standing in the class on my university web page.  To have your
  information posted you need to print your name, the class
  (MATH 420), and a code on a sheet of paper. Then sign the
  paper and physically hand it to me. The code is to be a
  sequence of up to 23 symbols I can type on a keyboard.

	

\subsection{Total Points}\label{total} \
   \begin{tabular}{|c|r|}		   		\hline
	Homework:	 	&   64\% 		\\ \hline
    Examinations:  	&   27\%        \\ \hline
	Final Examination: &   9\%		\\ \hline   \hline
%	TOTAL		&   750 - 800 		\\	\hline
		\end{tabular}
		
		
\subsection{Ungraded Homework Assignment}\label{firstassignment}
%   \textbf{(Due Friday September 7 at 5:00 P.M.)}
   
   Look over both my university web page
   \url{http://math.ups.edu/~bryans/} \cite{myweb} and the course
   webpage for MATH 420 you'll find there. Then send an e-mail message
   to me at bryans [at] ups.edu that includes brief descriptions
   of both your background in mathematics and any aspects of your 
   post-graduation 
   plans. 	

\begin{thebibliography}{9}
\bibitem{myweb}
Bryan Smith's Homepage \\
\url{http://math.ups.edu/~bryans/}

\bibitem{420}
Math 420A Course Webpage                  \\
\url{http://math.ups.edu/~bryans/Current/Spring_2009/420Index_Spring2009.html}

\bibitem{logger}
University Academic Handbook (The Logger)   \\
\url{http://www.ups.edu/x4716.xml}

\bibitem{miktex}
Location of MikTeX package for using \LaTeX{} \\
\url{miktex.org}
        
\bibitem{texeditors}
Development tools for composing \LaTeX{} documents \\
\url{miktex.org/Links.aspx} \\
\url{http://www.esm.psu.edu/mac-tex/}

\bibitem{nuts}
``The Nuts and Bolts of Proofs'', Antonella Cupillari  \\
\url{http://www.amazon.com/exec/obidos/tg/detail/-/0120885093/}

\end{thebibliography}

\end{document}
