% Filename: 290inf_Spring2010.tex
%  Linear Algebra 
% Written: January 6, 2010
%

\documentclass[12pt]{article}

\usepackage{amsfonts,amsmath,hyperref} % allows internal hyperlinks
% \input{tcilatex} % to allow rubric to print

\usepackage[usenames]{color}
\usepackage{geometry}
\geometry{paper=letterpaper, 
		  body={7.40in, 9.8in}, 
		  lmargin=0.55in, 
%		  rmargin=0.75in, 
		  vmarginratio={2:1}
		  }



\title{MATH 290, Linear Algebra  \\
			Spring 2010
}

\date{January 8, 2010}
\author{Bryan Smith}


\pagestyle{headings}
\begin{document}
\maketitle
\thispagestyle{empty}
\tableofcontents
\setcounter{page}{0}
\newpage

%%%%%%%%% Commands and macros
%% Since the test day might change from semester to 
%% 	semester, we initialize \testday as part of the template
%%  and specify it at the exam location in the file.
\newcommand{\testday}{}

%% Notes to me for first day walk-through of handout
\newcommand{\mention}{} %{\color{blue}\textbf{Mention briefly}}}
\newcommand{\highlight}{} %{\color{green}\textbf{Highlight for effect}}}
\newcommand{\important}{} % {\color{red}\textbf{Important To Point Out}}}

\section{Introduction}
  For an official description of this course, see the 
  \href{http://www.math.ups.edu/~matthews/Syllabi/MATH290_May2006.pdf}
  {MATH 290 Syllabus}\cite{290syl}.

\mention
  The prerequisite for this course is MATH 181 (second semester calculus)
  but do not expect it to be like calculus -- it is an algebra course
  through and through. However, linear algebra is used extensively in
  multivariate calculus, physics, chemistry, economics, and computer
  science so, during the semester, we will take a little time away from the
  algebra to introduce some of these examples.

\mention
  Linear algebra is the first ``proof-based'' course offered in Puget
  Sound's mathematics curriculum and serves as the gateway course to
  upper-division mathematics. Since it also meets the university's
  ``Writing in the Major'' requirement, there will be at least as much
  focus on developing mathematical writing skills as on linear algebra
  itself. More details are provided in the \hyperlink{writing}{Writing
  Projects} section below.

\important
 You should expect to spend at least as much time writing correct proofs of
 your results as you spend figuring out those proofs. In fact, one of the
 most important goals of this course is for you to deeply appreciate that
 you don't really understand a concept unless you can clearly explain it to
 someone else.

\subsection{Goals} By the end of the semester, you should understand linear
equations and their solutions, see how vector spaces arise naturally from
generalizing standard methods for solving systems of linear equations, and
see their utility in a range of applications. You should also be able to
read a mathematical text for content and deep understanding (see
\href{http://www.cse.buffalo.edu/~rapaport/howtostudy.html}{``How to
Study''}\cite{study} for an excellent description of how to read
mathematics and other efficient ways to study), analyze a given problem to
determine which linear algebra tools should be used in its solution, use a
variety of strategies to determine and prove a solution of the given
problem, and follow accepted mathematical style to present an accurate and
carefully written formal proof of that solution.

During a normal class day we will work to achieve these goals by discussing
new material and addressing questions that arise from reading the text or
working on homework problems.

%When we discuss new material, we will look at these ideas
%in their simplest form to highlight how they fit together into the
%logical whole that is the ``big picture'' and will save discussion of
%the details and refinements necessary for a deeper understanding for a
%second (or third) pass through the material. You are to prepare outside
%of class for these discussions by carefully reading the text
%and working on the assigned problems. Then, during class, we will
%address these deeper refinements by responding to questions on the
%reading and the problems that you bring to class. 


\section{Attendance} 
\highlight
Daily attendance is both required and expected. You are also expected to
participate fully in class by pre-reading the material to be covered,
seeking clarification for unclear points, and engaging in mannerly
discussions of the topics.


\section{Academic Honesty} 
\highlight
Unless specifically told otherwise, all graded materials are to be your own
work. This includes the reading and writing assignments. You are expected
to be familiar with the university's 
\href{http://www.pugetsound.edu/student-life/student-resources/student-handbook/student-integrity-code/}
	{Student Integrity Code} \cite{integrity} and will be
asked to affirm you abide by it on every assignment and exam.

\section{Course Information}\label{courseinfo}
\subsection{Textbook}\label{textbook}
\mention	
	The textbook is {\em A First Course in Linear Algebra, (Version
	2.20),\/} by Robert A, Beezer, \copyright2009, and is published by
	Professor Beezer under the GNU Free Documentation License rather than
	by a commercial publishing house.
	
	You can	purchase a copy of version 2.0 (Waldron Edition) from
	\href{http://www.lulu.com/linearalgebra}{Lulu.com} for around \$40.00
	plus shipping. 

	Since this is likely to be your first exposure to proof-based
	mathematics, you should also consider buying one of the many books on
	how to do proofs. I recommend ``The Nuts and Bolts of Proofs'' and
	can give you names of several others on request. 

\subsection{Calculator}\label{calculator}
\mention	
	I \textbf{require} a calculator for this course. It must be able to
	perform the following matrix operations: row operations, reduced row
	echelon form, transpose, determinant, and eigenvalues/eigenvectors. I
	will allow the calculator to be used on examinations but will not allow
	its use for some problems.
	
	If you do not have a
	manual for your calculator, you should be able to find one on the
	internet -- for example at \\
	\url{http://education.ti.com/us/product/tech/83/guide/83guideus.html}
	\cite{TI}. Be advised that some students have had trouble getting a TI
	83 to do all of the necessary computations.

	Here is a link to the department's
	\href{http://www.math.pugetsound.edu/info/calcpolicy200608.pdf}{Calculator
	Policy} \cite{calculator}.

	

% excerpted paragraph on symbolic word processors


\subsection{Basic Information}\label{basicinfo}
\mention
    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 290 link.
  
  \href{http://math.pugetsound.edu/~bryans/}
  {http://math.pugetsound.edu/\mbox{$\sim$}bryans/} \cite{myweb}

\mention
\subsubsection{Logistics}\label{logistics}
Classes meet for $50$ minutes except on examination days when we meet for $80$ minutes.

\begin{tabular}{|l|c|l|l|l|l|} \hline
    \textbf{Prof. Bryan Smith}& TH 390D & 879-3562 & bryans[at]ups.edu  & \  & \  \\
	\hline \hline
	Math 290 & TH 197 & M, F & 12:00 - 12:50  PM 	& \  & \   	 \\ \hline
		\ 	 &	\ 	  &	T, Th & 12:30 - 1:30 PM	    & \  & \     \\ \hline
  															        \hline
   \textbf{Office Hours}& \ & Tue, Thu		& 9:30-10:00 AM 	& 1:30-2:00 PM	 & 3:00-3:30 PM		\\ \hline
			\ 			 & \ & Wed	 		& 3:00-4:30 PM  	& \ 			 & \ 				\\ \hline
			\ 			 & \ & Others		& By Appointment 	& \ 			 & \ 			  	\\ \hline
  													  		   		 							   	   \hline
\end{tabular}
	
	I am also happy to make appointments for other times. 

%  information examination 

\renewcommand{\testday}{Thursday}
\subsection{Examinations}\label{exams}
\highlight
	All examinations are scheduled for \testday{}. On test weeks,
	if there is interest, there will be a review session the night
	before from 7:00 until 8:15 P.M. Note that the exam period
	will run for 80 minutes (be sure to know when class starts and
	ends on an examination day).

	There will be four (4) 50-minute, in-class examinations and the 
	lowest score will be dropped. I do not give make-up
	examinations except for truly exceptional circumstances. 
	You \textbf{should not} expect all examination questions to
	closely mimic textbook examples or assigned homework
	problems. 

	There are copies of old exams on my web site. They might
	contain typos or even errors. They are offered ``as is'' for
	those who wish to use then as a study aid. But they are
	\textbf{not} part of this semester's course.

   	  \begin{tabular}{lll}
   		Examination One	&	\testday{} & February 11	\\
   		Examination Two	&	\testday{} & March 4  \\
		Examination Three & \testday{} & April 8  \\
		Examination Four &  \testday{} & April 29 \\
      \end{tabular}


\subsection{Final Examination}\label{final}
	The final examination is scheduled for 

   	  \begin{tabular}{rrr}
   		Math 290B &	Mon, 10 May 2010	& 12:00 - 2:00 P.M. 
	  \end{tabular}

\highlight
 The final examination will be comprehensive and \textbf{cannot be
	rescheduled} so do not plan plane flights (or anything else) that will
	conflict with it. I will allow you to work longer than the two hours
	scheduled for the final.

%  information homework 
\hypertarget{writing}{
\subsection{Writing Projects}\label{projects}
}
\important
	In order to meet the Writing in the Major requirement, I will assign a
	writing exercise each week (about two per chapter). You are to
	determine a solution for each and then write up a careful proof. These
	papers will be graded pass/fail for both mathematical content and
	written presentation.  They are due in class on every Thursday. You may
	resubmit each problem repeatedly provided: 1) you make a serious effort
	on each retry and 2) it has not been more than two weeks since you last
	submitted the problem. Problems that are not submitted within the two
	week deadline receive an automatic fail.  All work on these proofs is
	to be your own with two exceptions: you are allowed to discuss problems
	with me and you may use any ideas that you witness during a classroom
	exchange.
	
	Note specifically that 
	\begin{enumerate}
		\item You may not discuss any aspect of these problems with anyone
		except me.
		\item You may not use any written resources other than your
		textbooks for this semester.
		
	\end{enumerate}

 	See the \hyperlink{rubric}{grading rubric} on the last page of this
	document for further details pertaining to written mathematics.
	

\subsection{Homework}\label{homework}
\mention
    It is wise to work most, if not all, of the homework problems in the
	textbook. Although they will not be collected, they will form the basis
	for much of our in-class discussions.

\subsection{Reading Questions}\label{reading}
	It is very important that you read the material at least twice. Once
	before and once after it is discussed in class. It is also important
	that you read correctly. Mathematics requires that you read
	\textbf{slowly} and with a pencil and paper at hand. (See
	\href{http://www.cse.buffalo.edu/~rapaport/howtostudy.html} {``How to
	Study''}\cite{study} on the course webpage for more details.)

    There are reading questions at the end of each section of the book. You
	are to read these \textbf{before} we cover that material (see the
	\href{http://math.pugetsound.edu/~bryans/Current/Spring_2010/290ScheduleS10.html}
		{tentative schedule} 
	and email your answers to me by 7:00 AM the morning we
	discuss that section in class. Note that these will not be accepted
	late.


	When submitting your answers to the questions use the following structure.
	\begin{enumerate}
		\item Sent to me at bryans(at)pugetsound.edu 
		\item The ``Subject" line must contain ``290" followed by the section acronym.
			For example, the first reading assignment should have ``290'' and  ``WILA'' 
			in it's  subject line. 
		\item Have your full name as the first line of your response.
		\item Do not type the questions into your email -- just answers.
		\item Give very brief answers. Do not include computations for 
			numerical questions but do give brief reasons.
		\item Send only pure text. Do not send attachments, WORD files, 
			or graphics. Do not send your answer in HTML if you can avoid it. 
		\item Mathematical notation is cumbersome in text-only email 
			but don't worry too much about it. I should be able to decipher
			most reasonable attempts. 
	\end{enumerate}
 
		
\subsection{Course Information Updates}\label{grades} If you wish, I will
  periodically post a grade report of your current standing in the class on
  my university web page. You should keep track of your grades on the
  various assignments and check them against these reports. If there are
  any discrepancies they should be dealt with immediately.

\mention
  To have your information posted you need to print your name, the class
  (MATH 290), 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} \
\mention
   \begin{tabular}{|c|r|}		   		\hline
	Writing Projects&   	25\%		\\	\hline 
	Reading Questions&   	10\%		\\	\hline
	Examinations	&   	45\% 		\\	\hline
	Final Examination	&   20\%	\\	\hline	\hline
%	TOTAL		&   750 - 800 		\\	\hline
		\end{tabular}
		
	

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

\bibitem{290}
Math 290 Course Webpage                  \\
\url{http://math.pugetsound.edu/~bryans/Current/Fall_2009/290Index_Spring2010.html}

\bibitem{integrity}
Student Integrity Code
\url{http://www.pugetsound.edu/student-life/student-resources/student-handbook/student-integrity-code/}

\bibitem{calculator}
Department Calculator Policy            \\
\url{http://www.math.pugetsound.edu/info/calcpolicy200608.pdf}

\bibitem{290syl}
Department Syllabus for MATH 290    \\
\url{http://www.math.ups.edu/~matthews/Syllabi/MATH290_May2006.pdf}

\bibitem{study}
William Rapaport's ``How to Study''   \\
\url{http://www.cse.buffalo.edu/~rapaport/howtostudy.html}

\bibitem{TI}
TI-83 Guidebook    \\
\url{http://education.ti.com/us/product/tech/83/guide/83guideus.html}

% \bibitem{bloch}
% ``Proofs and Fundamentals: A First Course in Abstract Mathematics'',  Bloch \\
% \url{http://www.amazon.com/exec/obidos/ASIN/0817641114/}
% 
% \bibitem{nuts}
% ``The Nuts and Bolts of Proofs'', Antonella Cupillari  \\
% \url{http://www.amazon.com/exec/obidos/tg/detail/-/0120885093/}
% 
% \bibitem{think}
% ``Thinking Mathematically'', Mason/Burton/Stacey     \\
% \url{http://www.amazon.com/exec/obidos/ASIN/0201102382/}
% 
% \bibitem{solow}
% ``How to Read and Do Proofs'', Solow         \\
% \url{http://www.amazon.com/exec/obidos/ASIN/0471406473/}
% 
% \bibitem{vell}
% ``How to Prove It: A Structured Approach'', Velleman     \\
% \url{http://www.amazon.com/exec/obidos/ASIN/0521446635/}
% 	
% \bibitem{west}
% ``Mathematical Thinking: Problem-Solving and Proofs'', West and D'Angelo \\
% \url{http://www.amazon.com/exec/obidos/ASIN/0130144126/}	
	
\end{thebibliography}

\newpage

% Writing Project grading rubric

\hypertarget{rubric}
{
\section{Math 290 Writing Projects \hspace{1.5in} Grading Rubric}
}

\vspace{1pt}

\vspace{1pt}%

\begin{tabular}{|c|c|}
\hline\hline
\textbf{Code} & \textbf{Logic and Mathematics} \\ \hline\hline
Accept & \multicolumn{1}{|l|}{Arguments are correct, complete and without
inappropriate material.} \\ \hline
L & \multicolumn{1}{|l|}{Logic or Mathematics are incorrect} \\ \hline
T & \multicolumn{1}{|l|}{Terminology or notation is incorrect} \\ \hline
W & \multicolumn{1}{|l|}{Writing does not adhere to the guidelines.} \\ \hline
\end{tabular}

\
\vspace{1pt}

\subsection{Writing Guidelines}

It is best to think of these projects as weekly writing assignments in
which you completely explain and justify your analyses of the problems.
There is to be no collaboration at all when you work these problems and
write them up. Your sole outside resources are direct discussions with me
or discussions that occur during class.

In addition I expect your papers to be

\begin{enumerate}
\item Fully documented -- specifically:

	\begin{enumerate}
		\item Any idea obtained during in-class brainstorm sessions or in
		discussions with me is cited in-line.

		\item All textbook results (theorems, propositions, and lemmas)
		are cited in-line and include the acronym of the result.

		\item Any use of technology is cited in-line.
	\end{enumerate}

\item Carefully handwritten in ink or written with a word processor. (I
will show you how to use \LaTeX and Sage for this. You can also use
Scientific Notebook, Mathematica or Microsoft Word. Please check with me
before using any other program.)

\item Written using complete, accurately punctuated sentences.

\item Presented in active voice, the first person plural and with a clear,
easy-to-follow expository style.

\item Targeted at an audience consisting of students not in this class but
with an equivalent mathematical background -- say those currently in
another section of this course.

\end{enumerate}


\end{document}
