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		{\Large  Math 300    \hspace{1in}   Geometry 
 }
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\section*{Goals}
\textbf{Non-Euclidean Geometry} We will explore the 2000 year
	history and development of one of the most perplexing, and
	hence interesting ideas to arise in western civilization.
	Our approach will follow that of our author (Greenberg) who
	uses historical vignettes as motivation and the axiomatic
	method as the primary tool for understanding the basics of
	logic, proof, Euclidean, and non-Euclidean Geometry.
	
\textbf{Reading/Writing} It is important that you read the
    text. In fact, developing the ability to read technical
    material with understanding is one of the primary goals of
    this course.  Another goal is to fine-tune the ability to
    present written arguments clearly and gracefully. It is
    easier to learn the basics of written argumentation in
    mathematics than in most other disciplines since standard
    practice in mathematics requires explicitly justifying every
    claim.
	
\textbf{Proof} Most of this course, either directly or
	indirectly, is pointed at the related issues of proof and
	communication. In particular, you will learn what it means
	when a mathematician claims to have ``proved'' a fact and,
	through the assigned paper, you will have the opportunity to
	explore other notions of communication. Our primary tools for
	this study of mathematical proof are exactly the same as those
	used by our primary author (Greenberg) in his presentation of
	non-Euclidean geometry: elementary formal logic and the
	axiomatic method. We will use our second text (Books I-VI of
	Euclid's Elements) to provide additional historical context to
	our studies. 

%	Since much of what we will see is directly linked to seeing
%	the power of axiomatized mathematics to unambiguously
%	communicate (certain) ideas, we will piggy-back on the visit
%	of Keith Devlin (NPR's "Science Guy") in April. One of
%	Devlin's research areas concerns ``what it is to think, to
%	reason, and to engage in conversation.'' We will meet with
%	him in late March or early April to discuss his book
%	\emph{Goodbye Descartes (The End of Logic and the Search for
%	a New Cosmology of the Mind}.


%	Our second text (Lakatos) explores the philosophical development of
%	mathematical proof by looking at the history of a particular
%	mathematical result. His presentation highlights many points among
%	which is the interplay between the methodology of mathematical
%	research and the development of what we now call a mathematical
%	``proof''.  As in any philosophical discussion, there are arguments
%	both for and against Lakatos' view.  A simple search (using google) on the web
%	using ``Lakatos proofs refutations'' results in a large number of
%	hits. For two brief reviews look at
%	http://www.rbjones.com/rbjpub/philos/bibliog/lakato76.htm  and 
%	http://www.rbjones.com/rbjpub/philos/bibliog/lakato76.htm. 

          
\section*{Course Information}
\textbf{TEXTS} 
	\emph{Euclidean and Non-Euclidean Geometries \cite{greenberg}
	\/}, Fourth Edition, Marvin Jay Greenberg, W.H.\ Freeman and
	Company, 2008.

	\href{http://www.gutenberg.org/etext/21076}{ The First Six
	Books of the Elements of Euclid}, John Casey (and Euclid),
	Project Gutenberg Online Book Catalog. \cite{euclid}
			
%			\item \emph{Proofs and Refutations}, Imre Lakatos,
%			Cambridge University Press, 1988.

  \subsection*{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 300A & Thompson 374 & M,T,Th,F & 10:00 - 10:50  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}

I am also available at other times. If you have trouble meeting
during office hours please make an appointment for a better
time.


% Day to Day Logistics

\textbf{Day to Day Structure} The class days will typically be
	devoted to interactive lectures on material in our textbooks.
	Expect at least one ``Brainstorming'' day for each homework 
	assignment and occasional days working at the blackboard. 

%  information examination 
\textbf{EXAMINATIONS} There will be three, 100 point, one hour,
	in-class examinations. Make-up examinations are at my
	discretion and their existence has the necessary (but not
	sufficient) condition that you make arrangements prior to the
	exam. Sufficient interest from the class can change examination
	dates or move the exams to a 2-hour, evening format.
    Examinations will typically consist of two questions from
	the homework and three questions you have not seen before. When
	taking the examinations you will be allowed to use your copy
	of my handout of definitions and theorems as a personalized
	resource. The examinations are tentatively scheduled for the
	following days:

   	  \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. 
 
\textbf{FINAL EXAMINATION: Friday May 15, 8:00 A.M.} The
	Final will actually be a fourth examination on the material
	covered since the third in-class examination.

%  information homework 
\subsection*{HOMEWORK} There will be homework assignments every
	week and problems will be graded using the
	\hyperlink{rubric}{rubric} attached at the end of these notes.
	Think of these take-home assignments as weekly papers in which
	you first analyze and solve a problem and then completely
	explain that analysis and solution.  At the very least you
	should type your papers using complete sentences, in the first
	person plural, with accurate punctuation, for an audience
	consisting of students not in this class but with an
	equivalent background, and in a clear, easy to follow
	expository style.


You are not to work with anyone when doing these assignments. However, 
\begin{itemize}
	\item you may use (with citation) any idea verbalized during a
	``brainstorming'' session.
	\item you may use (with citation) any idea you obtain in
	discussion with me.
	\item you may collaborate with other students if I explicitly 
	allow you to do so. 

\end{itemize}

As long as you cite it, feel free to use (or not) any technology
  that you like (e.g., CABRI, Geometers Sketchpad, calculators,
  \emph{Mathematica}, MATLAB, etc.).

%%  Information Writing
%	\subsection*{Paper} There will be one paper assigned around midterm.
%
%	The primary goal of this course is for you to learn the
%	basics of `mathematical reasoning' or `mathematical ways of
%	knowing'. This is addressed in the course itself by giving
%	you extensive practice at the mathematical way of addressing
%	the related concepts of proof, communication, meaning, and
%	truth.
%%	as well as the methodology of mathematical research. 
%	To provide contrast with or context for this mathematical
%	methodology, your paper will examine how some other discipline
%	(your major, minor or some other field of interest) approaches
%	these same fundamental concepts.
%%	 or you will further develop some concept
%%	presented in Devlin's book. 
%	You can find examples of such papers at
%
%	\href{math.ups.edu/~bryans/Current/HTML/journalhome.html}{
%		The Journal of Undergraduate Mathematics at Puget Sound}
%		\cite{journal}
%	
%	These ideas are at the heart of much philosophical debate and 
%	have been the subject of many large books. But you will only 
%	have 2-4 weeks for your paper so keep your topic tightly focussed. 
%	Remember, the primary goal of the paper is for you to
%	\emph{begin} to explore such philosophical fundamentals as 
%	proof, communication, and truth. 
%
%   \subsection*{Paper Logistics} \ 
%		
%		\textbf{Due February 27:} Meet with me to discuss your list
%		of possible topics for your paper. 
%		
%		\textbf{Due March 10:} Last day to have a topic \textbf{accepted}. 
%						
%		\textbf{Due April 10:} Turn in 3 copies of a draft of the
%			 paper (please print on both sides to save paper). I
%			 will distribute 2 of those copies to your referees.
%			 (This means each of you will referee two papers.) The
%			 referees will comment (in written form) on the
%			 accuracy, clarity of exposition and appropriateness
%			 of these papers for the \emph{Journal of
%			 Undergraduate Mathematics at Puget Sound} as outlined
%			 in the \emph{Journal}
%			 \href{http://math.ups.edu/~bryans/Current/HTML/JournalGuidelines.html}	{
%			 Guidelines for Authors}. \cite{journal}
%			
%		\textbf{Due April 17} Referees give their reports to authors. 
%
%		\textbf{Due April 24:} Turn in the final version of the
%			paper in both paper and electronic (.PDF, .PS or .DOC) form along with all
%			referee comments.  If the paper receives a passing
%			grade, it will be published in the journal.
%
%		The author will receive a grade for the paper itself and the
%			referees will receive grades for the quality of their comments.  
%
%		Students who are majoring in mathematics or science
%		should not use a standard word processor for writing
%		their paper. Instead, they should use the \LaTeX{}
%		typesetting package.  For those who are interested, I
%		will be happy to give a brief workshop on how to install
%		and use this package.

  \subsection*{Course Information Updates} If you wish, I will post (and
  update throughout the semester) a grade report on your current
  class standing 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.
 
	To have your information posted you need to print your name,
	the class (Math 300), and a code on a sheet of paper. Then
	sign the paper and physically hand it to me. The code must be 
	a sequence of up to 23 symbols I can type on a keyboard.


	

  \subsection*{TOTAL POINTS}
   \begin{tabular}{|c|r|}		   		\hline
	Homework		&   	64\%		\\	\hline 
%	Paper			&   	10\%		\\	\hline
%	Referee Reports	&		 4\%     	\\	\hline
	Examinations	&   	27\% 		\\	\hline
	Final Examination	&    9\%	\\	\hline	\hline
%	TOTAL		&   750 - 800 		\\	\hline
		\end{tabular}
		
   \subsection*{First Assignment} \textbf{(Due Friday January 23)} Find my
   university web page 
   \begin{center}
	   (http://math.ups.edu/  $ \rightarrow $ faculty  $ \rightarrow $
	   Bryan Smith)  \\
	\end{center}       
	and look around the web page for this course. Then send an
	e-mail message to me at bryans@ups.edu. This homework
	assignment will not be complete unless you receive an email
	from me acknowledging your email message.

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

\bibitem{300}
Course Webpage for Math 300A                   \\
\href{http://math.ups.edu/~bryans/Current/Spring_2009/300Index_Spring2009.html}{
\url{http://math.ups.edu/~bryans/Current/Spring_2009/300Index_Spring2009.html}}

\bibitem{300syl}
Department Syllabus for Math 300    \\
\href{http://www.math.ups.edu/~matthews/Syllabi/MA_300_Syllabus.pdf}{
\url{http://www.math.ups.edu/~matthews/Syllabi/MA_300_Syllabus.pdf}}

\bibitem{greenberg}
``Euclidean and Non-Euclidean Geometries''
Fourth Edition, Marvin Jay Greenberg, W.H.\ Freeman
and Company, 2008.

\bibitem{euclid}
``The First Six Books of the Elements of Euclid'', 
John Casey (and Euclid), Project Gutenberg Online Book Catalog.
\url{http://www.gutenberg.org/etext/21076}
			
\bibitem{journal}
\emph{The Journal of Undergraduate Mathematics at Puget Sound} \\
\href{http://math.ups.edu/~bryans/Current/HTML/journalhome.html}{
\url{http://math.ups.edu/~bryans/Current/HTML/journalhome.html}} \\
\href{http://math.ups.edu/~bryans/Current/HTML/JournalGuidelines.html}{
\url{http://math.ups.edu/~bryans/Current/HTML/JournalGuidelines.html}}

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

\pagebreak

%\vspace{-288pt}
\hypertarget{rubric}{
\subsection*{Homework (Writing Assignments) \hfill Non-Euclidean Geometry}
}
\begin{tabular}{|c|c|}
\hline\hline
\textbf{Points} & \textbf{Logic and Mathematics} \\ \hline\hline
5 & \multicolumn{1}{|l|}{Arguments are correct, complete and without
extraneous or misleading material.} \\ \hline
4 & \multicolumn{1}{|l|}{Arguments have only one of: a few minor errors,
omissions or inappropriate material.} \\ \hline
2 & \multicolumn{1}{|l|}{Arguments have at least two of: minor errors,
omissions and inappropriate material.} \\ \hline
0 & \multicolumn{1}{|l|}{Arguments are more seriously flawed.} \\ \hline
& \\
& \\
\hline\hline
\textbf{Points} & \textbf{Use of Terminology and Notation} \\ \hline\hline
2 & \multicolumn{1}{|l|}{All technical terms, concepts and notation are used
correctly.} \\ \hline
1 & \multicolumn{1}{|l|}{There are minor problems with terminology and or
concepts.} \\ \hline
0 & \multicolumn{1}{|l|}{\ There are major problems with terminology or
concepts.} \\ \hline
& \\
& \\
\hline\hline
\textbf{Points} & \textbf{Written Presentation} \\ \hline\hline
3 & \multicolumn{1}{|l|}{Follows citation requirements and all other writing
guidelines.} \\ \hline
2 & \multicolumn{1}{|l|}{Follows almost all of the guidelines with only one
or two minor lapses.} \\ \hline
1 & \multicolumn{1}{|l|}{Has more than one or two minor lapses on following
the guidelines.} \\ \hline
0 & \multicolumn{1}{|l|}{Has a major lapse in followingthe guidelines. } \\ 
\hline
\end{tabular}

\subsection*{Writing Guidelines}
It is best to think of these writing projects as officially
assigned papers in which you completely explain and justify your
analyses of the problems. Unless I say otherwise, 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{itemize}
\item Fully documented -- specifically:

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

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

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

\item Written with a word processor. (I can show you how to
install \LaTeX{}, use Scientific Notebook (in the labs) or you can
use 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{itemize}
\end{document}
