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\begin{document}

%\twocolumn 
\section{Probability Theory}
%\section{M591: Probability Theory with D. Ocone}
Probability Spaces \\
\tab Algebras and $\sigma$-algebras of collections of sets (Review) \\
\tab Probability spaces \\
\tab Probability spaces; elementary examples, coin tossing \\
\tab The monotone class theorem \\
\tab Independence and product spaces \\
Random Variables, Distribution Functions, and Expectation \\
\tab Random variables and distribution functions \\
\tab Laws of random variables and distribution functions \\
\tab Expected values \\
\tab Independence of random variables \\
\tab Some basic probability laws \\
\tab Convergence concepts for random variables \\
%\tab Stochastic processes and Kolmogorov's consistency theorem \\
Large Number Laws for Sequences of Random Variables \\
\tab The weak law of large numbers \\
\tab The Borel-Cantelli lemma \\
\tab Strong large number laws \\
\tab Convergence of infinite series of independent random variables and 
applications \\
Convergence in Distribution and the Central Limit Theorem \\
\tab Motivation: the central limit problem \\
\tab Weak convergence and convergence in distribution \\
\tab Characteristic functions; uniqueness and smoothing \\
\tab The continuity theorem \\
%\tab Proof of Lindeberg's central limit theorem \\
Conditional Expectation \\
\tab Definition of conditional expectation \\
\tab Properties of conditional expectation \\
Martingale Theory in Discrete Time \\
\tab Definitions and examples \\
\tab Stochastic integrals in discrete time and a fundamental theorem of 
Martingale theory \\
\tab Optional stopping of Martingale \\
\tab Martingale inequalities \\
\tab Martingale convergence theorems
\newpage


%\end{document}


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%\2s
\section{Combinatorics I \& II}
\noindent {\bf Basic Enumeration} 
	\begin{itemize}
	  \item Basic Counting
 	  \item Recurrence Relations
	  \item Generating Functions 
	  \item Principle of Inclusion--Exclusion
	\end{itemize}  



\noindent {\bf Partially Ordered Sets, Lattices}
	\begin{itemize}
   	  \item Dilworth's Thm
	  \item Sperner's Thm
	  \item Geometric and Distributive Lattices
 	  \item M\"{o}bius Functions
         \end{itemize}


\noindent {\bf Hypergraphs}
        \begin{itemize}
	  \item Block Designs
          \item Fisher's Ineq. \& Related
	  \item Erd\H{o}s--Ko--Rado Thm
	  \item Kruskal--Katona
          \item Hamming Cube \& Isoperimetry
	  \item Tur\'{a}n's Thm \& Erd\H{o}s--Stone
	  \item Baranyai
	\end{itemize}
 






\noindent {\bf Ramsey Theory}
	\begin{itemize}
	  \item Infinite Ramsey
	  \item Finite Ramsey
	  \item Van der Waerden's Thm, Szemer\'{e}di's Thm
	\end{itemize}

\section{Graph Theory}


\noindent {\bf Matching Theory}
	\begin{itemize}
	  \item Hall/K\"{o}nig \& Applications
          \item Max Flow Min Cut
          \item Tutte's 1--factor Thm
        \end{itemize}



\noindent {\bf Connectivity}
 	\begin{itemize}
	  \item 2--connected graphs
	  \item Menger's Thm
	\end{itemize}

\noindent {\bf Graph Coloring}
	\begin{itemize}
	  \item Vertex Colorings
	  \item Edge Colorings
	 % \item List--Colorings
	\end{itemize}

	
\noindent {\bf Planar Graphs}

\noindent {\bf Matroids}


\section{Probabilistic Methods}

\noindent {\bf Lin. of Expectation \& ``Alterations''}

\noindent {\bf Second Moment Method}

\noindent {\bf Lov\'{a}sz Local Lemma}

\noindent {\bf Poisson Paradigm \& Janson Ineq.}

\noindent {\bf Correlation Inequalities}

\end{document}









 -=- MIME -=- 
  This message is in MIME format.  The first part should be readable text,
  while the remaining parts are likely unreadable without MIME-aware tools.
  Send mail to mime@docserver.cac.washington.edu for more info.

---559023410-1804928587-995486367=:28146
Content-Type: TEXT/PLAIN; charset=US-ASCII

Hi Professor Greenfield,

I have attached my syllabus for Combinatorics and Graph Theory (Major
Topic) along with my syllabus for Probability (Minor Topic). 
Feel free to identify my name with these syllabi.

--Eric

On Wed, 18 Jul 2001, Stephen J. Greenfield wrote:

> 
> I think this message is going to grad students who have passed their
> oral exams fairly recently. There is some mystery about these exams,
> among both students and faculty. Part of the mystery deals with the
> content of the syllabi for the exams. Perhaps posting a syllabus or
> two on the web would be useful. I'd like your help with this, if is
> possible and if you would like.
> 
> If you consent and if you have a TeX version of your syllabus, could
> you send me a copy of the syllabus and identify exactly what the
> topics were. If it is appropriate, perhaps you could also tell which
> of these topics was the major topic and which was the minor. I'd also
> like to identify on the web the student who submitted the document,
> unless that person would prefer to be anonymous.
> 
> If you don't have a TeX copy of this or if it would not be convenient
> to help at this time, please disregard this message. Thanks anyway. 
> 
> The message is going to a bunch of people, so probably you should be
> careful if you reply.
> 
> S. Greenfield
> 
> 


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