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\begin{document}
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\2s
\section{Combinatorics I \& II}
\noindent {\bf Basic Enumeration} 
	\begin{itemize}
 	  \item Stirling numbers:  $1^{st}, 2^{nd},$ unsigned 
 	  \item Representations of Permutations 
	  \item Generating Functions 
	\end{itemize}  

\noindent {\bf Principle of Inclusion--Exclusion} 
	


\noindent {\bf Partially Ordered Sets}
	\begin{itemize}
	  \item Dilworth's p.o. on $\{ \mbox{antichains}\}$
   	  \item Dilworth's Thm
	  \item Sperner's Thm
	\end{itemize}

\noindent {\bf Lattices}
	\begin{itemize}
	  \item Distributive
	    \begin{itemize}
	      \item Fund Thm Finite Distrib Lattices
	    \end{itemize}
	  \item Geometric
	    \begin{itemize}
       	      \item Birkhoff Covering Property
	      \item Jordan--Dedekind Chain Condition
	    \end{itemize}
         \end{itemize}

\noindent {\bf Closures}
	\begin{itemize}
	  \item Convex, Linear, Graphic, Ideal
	
	\end{itemize}  

\noindent {\bf M\"{o}bius Functions}
        \begin{itemize}
	  \item incidence algebra $I(P)$, $\zeta$, $\mu$
	  \item M\"{o}bius Inversion
	  \item Weisner's Thm
	  \item Dowling--Wilson Thm
	\end{itemize}

\noindent {\bf Hypergraphs}
        \begin{itemize}
	  \item Fisher's \& Generalized Fisher's Inequality
          \item Nonuniform:  Modular RC--W Thm
	\end{itemize}
 
\noindent {\bf Extremal Problems for Finite Sets}
	\begin{itemize}
	  \item Intersecting Families
	  \item Erd\H{o}s--Ko--Rado Thm
	  \item Shadows
	    \begin{itemize}
	      \item Kruskal--Katona Thm
	        \begin{itemize}
		  \item Numbers in KK
	        \end{itemize}
	      \item Lex Order, Upper Shadow
	    \end{itemize}
	  \item Tur\'{a}n's Thm
	    \begin{itemize}
	      \item Tur\'{a}n--type Problem
	    \end{itemize}
	\end{itemize}

\noindent {\bf Correlation Inequalities}
	\begin{itemize}
	  \item Positively Correlated, Percolation
	  \item Harris/Kleitman Thm
	  \item Chebyschev's Inequality
	  \item FKG Inequality
	  \item Ahlswede--Daykin ``Four Fcns Thm''
		\begin{itemize}
		\item Applications to Posets
		\end{itemize}
	\end{itemize}

\noindent {\bf Ramsey Theory}
	\begin{itemize}
	  \item Ramsey on Graphs
	    \begin{itemize}
	      \item Existence
	      \item Erd\H{o}s Bound 
	            $R(k,k) > \frac{k 2^{k/2}}{e \sqrt{2}}$
	    \end{itemize}
	  \item General Ramsey (on Hypergraphs)
	  \item Infinite Ramsey
        \end{itemize}
\section{Graph Theory}

\noindent {\bf Minimum Weight Spanning Tree}

\noindent {\bf Matching Theory}
	\begin{itemize}
	  \item Bipartite
	    \begin{itemize}
	      \item K\"{o}nig's Thm
	      \item Hungarian Method
	      \item Hall's Thm
	      \item SDRs
	      \item Latin Rectangles
		\begin{itemize}
		  \item Gale--Ryser Thm
		\end{itemize}	
	    \end{itemize}
          \item Baranyai's Theorem
	  \item Tutte's 1--factor Thm
	  \item Berge's Thm
	\end{itemize}

\noindent {\bf Max Flow Min Cut Theorem}

\noindent {\bf Menger's Thm}
	
\noindent {\bf Connectivity}

\noindent {\bf Vertex Colorings}
	\begin{itemize}
	  \item Brook's Thm		
	\end{itemize}

\noindent {\bf Edge Colorings}
	\begin{itemize}
	  \item Vizing's Thm
	\end{itemize}

\noindent {\bf Planar Graphs}
	\begin{itemize}
	  \item Euler's Formula
	    \begin{itemize}
	      \item 5--color Thm (Bondy--Murty Proof)
	    \end{itemize}
	  \item Kuratowski's Theorem
	\end{itemize}

\noindent {\bf Matroids}
	\begin{itemize}
	  \item Independence, Circuit, Rank, Base and Closure Axioms
	  \item Linear, Graphic, Cographic
	  \item Union of Matroids
	  \item Duality
	    \begin{itemize}
	      \item Abstract Duals
	      \item Whitney's ``Abstract Dual $\iff$
	            Planar'' Thm
	    \end{itemize}
	  \item Edmond's Intersection
                Thm
	  \item Matroid Union Thm
	\end{itemize}

\noindent {\bf Extremal Graph Theory}
	\begin{itemize}
	  \item[*] Tur\'{a}n $\ldots$ (Comb)
	  \item Erd\H{o}s--Stone Thm
	  \item Szemeredi's Regularity Lemma
	\end{itemize}

\section{Probabilistic Methods}

\noindent {\bf Chapters 1--6 and 8 in Alon--Spencer--Erd\H{o}s}


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