\documentstyle[12pt,twoside]{article}
\input{macros-course}

\begin{document}
\handout{course-outline}{Course Outline}{September 8, 1994}


\newcounter{lecnum}
%	`` \begin{lecture}{topic}{handouts} ''
\newenvironment{lecture}[2]{\stepcounter{lecnum}
   	\parbox[t]{1in}{\sf 
	Lecture \thelecnum :\\
		\hspace*{.1in} 
		\parbox[t]{.9in}{\footnotesize \sf \raggedright 
			#1} \\
	\vskip .1in  #2  \vskip .1in} }{}
\newenvironment{tutorial}[1]{
	\parbox[t]{1in}{\vspace{.1in} \sf Tutorial.\\ #1}}{}
\newenvironment{noclass}[1]{
	\parbox[t]{1in}{\vspace{.1in} \sf #1}}{}

\newcommand{\lec}[2]{\begin{lecture}{#1}{#2} \end{lecture}}
\newcommand{\tut}[1]{\begin{tutorial}{#1} \end{tutorial}}
\newcommand{\dayoff}[1]{\begin{noclass}{#1} \end{noclass}}
%\newcommand{\week}{\begin{tabular}{|p{1in}|p{1in}|p{1in}|p{1in}|p{1in}|}\hline}
\newcommand{\week}{\begin{tabular}{|p{1in}|p{1in}|p{1in}|p{1in}|p{1in}|}\hline}
\newcommand{\eweek}{\\ \hline\end{tabular}}
\newcommand{\recitation}{\parbox[t]{1in}{\vspace{.1in} \sf Recitation.}}
\newcommand{\mo}[1]{\llap{#1 \hspace{7pt}}\vspace*{-14pt}}

\newcommand{\heightstrut}{\rule[-1in]{0in}{.75in}}

\bigskip
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEKS 1 1/2

%%	(can't use ``\week'' here because I only want 3 days, so no ``\hline'')
\begin{tabular}{p{1in}p{1in}|p{1in}|p{1in}|p{1in}|}
\cline{3-5}
	& &
7 	& 
8 	\lec{Proofs, divisibility, well-ordering principle, gcd.}{PSet 1 out.} & 
9 	\recitation \\
\cline{3-5}
\end{tabular}


\week

\mo{Sept}
12	\tutorial{PSet 1 due.} & 
13	\lec{Mathematical induction, unique factorization.}{PSet 2 out.} & 
14	&
15  	\lec{Structural induction, Euclid's alg., solving linear Diophantine equations.}{} & 
16 	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 2

\week

\mo{Sept}
19 	\dayoff{MIT HOLIDAY.\\No tutorials.} & 
20 	\lec{Logic, Peano's Postulates.}{No tutorials.\\PSet 2 due.\\PSet 3 out.} &
21   	&
22  	\lec{Equivalence of inductions, undirected graphs.}{} &
23	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 3

\week 

\mo{Sept}
26 	\tutorial{PSet 3 due.} &
27 	\lec{Directed graphs, relations, equivalence relations, posets.}{PSet 4 out.} & 
28    	&
29  	\lec{Functions and relations, composition, transitive closure, pigeonhole principle.}{} &
30  	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 4

\week

\mo{Oct}
3  	\tutorial{PSet 4 due.} &
4  	\lec{Functions, cardinality, countability.}{PSet 5 out.} & 
5    	&
6   	\lec{Growth of functions, asymptotics, analysis tools.}{} & 
7   	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 5

\week
\multicolumn{2}{|p{2.165in}|}{
\mo{Oct} 10 \makebox[1.9in]{11}
	\parbox[t]{2in}{\vspace*{.1in} \sf \hfil COLUMBUS DAY \hfil }} & 
12	&
13 	\lec{Series, analysis tools, Stirling's formula.}{} & 
14   	\recitation 

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 6

\week

\mo{Oct}
17  	\tutorial{PSet 5 due.} &
18   	\lec{Recurrences, substitution method.}{PSet 6 out.} & 
19   	\dayoff{Quiz 1,\\ \hspace*{.1in} 7--9 PM}  & 
20   	\lec{Linear recurrences, characteristic equation method.}{} & 
21   	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 7

\week

\mo{Oct}
24 	\tutorial{PSet 6 due.} & 
25  	\lec{Permutations, combinations, binomial coefficients.}{PSet 7 out.}& 
26     	&
27  	\lec{Permutations and combinations of multisets.}{} & 
28   	\recitation

\eweek


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 8

\week

\mo{Nov}
31	\tutorial{PSet 7 due.} &
1 

\lec{Binomial theorem, principle of inclusion/\\ exclusion}{PSet 8 out.} &
2 	&
3	\lec{Generating functions.}{} &
4	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 9

\week

\mo{Nov}
7	\tutorial{PSet 8 due.} &
8	\lec{Generating functions.}{PSet 9 out.} &
9	&
10	\lec{Introduction to probability, sample points and spaces}{} &
11	\dayoff{VETERANS DAY} 

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 10

\week

\mo{Nov}
14	\tutorial{PSet 9 due.} &
15	\lec{Probability laws, events, conditional probability.}{PSet 10 out.} &
16	&
17	\lec{Independence, birthday paradox, failure analysis.}{} &
18	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 11

\week

\mo{Nov}
21 	\tutorial{PSet 10 due.} &
22 	\lec{Random variables, indicator functions, common distributions.}{} &
23 	& 
\multicolumn{2}{|p{2.165in}|}{
24 \makebox[1.9in]{25}
	\parbox[t]{2in}{\vspace*{.1in} \sf \hfil THANKSGIVING \hfil }}

\eweek


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 12

\week

\mo{Nov}
28	\tutorial{} &
29	\lec{Functions of random vars, probability gen. fcns., central limit theorem, expectation.}{PSet 11 out.\\ Quiz 2,\\ \hspace*{.1in} 7--9 PM.} &
30	&
1	\lec{Linearity of expectation, laws of unlikely events.}{} &
2	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 13

\week

\mo{Dec}
5	\tutorial{PSet 11 due.} &
6	\lec{Markov's theorem, laws for expectation.}{} &
7	&
8	\lec{Variance, moments, Chebyshev's theorem.}{} &
9	\recitation

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%	WEEK 14

\week

\mo{Dec}
12	\tutorial{} &
13	\lec{Gambler's ruin.}{} & 
14	

\eweek

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\vfill

\begin{center}
\large
Lecture topics are subject to change.
\end{center}

\end{document}


\remove{	%% OLD WEEK 5
  \multicolumn{1}{|p{1in}}{\mo{Oct} 10} & 11 & 12  & 13 & 14 \\
  \multicolumn{2}{|c|}{\parbox[t]{2in}{\vspace*{.1in} 
			  \sf \hfil COLUMBUS DAY \hfil }} &
	  &
	  \lec{Series, analysis tools, Stirling's formula.}{} & 
	  \recitation 
}




