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\centerline{Mathematics 242 -- Principles of Analysis}
\centerline{Information on Exam 1}
\centerline{September 24, 2004}
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\noindent
{\it General Information}
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The first exam for the course will be given in class on
Friday, October 1.  This will 
be an individual, in-class, closed book exam.  I will be happy 
to hold a late afternoon or evening review session to help you 
prepare.  Wednesday, September 29 will probably be the best day for 
that.
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\noindent
{\it Topics to be Covered}
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The exam will cover the material we have covered since the start of the 
semester up to and including class on September 24.  This includes
material from sections 1-8 and 10-11 in the text.  Those sections
also contain some topics we did not discuss in class; you 
{\it will not be responsible for those}. 
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\item{1)}  Logical connectives, truth tables, quantifiers, 
converse, contrapositive, and inverse statements of implications and 
their uses in proofs.
\item{2)}  Sets, set operations and their properties
\item{3)}  Relations, especially equivalence relations
\item{4)}  Functions and their properties (especially injectivity,
surjectivity)
\item{5)}  What it means for sets to be equinumerous (or not)
\item{6)}  Mathematical induction
\item{7)}  The ordered field properties 
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\noindent
{\it What to Expect}
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The exam will have four or five questions, each possibly with several
parts.  Some questions will ask for a precise statement of a 
definition or a theorem we have discussed.  Be prepared to give
careful statements of 
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\item{1)}  All definitions for the first three definitions quizzes
(see the course homepage). 
\item{2)}  The Well Ordering Property (axiom) for the natural
numbers 
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\noindent
Also know the following proofs:
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\item{1)}  The set of all integers is denumerable
\item{2)}  The open interval $(0,1)$ in ${\bf R}$ is {\it not}
denumerable (the Cantor ``diagonal argument'')
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The other questions will be similar to questions from the problem sets
and discussions.  Some good review problems to look at are
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\item{} Section 1/5,8,10,12; 
\item{} Section 2/6, 11,12; 
\item{} Section 3/questions like 3,4,5,7,10 (directions should say ``repeat 9''); 
\item{} Section 4/6,8,9,13;
\item{} Section 5/4,6,7 (try working out your own proofs first, 
then check them against the partial proofs given in the problems), 15 (and 
then prove the given statements);
\item{} Section 6/5efgh, 11 
\item{} Section 7/15, 16, 17, 18; 
\item{} Section 8/3cd,10
\item{} Section 10/4,5,8,9
\item{} Section 11/3, 7
\bye
