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\centerline{\bf Analysis II }
\centerline{Math 414, Spring Semester, 2006}
\centerline{12 noon, 219 Taft Hall}
\centerline{Call \#16476 (undergrad), \#19323 (grad)}
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\begin{itemize}
\item{Instructor:} Steve Hurder  \hfill \break
Office: 505 SEO; Phone (312) 413-2154 \hfill \break
DGS Office: 341 SEO; Phone (312) 996-5119 \hfill \break
Office Hours: 1-2  MWF, or by appointment \hfill \break  
Email:  hurder@uic.edu \hfill \break
Web: http://www.math.uic.edu/$\sim$ hurder

 
Grader: Raymond Mess, 632 SEO, rjmess@yahoo.com
 

MLC Coordinator: Marcy Robertson, mrober5@uic.edu

 

\bigskip
\item{Text:} {\it Understanding Analysis}   by Stephen Abbott, Springer-Verlag


\item{Description:} Calculus ``done right'' continues.    We will start with Chapter 3, and introduce ``Topology on $\mathbb R$'', which is more powerful way to do $\epsilon$--$\delta$ proofs.  Next, we present continuity and derivatives of functions using the ideas of topology. Some of this is review from Math 313, other parts are new because it will be presented using the ideas of Topology. Chapter 6 considers sequences of functions, not just sequences of points. (So, now a function is a point in the space of functions...) Chapter 7 presents 
the theory of the Riemann Integral. Math 313 covered   the basic ideas of the Riemann Integral; now we start to introduce the ideas of measure theory, sets of measure zero, and ways to extend the Riemannn integration   to limits of sequences of functions. Chapter 8 give three further topics which introduce more ideas of analysis. 

 

\item{Web:}   http://www.math.uic.edu/math414/ is the course web page and   has the homework assignments, problems, and supplemental material for the class. 
 

\item{Homework:} There will be frequent homework assignments. 

You may discuss homework problems with other students, but you must write up your solution independently. All proofs should be written neatly with complete grammatical sentences. 

There are three kinds of problems we will encounter: 

\begin{itemize}
\item Problems without a star    should be doable if you understand the material --   they are a good test of whether you follow the main ideas;
\item  Problems with one star  ``*'' are more difficult -- they are challenging, and worth putting the effort into. 
\item  Problems with two stars  ``**'' are most  difficult -- they require you think hard and maybe have some new insight into the subject, or maybe just get lucky.
\end{itemize}
 
 
\item{Grades:} There will be two Hour Exams   and a Final   for the class. Course grades will be based on your scores on these   exams, your performance on the homework, and participation in class. 

\end{itemize}

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