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\begin{document}
\bigskip\begin{center}
{\large \bf Math 8174: Topics in Algebra I, Fall 2002}\\
{\bf Text:  The Structure of Finite Algebras\\
by Hobby \& McKenzie

\bigskip

\begin{tabular}{lll}
{\bf Section 1:} &MWF 4:00--4:50 &MATH 220
\end{tabular}}
\end{center}

\bigskip

\noindent
\begin{tabular}{lll}
{\bf Professor:}  Keith A. Kearnes&\hspace{.35in}&{\bf Email:} kearnes{\char64}euclid.colorado.edu\\
{\bf Office:}  Mathematics 233&&{\bf Phone:} 492--5203\\
{\bf Hours:}  \underline{\hphantom{MWF 10--11--12--1--2}} &&{\bf WWW:} http://spot.colorado.edu/\~{}kearnes\\
\end{tabular}

\bigskip

\noindent
{\bf Course Outline:}
During the last twenty years a localization theory 
for algebraic structures has been developed.
The viewpoint of the theory is that an algebraic
structure ${\bf A}$ can be treated as if it were
a manifold. Given a point $p\in A$, a ``neighborhood''
of $p$ is a subset $U\subseteq A$ definable
by a special type of formula. One can restrict
the structure of ${\bf A}$ to the neighborhood $U$
to obtain a ``local algebra'', ${\bf A}|_U$,
that approximates ${\bf A}$ on the set $U$.
(Examples: a Sylow subgroup of a finite
group is a neighborhood of that group,
the Jacobson radical of a finite 
ring is a neighborhood of that ring, and
an interval in a finite lattice is a neighborhood of that lattice.)

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\noindent
If a set of neighborhoods ${\mathcal U} = \{U_i\;|\;i\in I\}$
``covers'' ${\bf A}$ (in an algebraic sense), then
${\bf A}$ can be reconstructed from its localizations
$\{{\bf A}|_U\;|\;U\in {\mathcal U}\}$ using
a ``decomposition formula'' that 
explains how the localizations fit together.

Although this localization theory makes sense for infinite
algebras (and infinitary algebras), it is a deeper theory for finite
algebras because there is a classification of finite
minimal local algebras. Surprisingly,
there are only five types of minimal local algebraic
structures: $G$-sets, vector spaces, fields, lattices,
and semilattices. Therefore, to complete
a calculation in ${\bf A}$, one localizes to minimal
neighborhoods, uses the classification to complete the 
corresponding local
calculation, and then fits the results together to
get a global result. 
%(So, every finite algebra
%is constructible from these five types of algebras.)

\medskip

In this course we will develop the basic theory from Chapters 0--7
of the book by Hobby \& McKenzie, then we will apply the 
theory to the following question:
Which finitely generated varieties of algebras
have a structure theory?  (From chapters 8 \& 11 of Hobby--McKenzie.)

\bigskip

\noindent
{\bf Grades:}
This is a high--level graduate class that
will be run much like a seminar.
Students are be expected to try all of the 
exercises from the book.
Students will lecture over parts of the material.
Course grades will be determined by
participation.

\pagebreak

\noindent
{\bf Getting Help:}
Don't wait until it is too late if you need help. Ask questions!
I am available 
during the office hours listed above and also at many other times.  
If you can't see me during office hours,  then make an appointment 
with me to see me at a different time. I will also give short
answers to questions sent by email.

\vfill

\noindent
{\bf WWW:} 
Information concerning our class will be posted
on my web page under {\bf information for students}.
Copies of documents I hand out in class will be accessible
from this page. 

\vfill

\noindent
{\bf Classroom Behavior:} A new classroom behavior policy and associated new
procedures have been adopted by the university.  
Details can be found at \\
{\tt http://www.colorado.edu/policies/classbehavior.html}

\vfill

\noindent
{\bf Students with Disabilities:} 
Students with disabilities who qualify for academic accommodations
must provide a letter from Disability Services (DS) and discuss 
specific needs with me, preferably during the first two weeks of 
class.  DS determines accommodations based on documented 
disabilities (303-492-8671, Willard 322,
{\tt http://www.colorado.edu/sacs/disabilityservices}).

\vfill

\noindent
{\bf Observance of Religious Holidays:} 
If, because of religious obligations, a student has a conflict 
with scheduled exams, assignments, or other required attendance, 
the student should notify me at least two weeks in advance of 
the conflict to request special accommodation. 
I will provide the opportunity for a makeup exam 
or an equivalent assignment, or arrange for an increased 
flexibility in assignment due date.

\vfill

\noindent
{\bf Honor Code:} 
The new Student Honor Code system has now been implemented in all
schools and colleges. Details can be found at \\
{\tt http://www.colorado.edu/academics/honorcode/}, \\
{\tt http://www.colorado.edu/policies/honor.html}, and \\
{\tt  http://www.colorado.edu/policies/acadinteg.html}.\\
Sanctions for honor violations may include: a failing grade 
for a particular assignment; a failing grade for a particular 
course; and/or suspension for various lengths of time or 
permanent expulsion from the university.

The university administration has asked faculty to
provide very clear, explicit and detailed instructions about what constitutes plagiarism.
In this course we will adhere to the definition drafted by the CU Law School:
Plagiarism is the use of any written material which is submitted in a manner which 
purports or suggests that it is the work and effort of the person submitting it and 
that it was prepared by him or her as part or all of the task of completing the 
assignment, but which material is in substance the work of another or is material 
previously prepared by the student and which was previously submitted for, 
and which received, academic credit of any kind and the subsequent use of such 
material was not, in advance, specifically authorized by the faculty member for 
whom the work was being done.

\vfill\vfill
\end{document}
