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\centerline{\bf COMBINATORIAL MATHEMATICS}
\centerline{\bf MATH 145, course information}
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\noindent {\bf Meetings:} MWF 14:10pm-15:00 pm,  Room 115 HUTCHINSON
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\noindent {\bf Instructor:} Jes\'us A.  De Loera.

\noindent  email: deloera@math.ucdavis.edu

\noindent http://www.math.ucdavis.edu/$\tilde{ }$deloera/TEACHING/MATH145/courseinfo/115A.html


\noindent Phone: (530)-754 70 29
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\noindent {\bf Office hours}: Monday and Friday 3:00pm-4pm, Wednesday
9:00am-10am or by appointment.  My office is 3228 MSB. The TA for this
class is ???? , his office hours are ?????.  I will be glad to help
you with any questions, concerns or problems you may have.
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\noindent {\bf Text}: I will follow ``Discrete Mathematics,
elementary and beyond'' by L. Lov\'asz, J. Pelik\'an, and
K. Vesztergombi, Springer, but I will certainly add or supplement
the text several times. In particular, I will add many exercises.


\noindent {\bf Description}: This is an undergraduate-level
introduction to {\bf Combinatorics}, a truly beautiful part of
mathematics dealing with structure and properties of sets with
finitely many objects. We will discuss the basic methods to count
(binomials coefficients, permutations, etc) and basic properties of
graphs. Since this is a transition course to more advanced
mathematics, there will an emphasis on learning to write proofs and on
problem solving. When possible, I will try to make you aware of the
applied importance of the field. Combinatorial mathematics is
relevant in operations research, cryptography, and other tools in
modern information technology.
 
These are the exact topics to be covered in 145, about 2 weeks will
be spent on each of them.

\begin{enumerate}
\item Basic Combinatorial Tools (Subsets, permutations, partitions, Pigeonhole and
Inclusion-Exclusion principles) Chapters 1,2
\item Binomial coefficients, Pascal's triangle Fibonacci
numbers. Chapters 3,4.
\item Graphs, Trees. Chapters 7,8.
\item Optimization problems, Matchings. Chapters 9,10
\item Planar graphs, and coloring maps  Chapters 12, 13.
\end{enumerate}

\noindent {\bf Grading policy}: There are 100 points possible
in the course.

\begin{itemize}
\item There will be 2 midterms, first on April 25th 2006, the second
on June 5th 2006 each counting 35 points. I will drop the lowest
of the two for the calculation of the grade. Use of books, notes, and
calculators will not be allowed on any exam. The final exam is
comprehensive and will count 40 points.

\item Homework will be assigned and collected every week, {\bf
on Wednesdays}, for a total of 7 homeworks (about 10 problems in each
homework). Each homework is worth 5 points. Two of the problems will
be chosen for grading but you will receive one point if you wrote
solutions for all problems assigned. The remaining 4 points will be
awarded in the 2 problems being graded.  I will drop the two lowest
scores from the calculation of the final grade, this is for a maximum
of 25 points.


\item I will assign grades based on an statistical information of the
points obtained by all students (I compute the mean, standard
deviation, etc. and set letter grades according with those
numbers), but typically 60 points or higher are required to pass the class.


\item I will handle all grades via the myucdavis grade
system. This means that if you are registered students at UC Davis you
can access grade information for this class via the internet (check
https://my.ucdavis.edu/ for details). This is a secure and private
web page assigned to each student. You can see your standing in the
class, important statistics on exams, and your final grade there! I
will not disclose your grade in any other form.
\end{itemize}


\noindent {\bf Important rules:} 
\begin{itemize}

\item New homework exercises will be posted on my web page (see the
end of the page). I may write a few new problems after each class, so
please check the web page often.  Please remember {\bf there are NO
make-up exams or quizzes}, instead I am dropping the lowest score as a
compensation of possible problems or emergencies. Graded homeworks
will be distributed in the boxes in Wellman hall or in
recitation. {\bf Please check the course web page often!}


\end{itemize}

\noindent {\bf Prerequisites and Expectations}: MAT 21D or
equivalent are a pre-requisite. If in doubt, please ask me. You are
expected to work intensively outside the classroom solving exercises,
reading the book, thinking about the theorems, etc. I estimate a
minimum of 3 hours work at home per lecture. The most important thing
is what YOU learn. Mathematics is fun and pretty, try to get the
material in your soul! Rote memorization of facts is useless and you
are expected to think about the material everyday. It is easy to fall
behind, please be careful!  I am here to help you and I hope you enjoy
the course.

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\noindent{\bf HOMEWORK:} It is already posted in the web site!


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