**Instructor:** Jesús A. De Loera.

**email and phone: ** deloera@math.ucdavis.edu, (530) 754 70 29.

http://www.math.ucdavis.edu/~deloera/TEACHING/MATH145/courseinfo/145.html

**Office hours**: Monday 12pm-1pm Wednesday 9-10am or by appointment.
My office is 3228 MSB. The TA for this
class is Mr. Pierre Dueck , his office hours are Fridays 12:10 - 2:00
at MSB 3202. We will be glad to help you with any questions, concerns or
problems you may have, I hope you enjoy the course!

**Text**: I will follow ``Discrete Mathematics,
elementary and beyond'' by L. Lovász, J. Pelikán, and
K. Vesztergombi, published by Springer, but I will certainly add or supplement
the text several times. In particular, I will add exercises.

**Description**: This is an undergraduate-level
introduction to **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.

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

**Grading policy**: There are 100 points possible in the course.

- There will be 2 midterms, first on April 28th 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 35 points.
- Homework will be assigned and collected almost once a week,
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 (without checking).
The remaining 4 points will be awarded in the 2 problems being graded.
I will drop the lowest scores from the calculation of the final grade,
this is for a maximum of 30 points from homeworks.
- 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 my rule is
**At least 60 points are required to pass the class.** - 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.

**Important rules:**

- 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
**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.**Please check the course web page often!**

**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!

**HOMEWORKS:** It is already posted in the web site!

homework 1 due April 10, 2006

homework 2 due April 21, 2006

homework 3 due April 28, 2006

homework 4 due May 8, 2006

homework 5 due May 15, 2006

homework 6 due May 24, 2006

homework 7 due June 5 2006

Jesus De Loera 2006-03-22