COMBINATORIAL MATHEMATICS MATH 145, course information

Meetings: MWF 14:10pm-15:00 pm, Room 115 HUTCHINSON

Instructor: Jesús A. De Loera. email: deloera@math.ucdavis.edu http://www.math.ucdavis.edu/d̃eloera/TEACHING/MATH145/courseinfo/115A.html Phone: (530)-754 70 29

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.

Text: I will follow “Discrete Mathematics, elementary and beyond” by L. Lovász, J. Pelikán, and K. Vesztergombi, Springer, but I will certainly add or supplement the text several times. In particular, I will add many 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.

1. Basic Combinatorial Tools (Subsets, permutations, partitions, Pigeonhole and Inclusion-Exclusion principles) Chapters 1,2

2. Binomial coefficients, Pascal’s triangle Fibonacci numbers. Chapters 3,4.

3. Graphs, Trees. Chapters 7,8.

4. Optimization problems, Matchings. Chapters 9,10

5. 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 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.

• Homework will be assigned and collected every week, 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.

• 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.

• 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.

HOMEWORK: It is already posted in the web site!