MATH 145, course information
Meetings: MWF 14:10pm-15:00 pm, Room 115 HUTCHINSON

Instructor: Jesús A. De Loera.

email and phone:, (530) 754 70 29.

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.

  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.

Important rules:

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