Math 6105 -Discrete Mathematics

Monday through Friday, July 9 to July 20, 2007

Instructor: Dr. Harold Reiter,


Please complete this Form. There is no text for the course. Roughly speaking, we'll spend four days on Number Theory, two days on Combinatorics, two days on relations and graphs, and two days hearing students present solutions. Please note that there is considerably more material here than anyone starting from scratch could possibly learn. However, if this is your first encounter with discrete math, you are not expected to learn the whole course. Just do the best you can including an hour or two EVERY night while the course is meeting. The CMS sponsored students will receive a copy of Solving Mathematical Problems: A Personal Perspective (Paperback) by Terence Tao, Mathew Crawford's Introduction to Number Theory, and Richard Trudeau's Introduction to Graph Theory the first day of class. The class will meet from 8:30 am to 3:30 pm daily in Cone Center Room 113 with a 15 minute morning break and a 45 minute lunch break. The room is located on a lower level of the Cone Center near the outside walkway. The assistant for the course is Drew Boyuka,

We start the by course with four days of Number Theory and combinatorial games.

Then we study combinatorics for two days.

And we finish with a day or two of graph theory and relations.

  • I hope to discuss one-to-one correspondence and sizes of infinity on Wednesday. Problems to be determined.
  • If you want to read ahead, here is a paper discussing Relations and Digraphs. and here is the homework for Thursday, July 19. The Homework, and the Solutions
  • More on graphs and digraphs. Binary Relations. Equivalence relations, partially ordered sets, Hasse diagrams. Problems to be posted. These exercises are due Thursday morning, July, 19.
  • Copy this Practice Test and work these problems to prepare for the final exam. We talk about Instant Insanity, Utilities problem, Eulerian paths, Hamiltonian paths and the Practice Test Thursday afternoon. Turn in the practice test Friday morning, July 20. We'll work these problems Friday morning before taking the final exam Friday afternoon.

Here's the 2004 Final Exam, with answers. We'll work some of these problems Friday morning.
Here's the 2005 Final Exam, and the 2005 Final Exam, with answers.
Here's the 2006 Final Exam, and the 2006 Final Exam, with solutions.
Here's the 2007 Final Exam, and the 2007 Final Exam, with solutions.

Here's a great list of references arranged chapter by chapter References. Anders Kaseorg devised the list and Drew Boyuka revised it. Thanks, Drew! Here's a reference on several discrete math topics provided by Bill Carey, a student in the workshop: Larry Bowen's Contemporary Mathematics.

The following is a pointer to the lectures notes and homework exercises for the Discrete course I teach at UNCC. It is especially appropriate for very strong students with an interest in mathematics and computing:
Lecture notes and homework sets for the course

Other websites of interest:

Nim and other Puzzles/Games