Monday through Friday, July 9 to July 20, 2007

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

- We begin considering alternative methods of representing integers and rational numbers Games and Representations. These problems are due Tuesday morning, July 10. The solutions are here. Also, copy this list of Binary Cards and this Sieve for use on Tuesday or Wednesday.
- Wednesday We'll talk more number theory: Euclidean Algorithm and decanting. These Decanting Problems. The solutions are here are due Wednesday morning, July 11. This paper on modular arithmetic is included for your reading pleasure. The problems are not meant for homework.
- Due on Thursday, July 12 Place value Problems. The solutions are here. Also due on Thursday is the problem set on Safe/Unsafe classification, whose solutions are here.
- To be handed in on Friday, June 23 Nim Problems. The solutions are here. and Integer (and rational number) Representations and the solutions are here.

Then we study combinatorics for two days.

- And Just the Factors Ma'am. These problem solutions are due Monday, July 16. The solutions are here. Read Closed Form, Recursion, and Mind-reading; Defining Sequences by Various Means over the weekend. For a discussion of the problem we talked about in class dealing with counting the number of regions determined by chords joining n points of a circle, see this paper. You can work these problems for extra credit. Counting Problems are due Tuesday morning, July 17. The solutions are here. Also due on Tuesday is the problem set on Grundy Values, whose solutions are here.
- Proof by Mathematical Induction. Induction Problems. These are due Wednesday morning, July 18. The solutions are here. Furthermore, please do Inclusion/Exclusion Problems for Wednesday July 18 as well. The Solutions are here.

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:

- The Euclidean Algorithm, (thanks to Amy Webb for this reference)
- Doug Ensley's Games
- The second and third chapters of Joe Silverman’s Book A Friendly Introduction to Number Theory on Pythagorean Triples
- A great new site: Interactive Mathematics Miscellany and Puzzles
- The Math Forum (now at Drexel)
- Don Rideout’s Essay on Modular Arithmetic.
- COMAP
- Ken Rosen's Book
- Check out the site Mathematical Induction for lots of worked examples.

Nim and other Puzzles/Games

- This applet for playing Dynamic One Pile Nim is due to Drew Boyuka. Here's our unpublished paper The Secrets of Nim.
- This nice version of Nim comes from Robtex
- Try this one next: Coin Nim Game
- Here's a Base Converter from Math.com
- Timothy J. Rogers' Nim and other Games
- Kadon Enterprises Puzzles
- Cut the Knot's Nim website
- Cut the Knot's Whytoff's Game website
- Nim from Arkansas State University
- Erik Demaine's Combinatorial Games Page
- David Eppstein's Combinatorial Game Theory
- Nick Glover's base converter.