Welcome to the online resource for Dr. Joe DeMaio's Math 3322: Discrete Modeling I and Math 4322: Discrete Modeling II.

The spring 2008 offering of Math 4322 will be a continuation of the topics of Math 3322 with a special focus on the mathematics of chessboard puzzles. Chessboard topics will consist of the existence of Hamiltonian cycles, minimum dominating sets and maximum independent sets. Along with traditional lecture and an in-class testing component, students will also conduct original research culminating in an end-of-term paper. Students will work in teams and each project will contain a programming component. The best results will be combined into a scholarly article(s) to be submitted for publication.

dm ii syllabus.pdf

Schedule
1-8-08: DM I Review Problems
1-10-08: DM I Review Problems
1-15-08: Induction Lecture, DM I Review Problems
1-17-08: Induction Problems, Intro to Chess Problems Lecture
1-22-08: Domination Lecture
1-24-08: Domination Lecture
1-29-08: Review
1-31-08: Test 1
2-5-08: Rook’s Domination, King’s Domination
2-7-08: Bishop’s Domination
2-12-08: Queen’s Domination
2-14-08: HW problems and group projects
2-19-08: chromatic_number.pdf HW: 1-4, 6-10
2-21-08: chromatic_polynomial.pdf HW: 1-4, 7, 8,11-15
2-26-08: Review for Test 2
2-28-08: Test 2
Spring Break
3-11-08: inc_exc.pdf HW: 1-10
3-13-08: derangements.pdf HW 1-9
3-18-08: Rook polynomials (from derangements handout): HW 10-16
3-20-08: Rook polynomials
3-25-08: pigeon.pdf HW 1-10
3-27-08: No class. Work on rough draft of project paper!
3-31-08: Electronic Rough Draft of Project paper due. Also each student (not each group)
should separately fill out and return to Dr. DeMaio in a sealed envelope, Group_Questionnaire.pdf.
4-1-08: stirling_numbers.pdf HW 1-9, 8, 13 (see file and it will make sense)
4-3-08: Stirling numbers (continued) HW 9-12, 14
4-8-08: Review Test 3
4-10-08: Test 3
4-15-08: Project Presentations Prep Day
4-17-08: Project Presentations: Closed Knight’s Tours on the Hypercube; Knight’s Domination within the 3-D cube.
4-22-08: Project Presentations: Free Bishop Problem; Total Domination by the King for Small Values of m and n;
4-24-08: Project Presentations and final Group_Questionnaire.pdf. due from each student: Domination and Total Domination with the Cross within the Cube; Domination and Total Domination with the Cross on the Cube; Monochromatic Tours with the 1-2-3 Knight.
5-1-08: Final Exam

Brief and not-so-brief web articles of some chessboard puzzles:

Chess Piece Moves
Knight's Tour (Wikipedia) and notes
The Knight’s Tour is a special case of the travelling salesman problem (Wikipedia)
A recent paper of mine on the Closed Knight’s Tour in the Cube at the Electronic Journal of Combinatorics
Eight Queens (Wikipedia)
Queens Independence and Domination Mathworld
n+k Queens Page
MAA article on Chess Puzzles with links
A well written thesis on the total domination problem of queens

The required books will be your Math 3322 text and Across the Board (hardback or paperback). You should buy a pad or two of graph paper. In an emergency you can download a pdf file of custom made graph paper here or here. You are required to use Scientific Notebook for word processing of papers and projects. Scientific Notebook is available on KSU computers for student use.

DMI review problems Students will post solutions to these problems on the board during the first week of class.
Induction introduction/review

Some initial domination problems to get you started Students will post solutions to these problems on the board during the first week of class.
A second round of domination problems
Some Combinatorial Chess Problems

Sample Tests from a previous section of Math 3322:

Word Pro - fall 2003 dm test 1.pdf
Word Pro - dm1 test 2 fall 2003.pdf
Word Pro - dm1 test 3 fall 2003.pdf
Word Pro - fall 2003 test 4.pdf
Word Pro - fall 2003 test 5.pdf