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MA 351 Fall '01 Syllabus

Course Outline*

Lecture Topic(s) Notes Book(s)
1. Aug 21 What are discrete models: Fibonacci's rabbits
DMM §1
2. Aug 23 Graphs and digraphs: basic set theoretic definitions
DMM §2
3. Aug 28 (Di)Graphs continued: toric mesh, hypercube Class notes
4. Aug 30 Paths, reachability, connectedness
DMM §2.2
5. Sep 4 Vertex basis, strong components
DMM §2.3
6. Sep 6 Matrix representation, transitive closure
DMM §2.4
7. Sep 11 Return of homework 1; strong components via transitive closure

8. Sep 13 Catch-up

9. Sep 18 Return of homework 2; review for first exam
DMM §7
10. Sep 20 First Exam Counts 17.5%
11. Sep 25 Return of first exam; basic definition and examples of trees; rooting a tree

DMM §2.2, Ex 22
12. Sep 27 Fair division and apportionment Class notes (in pdf)
TA §3 and 4
Mon, Oct 1, 5pm Last day to drop the course
13. Oct 2 Expression trees, parenthesized strings Class notes

14. Oct 4 Depth-first-seach trees; strongly connected orientation in a graph
DMM§3.3
15. Oct 9 Testing for cycles in a digraph by DFS
DMM §3.3
16. Oct 11 Expression grammars and parse trees Class notes

Mon-Tue, Oct 15-16 Fall Break, no class
17. Oct 18 Linearization of parse trees; MathML and XML


18. Oct 23 Lindenmeyer systems; fractals
Online notes
TA §12
19. Oct 25 More fractals
Definition of Mandelbrot and Julia sets

20. Oct 30 Chromatic number

DMM §3.6
21. Nov 1 Planarity

DMM §3.6
22. Nov 6 Review for exam

23. Nov 8 Second exam Counts 17.5%
24. Nov 13 Return of exam; catch-up

25. Nov 15 Boolean expressions and propositional calculus
Class notes

26. Nov 20 Computing a k-element clique in a graph is as hard as factoring an integer
Class notes

Tue, Nov 20 Topic for term paper must be declared at 5pm
Thursday-Friday, Nov 22-23 Thanksgiving, no class
Mon, Nov 26 Approvals of topics for term papers by me are posted
27. Nov 27 Arrows axioms, impossibility
Arrow's autobio
DMM §7.2
28. Nov 29 Fair elections continued


29. Dec 4 Markov chains
DMM §5
30. Dec 6 Markov chains continued; presentations begin: 10h45-11h05: Dennis Jen

Thu, Dec 13, 010h00-13h00 Harrelson 366 Presentations continue
Presentation titles
10h00-10h20: Brock,
10h20-10h40: Helen,
10h40-11h00: Brenda,
 11h00-11h20: Mark,
11h20-11h40: Nick,
11h40-12h00: Trang,
 12h00-12h20: Dmitriy,
12h20-12h40: Brian,
12h40-13h00: Carrie.
* This is a projected list and subject to amendment.

Instruction Personnel

For instructor, office hours, telephone numbers, email and physical address see the homepages of Erich Kaltofen.

Textbook and Online Notes

Professor Helminck ordered the book. I will cover topics that are not in the book. I will put another book on reserve in the Hill library: The syllabus above refers to chapters in these books. For topics in neither book, handouts will be provided.

On-line information: All information on courses that I teach (except individual grades) is now accessible via html browsers, which includes this syllabus. My web page listing all my courses' is at

You can also find information on courses that I have taught in the past, and examinations that I have given.

Grading and General Information

Grading will be done with plus/minus refinement.

There will be five to six homework assignments of approximately equal weight, two mid-semester examinations during the semester, and a term paper and a short presentation of it at the end of the sememster.

I will check who attends class, including the paper presentations by your class mates on Dec 6. You will forfeit 5% of your grade if you miss 3 or more classes without a valid justification. I you miss a class because you are sick, etc., please let me know. I may require you to document your reason. If you need assistance in any way, please let me know (see also the University's policy).

For a term paper, you are asked to select and read a mathematical paper or a chapter/section in a book, whose topic is in discrete mathematical models. You can select a section in DMM that was not covered in class. The term paper is a 3-5 page summary (typed, single spaced). You will present the information to me in a 10-15 minute talk. I will give more details on what I expect from the presentation and the write-up during class.

I have not taught this course before, so there is no history of grades and there are not previous exams available.

Academic Standards

Examinations:The two examinations will be closed book-closed notes. However, you will be able to bring note sheets of paper with pertinent information to the examinations (1 for first exam and 2 for second exam).

Collaboration on homeworks: I expect every student to be his/her own writer. Therefore the only thing you can discuss with anyone is how you might go about solving a particular problem. You may use freely information that you retrieve from public (electronic) libraries or texts, but you must properly reference your source.

Late submissions: All programs must be submitted on time. The following penalties are given for (unexcused) late submissions:

Alleged cheating incidents: I will not decide any penalty myself, but refer all such cases to the proper judiciary procedures.

©2001 Erich Kaltofen. Permission to use provided that copyright notice is not removed.