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MA 351 Fall '12 Syllabus

Course Outline*

Lecture Topic(s) Notes Book(s)
1. Aug 16 What are discrete models: Fibonacci's rabbits
DMM §1
2. Aug 21 Graphs and digraphs: basic set theoretic definitions
DMM §2
3. Aug 23 (Di)Graphs continued: toric mesh, hypercube Class notes
4. Aug 28 Paths, reachability, connectedness
DMM §2.2
5. Aug 30 Vertex basis, strong components
DMM §2.3
6. Sep 4 Matrix representation, transitive closure
DMM §2.4
7. Sep 6 Strong components via transitive closure

8. Sep 11 Basic definition and examples of trees; rooting a tree
DMM §2.2, Ex 22
9. Sep 13 Return of homework 1; catch-up

10. Sep 18 Review for first exam

11. Sep 20 First Exam Counts 17.5%
12. Sep 25 Return of exam; fair division and apportionment
Class notes (in pdf)
TA §3 and 4
13. Sep 27 Expression trees, parenthesized strings Class notes; biography of Lukasiewicz.

14. Oct 2 Depth-first-seach trees; strongly connected orientation in a graph
DMM§3.3
Thurs-Fri, Oct 4-5 Fall Break, no class
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, Oct 15, 11:59pm Last day to drop the course
17. Oct 16 Lindenmeyer systems; fractals
Online notes
TA §12
18. Oct 18 More fractals; review for exam
Definition of Mandelbrot and Julia sets

19. Oct 23 Chromatic number; planarity (B. Boyer)
History of 4 color theorem
DMM §3.6
20. Oct 25 Arrows axioms, impossibility (B. Boyer)
Arrow's autobio
DMM §7.2
21. Oct 30 Second exam
Counts 17.5%

22. Nov 1 Fair elections continued (B. Boyer)


23. Nov 6 No class


Wed, Nov 7 Topic for term paper must be declared at 5pm
24. Nov 8 Linearization of parse trees; MathML and XML


Mon, Nov 12 Approvals of topics for term papers by me are posted
25. Nov 13 Return of exam; Boolean expressions

26. Nov 15 Boolean expressions and propositional calculus continued
Class notes

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

Wednesday-Friday, Nov 21-23 Thanksgiving, no class
28. Nov 27 Markov chains
DMM §5
29. Nov 29 Markov chains continued;
presentations start: Clare, Nicole


Thur, Dec 6, 10h00-12h00 and 14h00-16h00, NEW SAS 4201. Presentations continue
Presentation titles
10h00-10h15: Ty,
10h15-10h30: Sam,
10h30-10h45: Kevin,
10h45-11h00: Dakota,
 11h00-11h15: Margaret,
11h15-11h30: Lauren,
11h30-11h45: Erin,
11h45-12h00: Joshua,
 14h00-14h15: J Trey F,
14h15-14h30: Elise,
14h30-14h45: William J,
14h45-15h00: ,
 15h00-15h15: James W W,
15h15-15h30: ,
15h30-15h45: Skyler,
15h45-16h00: Glen C.
Tue. Dec 11, 10h00-12h00 and 14h00-16h00, NEW SAS 4201. Presentations continue
10h00-10h15: Corey,
10h15-10h30: David McA,
10h30-10h45: Anastasia,
10h45-11h00: Jasmine,
 11h00-11h15: Emily,
11h15-11h30: Neil,
11h30-11h45: Jarrett,
11h45-12h00: Caroline N,
 14h00-14h15: Andrew S,
14h15-14h30: Kelsie,
14h30-14h45: William Br,
14h45-15h00: Frisco,
 15h00-15h15: Hayden,
15h15-15h30: Matthew G,
15h30-15h45: ,
15h45-16h00: .
* 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

We will use 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 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. 3, 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.

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.

If you need assistance in any way, please let me know (see also the University's policy).

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.

©2012 Erich Kaltofen. Permission to use provided that copyright notice is not removed.