Outline People Reading Grading Academics Homepage

MA 351 Fall '13 Syllabus

Course Outline*

Lecture Topic(s) Notes Book(s)
1. Aug 22 What are discrete models: Fibonacci's rabbits
DMM §1
2. Aug 27 Graphs and digraphs: basic set theoretic definitions
DMM §2
3. Aug 29 (Di)Graphs continued: toric mesh, hypercube Class notes
4. Sep 3 Paths, reachability, connectedness
DMM §2.2
5. Sep 5 Vertex basis, strong components
DMM §2.3
6. Sep 10 Matrix representation, transitive closure
DMM §2.4
7. Sep 12 Strong components via transitive closure

8. Sep 17 Basic definition and examples of trees; rooting a tree
DMM §2.2, Ex 22
9. Sep 19 Return of homework 1; catch-up

10. Sep 24 Review for first exam

11. Sep 26 First Exam Counts 17.5%
12. Oct 1 Return of exam; fair division and apportionment
Class notes (in pdf)
TA §3 and 4
13. Sep 3 Expression trees, parenthesized strings Class notes; biography of Lukasiewicz.

14. Oct 8 Depth-first-search trees; strongly connected orientation in a graph
DMM§3.3
Thurs-Fri, Oct 10-11 Fall Break, no class
15. Oct 15 Testing for cycles in a digraph by DFS
DMM §3.3
16. Oct 17 Expression grammars and parse trees Class notes

Fri, Oct 18, 11:59pm Last day to drop the course
17. Oct 22 Lindenmeyer systems; fractals
Online notes
TA §12
18. Oct 24 More fractals
Definition of Mandelbrot and Julia sets

19. Oct 29 Linearization of parse trees; MathML and XML; review for exam


20. Oct 31 Second exam
Counts 17.5% Arrow's autobio

21. Nov 5 Return of exam; Boolean expressions

22. Nov 7 Boolean expressions and propositional calculus continued
Class notes

Thur, Nov 7 Topic for term paper must be declared at 5pm
23. Nov 12 Chromatic number; planarity (B. Boyer)
History of 4 color theorem
DMM §3.6
24. Nov 14 Planarity continued (B. Boyer)


25. Nov 19 Arrows axioms, impossibility (B. Boyer)
Arrow's autobio
DMM §7.2
26. Nov 21 Fair elections continued (B. Boyer)


27. Nov 26 No class


Wednesday-Friday, Nov 27-29 Thanksgiving, no class
28. Dec 3 Markov chains
DMM §5
29. Dec 5 Markov chains continued;
presentations start: Marschall, U. Daniel Choi


Tue, Dec 10, 10h00-12h00 and 14h00-16h00, SAS 4201. Presentations continue
Presentation titles
10h00-10h15: Justin S.,
10h15-10h30: Sarah,
10h30-10h45: D. Rochelle,
10h45-11h00: Joey H.,
 11h00-11h15: Joshua B.,
11h15-11h30: Casey B.,
11h30-11h45: Carmina,
11h45-12h00: Shelby J.,
 14h00-14h15: Justin T.,
14h15-14h30: Joseph W.,
14h30-14h45: Michelle,
14h45-15h00: James B.,
 15h00-15h15: Stephen W.,
15h15-15h30: Matthew F.,
15h30-15h45: Brittany,
15h45-16h00: Robert L..
Thur. Dec 12, 10h00-12h00 and 14h00-16h00, SAS 4201. Presentations continue
10h00-10h15: Cailee St.,
10h15-10h30: Rachel. McCl.,
10h30-10h45: Marianne L.,
10h45-11h00: Chris G.,
 11h00-11h15: Joanna,
11h15-11h30: Jordan C.,
11h30-11h45: Tyeshaun G.,
11h45-12h00: Christopher T.,
 14h00-14h15: Cory Sch.,
14h15-14h30: Sean,
14h30-14h45: Scott P.,
14h45-15h00: Daniel C.,
 15h00-15h15: Karthik,
15h15-15h30: Melissa,
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.

©2013 Erich Kaltofen. Permission to use provided that copyright notice is not removed.