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Course Outline*  
Lecture  Topic(s)  Notes  Book(s)  

1. Aug 19  What are discrete models: Fibonacci's rabbits  DMM §1  
2. Aug 24  Graphs and digraphs: basic set theoretic definitions  DMM §2  
3. Aug 26  (Di)Graphs continued: toric mesh, hypercube  Class notes  
4. Aug 31  Paths, reachability, connectedness  DMM §2.2  
5. Sep 2  Vertex basis, strong components  DMM §2.3  
6. Sep 7  Matrix representation, transitive closure  DMM §2.4  
7. Sep 9  Return of homework 1; strong components via transitive closure  
8. Sep 14  Catchup 


9. Sep 16  Return of homework 2; review for first exam 



10. Sep 21  First Exam  Counts 17.5%  
11. Sep 23 
Return of first exam;
fair division and apportionment

Class notes (in pdf)

TA §3 and 4


12. Sep 28  Basic definition and examples of trees; rooting a tree 

DMM §2.2, Ex 22


Wed, Sep 29, 5pm  Last day to drop the course 

13. Sep 30  Expression trees, parenthesized strings 
Class notes;
biography of Lukasiewicz.



14. Oct 5  Depthfirstseach trees; strongly connected orientation in a graph 

DMM§3.3


ThursFri, Oct 78  Fall Break, no class  
15. Oct 12  Testing for cycles in a digraph by DFS 

DMM §3.3


16. Oct 14  Expression grammars and parse trees 
Class notes



17. Oct 19 
Linearization of parse trees;
MathML and XML




18. Oct 21 
Lindenmeyer systems;
fractals

Online notes

TA §12


19. Oct 26 
More fractals

Definition
of Mandelbrot and Julia sets



20. Oct 28 
Chromatic number; planarity

History of 4 color theorem

DMM §3.6


21. Nov 2  Review for exam; catchup 

22. Nov 4  Second exam  Counts 17.5%  
23. Nov 9  Return of exam; Boolean expressions 


24. Nov 11 
Boolean expressions and propositional calculus continued

Class notes



25. Nov 16 
Computing a kelement clique
in a graph is as hard as factoring
an integer

Class notes



Wed, Nov 17  Topic for term paper must be declared at 5pm  
26. Nov 18 
Arrows axioms, impossibility

Arrow's autobio

DMM §7.2


Mon, Nov 22  Approvals of topics for term papers by me are posted  
27. Nov 23 
Fair elections continued




ThursdayFriday, Nov 2526  Thanksgiving, no class  
28. Nov 30  Markov chains  DMM §5  
29. Dec 2  Presentations can begin  
Tue, Dec 14, 09h0012h00 and 14h0017h00 Harrelson 330.  Presentations continue  
Presentation titles

Online 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
There will be five to six homework assignments of approximately equal weight, two midsemester 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.
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 35 page summary (typed, single spaced). You will present the information to me in a 1015 minute talk. I will give more details on what I expect from the presentation and the writeup during class.Grade split up  
Accumulated homework grade  40% 
Term paper + presentation  20% 
First midsemester exam  17.5% 
Second midsemester exam  17.5% 
Class attendance  5% 
Course grade  100% 
If you need assistance in any way, please let me know (see also the University's policy).
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:
©2004 Erich Kaltofen. Permission to use provided that copyright notice is not removed.