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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; catchup 


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  Depthfirstseach trees; strongly connected orientation in a graph 

DMM§3.3


ThursFri, Oct 45  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 kelement clique
in a graph is as hard as factoring
an integer

Class notes



WednesdayFriday, Nov 2123  Thanksgiving, no class  
28. Nov 27  Markov chains  DMM §5  
29. Nov 29 
Markov chains continued; presentations start: Clare, Nicole 

Thur, Dec 6, 10h0012h00 and 14h0016h00, NEW SAS 4201.  Presentations continue  
Presentation titles


Tue. Dec 11, 10h0012h00 and 14h0016h00, NEW SAS 4201.  Presentations continue  

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