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

1. Aug 17  What are discrete models: Fibonacci's rabbits  DMM §1  
2. Aug 22  Graphs and digraphs: basic set theoretic definitions  DMM §2  
3. Aug 24  (Di)Graphs continued: toric mesh, hypercube  Class notes  
4. Aug 29  Paths, reachability, connectedness  DMM §2.2  
5. Aug 31  Vertex basis, strong components  DMM §2.3  
6. Sep 5  Matrix representation, transitive closure  DMM §2.4  
7. Sep 7  Strong components via transitive closure  
8. Sep 12  Basic definition and examples of trees; rooting a tree 

DMM §2.2, Ex 22


9. Sep 14  Return of homework 1; Catalan numbers 
wikipedia article on Catalan



10. Sep 19  Review for first exam 



11. Thur, Sep 21  First Exam  Counts 17.5%  
12. Sep 26 
Return of first exam;
fair division and apportionment

Class notes (in pdf)

TA §3 and 4


13. Sep 28  Expression trees, parenthesized strings 
Class notes;
biography of Lukasiewicz.



14. Oct 3  Depthfirstseach trees; strongly connected orientation in a graph 

DMM§3.3


ThursFri, Oct 56  Fall Break, no class  
15. Oct 10  Testing for cycles in a digraph by DFS 

DMM §3.3


16. Oct 12  Expression grammars and parse trees 
Class notes



Fri, Oct 13, 11:59pm  Last day to drop the course 

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




18. Oct 19 
Lindenmeyer systems;
fractals

Online notes

TA §12


19. Oct 24 
More fractals

Definition
of Mandelbrot and Julia sets



20. Oct 26 
Chromatic number, planarity


DMM §3.6


21. Oct 31  Review for exam; catchup 

22. Thur, Nov 2  Second exam  Counts 17.5%  
23. Nov 7  Return of exam; Boolean expressions 


Wed, Nov 8  Topic for term paper must be declared at 5pm  
24. Nov 9 
Boolean expressions and propositional calculus continued

Class notes



Mon, Nov 13  Approvals of topics for term papers by me are posted  
25. Nov 14 
Computing a kelement clique
in a graph is as hard as factoring
an integer

Class notes



26. Nov 16 
Arrows axioms, impossibility

Arrow's autobio

DMM §7.2


27. Nov 21 
Fair elections continued




WednesdayFriday, Nov 2224  Thanksgiving, no class  
28. Nov 28  Markov chains  DMM §5  
29. Nov 30 
Markov chains continued; Presentations start: Rachel N., 2 speaker slots available 

Tues. Dec 5, 10h0012h00 and 14h0016h00, NEW SAS 4201.  Presentations continue  
Presentation titles


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


Sun. Dec 17, 11:59pm  Fall grades due 
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% 
Grade distribution of Fall 2016.
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:
©2010, 2016, 2017 Erich Kaltofen. Permission to use provided that copyright notice is not removed.