Outline | People | Reading | Grading | Academics | Homepage |
Course Outline* | ||||||
Lecture | Topic(s) | Notes | Book(s) | |||
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1. Aug 23 | What are discrete models: Fibonacci's rabbits | DMM §1 | ||||
2. Aug 28 | Graphs and digraphs: basic set theoretic definitions | DMM §2 | ||||
3. Aug 30 | (Di)Graphs continued: toric mesh, hypercube | Class notes | ||||
4. Sep 4 | Paths, reachability, connectedness | DMM §2.2 | ||||
5. Sep 6 | Vertex basis, strong components | DMM §2.3 | ||||
6. Sep 11 | Matrix representation, transitive closure | DMM §2.4 | ||||
7. Sep 13 | Return of homework 1; strong components via transitive closure | |||||
8. Sep 18 | Catch-up |
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9. Sep 20 | Review for first exam |
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10. Sep 25 | First Exam | Counts 17.5% | ||||
11. Sep 27 |
Return of first exam;
fair division and apportionment
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Class notes (in pdf)
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TA §3 and 4
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12. Oct 2 | Basic definition and examples of trees; rooting a tree |
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DMM §2.2, Ex 22
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Wed, Oct 3, 5pm | Last day to drop the course |
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13. Oct 4 | Expression trees, parenthesized strings |
Class notes;
biography of Lukasiewicz.
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14. Oct 9 | Depth-first-seach trees; strongly connected orientation in a graph |
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DMM§3.3
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Thurs-Fri, Oct 11-12 | Fall Break, no class | |||||
15. Oct 16 | Testing for cycles in a digraph by DFS |
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DMM §3.3
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16. Oct 18 | Expression grammars and parse trees |
Class notes
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17. Oct 23 |
Linearization of parse trees;
MathML and XML
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18. Oct 25 |
Lindenmeyer systems;
fractals
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Online notes
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TA §12
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19. Oct 30 |
More fractals
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Definition
of Mandelbrot and Julia sets
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20. Nov 1 |
Chromatic number; planarity
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History of 4 color theorem
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DMM §3.6
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21. Nov 6 | Review for exam; catch-up |
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22. Nov 8 | Second exam | Counts 17.5% | ||||
23. Nov 13 | Return of exam; Boolean expressions |
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Wed, Nov 14 | Topic for term paper must be declared at 5pm | |||||
24. Nov 15 |
Boolean expressions and propositional calculus continued
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Class notes
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Mon, Nov 19 | Approvals of topics for term papers by me are posted | |||||
25. Nov 20 |
Computing a k-element clique
in a graph is as hard as factoring
an integer
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Class notes
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Wednesday-Friday, Nov 21-23 | Thanksgiving, no class | |||||
26. Nov 27 |
Arrows axioms, impossibility
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Arrow's autobio
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DMM §7.2
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27. Nov 29 |
Fair elections continued
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28. Dec 4 | Markov chains | DMM §5 | ||||
29. Dec 6 |
Markov chains continued;
presentations start
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Thu, Dec 13, 09h00-12h00 and 14h00-17h00, NEW HA 274. | Presentations continue | |||||
Presentation titles
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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
There will be five to six 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 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 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.Grade split up | |
Accumulated homework grade | 40% |
Term paper + presentation | 20% |
First mid-semester exam | 17.5% |
Second mid-semester 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:
©2007 Erich Kaltofen. Permission to use provided that copyright notice is not removed.