Outline | People | Reading | Grading | Academics | Homepage |
Course Outline* | ||||||
Lecture | Topic(s) | Notes | Book(s) | |||
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1. Aug 21 | What are discrete models: Fibonacci's rabbits | DMM §1 | ||||
2. Aug 26 | Graphs and digraphs: basic set theoretic definitions | DMM §2 | ||||
3. Aug 28 | (Di)Graphs continued: toric mesh, hypercube | Class notes | ||||
4. Sep 2 | Paths, reachability, connectedness | DMM §2.2 | ||||
5. Sep 4 | Vertex basis, strong components | DMM §2.3 | ||||
6. Sep 9 | Matrix representation, transitive closure | DMM §2.4 | ||||
7. Sep 11 | Strong components via transitive closure | |||||
8. Sep 16 | Return of homework 1; catch-up |
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9. Sep 18 | Review for first exam |
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10. Sep 23 | First Exam | Counts 17.5% | ||||
11. Sep 25 |
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. Sep 30 | Basic definition and examples of trees; rooting a tree |
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DMM §2.2, Ex 22
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13. Oct 2 | Expression trees, parenthesized strings |
Class notes;
biography of Lukasiewicz.
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14. Oct 7 | Depth-first-seach trees; strongly connected orientation in a graph |
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DMM§3.3
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Thurs-Fri, Oct 9-10 | Fall Break, no class | |||||
15. Oct 14 | Testing for cycles in a digraph by DFS |
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DMM §3.3
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16. Oct 16 | Expression grammars and parse trees |
Class notes
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Fri, Oct 17, 5pm | Last day to drop the course |
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17. Oct 21 |
Linearization of parse trees;
MathML and XML
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18. Oct 23 |
Lindenmeyer systems;
fractals
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Online notes
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TA §12
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19. Oct 28 |
Chromatic number; planarity
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History of 4 color theorem
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DMM §3.6
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20. Oct 30 |
More fractals
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Definition of Mandelbrot and Julia sets
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21. Nov 4 | Review for exam; catch-up |
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22. Nov 6 | Second exam | Counts 17.5% | ||||
23. Nov 11 | Return of exam; Boolean expressions |
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Wed, Nov 12 | Topic for term paper must be declared at 5pm | |||||
24. Nov 13 |
Boolean expressions and propositional calculus continued
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Class notes
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Mon, Nov 17 | Approvals of topics for term papers by me are posted | |||||
25. Nov 18 |
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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26. Nov 20 |
Arrows axioms, impossibility
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Arrow's autobio
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DMM §7.2
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27. Nov 25 |
Fair elections continued
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Wednesday-Friday, Nov 26-28 | Thanksgiving, no class | |||||
28. Dec 2 | Markov chains | DMM §5 | ||||
29. Dec 4 |
Markov chains continued;
presentations start: Ken, Jeffrey B, Jeffrey P
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Tue, Dec 16, 09h00-12h00 and 14h00-17h00, NEW HA 307. | 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:
©2008 Erich Kaltofen. Permission to use provided that copyright notice is not removed.