Outline | People | Reading | Grading | Academics | Homepage |
Course Outline* | ||||||||
Lecture | Topic(s) | Notes | Book(s) | |||||
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1. Aug 20 | What are discrete models: Fibonacci's rabbits | DMM §1 | ||||||
2. Aug 22 | Graphs and digraphs: basic set theoretic definitions | DMM §2 | ||||||
3. Aug 27 | (Di)Graphs continued: toric mesh, hypercube | Class notes | ||||||
4. Aug 29 | Paths, reachability, connectedness | DMM §2.2 | ||||||
5. Sep 3 | Vertex basis, strong components | DMM §2.3 | ||||||
6. Sep 5 | Matrix representation, transitive closure | DMM §2.4 | ||||||
7. Sep 10 | Return of homework 1; strong components via transitive closure | |||||||
8. Sep 12 | Catch-up |
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9. Sep 17 | Return of homework 2; review for first exam |
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10. Sep 19 | First Exam | Counts 17.5% | ||||||
11. Sep 24 |
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 26 | Basic definition and examples of trees; rooting a tree |
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DMM §2.2, Ex 22
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Mon, Sep 30, 5pm | Last day to drop the course |
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13. Oct 1 | Expression trees, parenthesized strings |
Class notes
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14. Oct 3 | Depth-first-seach trees; strongly connected orientation in a graph |
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DMM§3.3
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15. Oct 8 | Testing for cycles in a digraph by DFS |
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DMM §3.3
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16. Oct 10 | Expression grammars and parse trees |
Class notes
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Mon-Tue, Oct 14-15 | Fall Break, no class | |||||||
17. Oct 17 |
Linearization of parse trees;
MathML and XML
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18. Oct 22 |
Lindenmeyer systems;
fractals
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Online notes
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TA §12
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19. Oct 24 |
More fractals
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Definition
of Mandelbrot and Julia sets
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20. Oct 29 |
Chromatic number
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History of 4 color theorem
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DMM §3.6
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21. Oct 31 |
Planarity
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DMM §3.6
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22. Nov 5 | Review for exam |
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23. Nov 7 | Second exam | Counts 17.5% | ||||||
24. Nov 12 | Return of exam; catch-up |
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25. Nov 14 |
Boolean expressions and propositional calculus
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Class notes
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26. Nov 19 |
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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Wed, Nov 20 | Topic for term paper must be declared at 5pm | |||||||
27. Nov 21 |
Arrows axioms, impossibility
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Arrow's autobio
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DMM §7.2
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Mon, Nov 25 | Approvals of topics for term papers by me are posted | |||||||
28. Nov 26 |
Fair elections continued
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Thursday-Friday, Nov 28-29 | Thanksgiving, no class | |||||||
29. Dec 3 | Markov chains | DMM §5 | ||||||
30. Dec 5 | Markov chains continued; presentations begin | |||||||
Thu, Dec 12, 010h00-13h00 and 15h00-17h00, Harrelson 263. | 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. If you need assistance in any way, please let me know (see also the University's policy).
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% |
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:
©2002 Erich Kaltofen. Permission to use provided that copyright notice is not removed.