Outline | People | Reading | Grading | Academics | Homepage |
Course Outline* | |||||||
Lecture | Topic(s) | Notes | Book(s) | ||||
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1. Aug 18 | What are discrete models: Fibonacci's rabbits | DMM §1 | |||||
2. Aug 23 | Graphs and digraphs: basic set theoretic definitions | DMM §2 | |||||
3. Aug 25 | (Di)Graphs continued: toric mesh, hypercube | Class notes | |||||
4. Aug 30 | Paths, reachability, connectedness | DMM §2.2 | |||||
5. Sep 1 | Vertex basis, strong components | DMM §2.3 | |||||
6. Sep 6 | Matrix representation, transitive closure | DMM §2.4 | |||||
7. Sep 8 | Strong components via transitive closure | ||||||
8. Sep 13 | Basic definition and examples of trees; rooting a tree |
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DMM §2.2, Ex 22
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9. Sep 15 | Return of homework 1; catch-up |
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10. Sep 20 | Review for first exam |
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11. Thur, Sep 22 | First Exam | Counts 17.5% | |||||
12. Sep 27 |
Fair division and apportionment
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Class notes (in pdf)
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TA §3 and 4
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13. Sep 29 |
Chromatic number; planarity
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History of 4 color theorem
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DMM §3.6
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14. Oct 4 | Return of exam; expression trees, parenthesized strings |
Class notes;
biography of Lukasiewicz.
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Thurs-Fri, Oct 6-7 | Fall Break, no class | ||||||
15. Oct 11 | Depth-first-seach trees; strongly connected orientation in a graph |
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DMM§3.3
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16. Oct 13 | Testing for cycles in a digraph by DFS |
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DMM §3.3
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Fri, Oct 14, 11:59pm | Last day to drop the course |
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17. Oct 18 | Expression grammars and parse trees |
Class notes
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18. Oct 20 |
Linearization of parse trees;
MathML and XML
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19. Oct 25 |
Lindenmeyer systems;
fractals
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Online notes
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TA §12
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20. Oct 27 |
More fractals
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Definition
of Mandelbrot and Julia sets
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21. Nov 1 | Review for exam; catch-up |
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22. Thur, Nov 3 | Second exam | Counts 17.5% | |||||
23. Nov 8 | Return of exam; Boolean expressions |
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Wed, Nov 9 | Topic for term paper must be declared at 5pm | ||||||
24. Nov 10 |
Boolean expressions and propositional calculus continued
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Class notes
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Mon, Nov 14 | Approvals of topics for term papers by me are posted | ||||||
25. Nov 15 |
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 17 |
Arrows axioms, impossibility
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Arrow's autobio
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DMM §7.2
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27. Nov 22 |
Fair elections continued
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Wednesday-Friday, Nov 23-25 | Thanksgiving, no class | ||||||
28. Nov 29 | Markov chains | DMM §5 | |||||
29. Dec 1 |
Markov chains continued; Presentations start: Elliot P.-S., Grant S., 3 speaker slots available |
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Thur. Dec 8, 10h00-12h00 and 14h00-16h00, NEW SAS 2106. | Presentations continue | ||||||
Presentation titles
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Mon. Dec 12, 10h00-12h00 and 14h00-16h00, NEW SAS 2102. | Presentations continue | ||||||
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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 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. 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 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% |
Grade distribution of Fall 2013.
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 Erich Kaltofen. Permission to use provided that copyright notice is not removed.