Outline | People | Reading | Grading | Academics | Homepage |
Course Outline* | |||||||
Lecture | Topic(s) | Notes | Book(s) | ||||
---|---|---|---|---|---|---|---|
1. Aug 17 | What are discrete models: Fibonacci's rabbits | DMM §1 | |||||
2. Aug 19 | Graphs and digraphs: basic set theoretic definitions | DMM §2 | |||||
3. Aug 24 | (Di)Graphs continued: toric mesh, hypercube | Class notes | |||||
4. Aug 26 | Paths, reachability, connectedness | DMM §2.2 | |||||
5. Aug 31 (held Sep 1, 10:15am) | Vertex basis, strong components | DMM §2.3 | |||||
6. Sep 2 | Matrix representation, transitive closure | DMM §2.4 | |||||
Mon, Sep 6 | Labor Day, no class | ||||||
7. Sep 7 | Strong components via transitive closure |
|
|
||||
8. Sep 9 | Basic definition and examples of trees; rooting a tree |
|
DMM §2.2, Ex 22
|
||||
9. Sep 14 | Catalan numbers; parenthesized strings |
wikipedia article on Catalan
|
|
||||
10. Sep 16 | Review for first exam |
|
|
||||
11. Tue, Sep 21 | First Exam | Counts 17.5% | |||||
12. Sep 23 | Expression trees; postfix notation |
Class notes;
biography of Lukasiewicz.
|
|
||||
13. Sep 28 | Return of first exam; fair division and apportionment |
Class notes (in pdf)
|
TA §3 and 4
|
||||
14. Sep 30 | Depth-first-seach trees; strongly connected orientation in a graph |
|
DMM§3.3
|
||||
Mon-Tue, Oct 4-5 | Fall Break, no class | ||||||
15. Oct 7 | Testing for cycles in a digraph by DFS |
|
DMM §3.3
|
||||
16. Oct 12 | Expression grammars and parse trees |
Class notes
|
|
||||
Wed, Oct 13, 11:59pm | Last day to drop the course |
||||||
17. Oct 14 |
Linearization of parse trees;
MathML and XML
|
|
|
||||
18. Oct 19 |
Lindenmeyer systems;
fractals
|
Online notes
|
TA §12
|
||||
19. Oct 21 |
More fractals
|
Definition
of Mandelbrot and Julia sets
|
|
||||
20. Oct 26 |
Chromatic number, planarity
|
|
DMM §3.6
|
||||
21. Oct 28 | Review for exam; catch-up |
||||||
22. Tue, Nov 2 | Second exam | Counts 17.5% | |||||
23. Nov 4 | Boolean expressions |
|
|||||
Fri, Nov 5 | Topic for term paper must be declared at 5pm | ||||||
24. Nov 9 |
Return of exam;
Boolean expressions and propositional calculus continued
|
Class notes
|
|
||||
Wed, Nov 10 | Approvals of topics for term papers by me are posted | ||||||
25. Nov 11 |
Computing a k-element 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 18 |
Fair elections continued
|
|
|
||||
28. Nov 23 | Markov chains | DMM §5 | |||||
Wednesday-Friday, Nov 24-26 🦃 | Thanksgiving, no class | ||||||
Mon Dec 6, 10h00-12h00 and 14h00-16h00, On zoom | Presentations | ||||||
Presentation titles
|
|||||||
Tue Dec 7, 10h00-12h00 and 14h00-16h00, On zoom | Presentations continue | ||||||
|
|||||||
Friday, December 10, 11:59am | Fall grades due |
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 with the last two of lesser 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 2019.
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: The following penalties are given for (unexcused) late submissions:
©2010, 2016, 2017, 2018 Erich Kaltofen. Permission to use provided that copyright notice is not removed.