MA-351 Introduction to Discrete Mathematical Models Fall 2016 SAS Hall 2102, Tue&Thu 10h15-11h30

Current Announcements

• NEW The course grades have been submitted to Registration and Records (Wed, Dec 14, 6:26pm). Here is a sorted anonymous list. 21 of 31 students earned 5/100 points for being absent fewer than 3 times. Have a Happy Holidays!
• The homework combined and homework 5 grades: sorted anonymous list. The 11 points of Homework 5 constitute 10.4% of the total homework grade, that is, 4.2% of the course grade.
• Average number of rounds to arrive in "D" state in Russian roulette Markov chain starting at "A" state (Maple):
sum(i*(5/6)^(i-1)*1/6,i=1..infinity) = 6.
• Instant-runoff is a non-monotonic voting system. The following example is from the Internet: The rankings of 4 candidates A,B,C,D is with the number of people choosing the rankings is:
```        7  6  5  3
first   A  B  C  D
second  B  A  B  C
third   C  C  A  B
last    D  D  D  A
```

D has the least first place votes and is eliminated. The instant-runoff is

```        7  6  5  3
first   A  B  C  C
second  B  A  B  B
third   C  C  A  A
```
B is eliminated next, and A with 13 first place votes wins.

Now suppose that the 3 voters find out that A will win (``everyone likes a winner'') and change their vote for A from LAST to FIRST place:

```        7  6  5  3
first   A  B  C  A
second  B  A  B  D
third   C  C  A  C
laste   D  D  D  B
```
D is eliminated first with 0 first place votes, then C, so we have
```        7  6  5  3
first   A  B  B  A
second  B  A  A  B
```
and B wins!
• The course web sites for Fall 2013, Fall 2012, Fall 2011, Fall 2010, Fall 2009, Fall 2008, Fall 2007, Fall 2006, Fall 2004, Fall 2003, Fall 2002, Fall 2001, and Fall 1999 contain old homeworks, mid-semester exams, and anonymous grade lists.
•  This semester's first and second midterm examinations (for dates see syllabus) Homework 1, due Thursday, Sep. 8 at 4:59pm, in my mailbox in SAS 3151. Homework 2, due Tuesday, Oct. 11 at 4:59pm, in my mailbox in SAS 3151. Homework 3, due Tuesday Nov 1 at 4:59pm, in my mailbox in SAS 3151. Homework 4, due Thursday Nov. 17 at 4:59pm, in my mailbox in SAS 3151. Homework 5, due Thursday, Dec 1 at 4:59pm, in my mailbox in SAS 3151. Web resources for the course Maple basic lesson from MA 141 W3C's XML index page. W3C's MathML 2.0 specification W3C's MathML 1.01 specification L-system tutorial Fractal microscope (Java applets)

Old Announcements

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