Math 160, Section D
Contemporary Mathematics
Fall 2007
MWF 1:30 pm, Cardwell 130

Monday, August 20: Introduction, Preference ballots and preference schedules, the plurality method

Wednesday, August 22:  The plurality method and Borda count method
READ sections 1.1-1.3 and bring in a 4x6 note card with the following:
- notes on the 3 sections
- answers to the following questions: What are the pros and cons of the plurality method?  Of the Borda method?
- a question that you have after doing the reading (something you don't understand, or something that you wonder about)

Friday, August 24: The plurality-with-eliminations method and the pairwise comparisons method
READ sections 1.4-1.5 and bring in a note card with the following:
- notes on the 2 sections
- answer to the following question: What are the pros and cons of these two methods?
- a question that you have

Monday, August 27: Ranking methods
READ section 1.6 and the chapter conclusion.
Question: What is the difference between an extended ranking system and a recursive ranking system?
(include notes and your own question as usual)

Wednesday, August 29: Wrapping up voting methods
Find an article (in a newspaper or magazine) that relates to the voting theory that we have been discussing in class.
Turn in a copy of this article, together with a note card containing:
- a summary of the article
- how it relates to the content from class
Homework 1 due by 5 pm in the mailboxes near the front doors of Cardwell.

Friday, August 31: Fair division problems
READ the introduction to chapter 3 and sections 3.1-3.2.
Question for the note card: Why it is better to be the chooser in the divider-chooser method for two players?
(include notes and your own question as usual)

Monday, September 3: NO CLASS - Labor Day Holiday

Wednesday, September 5: The lone divider method
Question: What is the main idea behind the lone divider method and why it works?
Homework 2 due by 5 pm in the mailboxes near the main doors of Cardwell.

Friday, September 7: The lone chooser method
Question: Which player or players have the advantage in the lone chooser method?

Monday, September 10: The last diminisher method
Question: Do you like this method better or worse than the two previous ones?  Why?

Wednesday, September 12: The method of sealed bids
Question: What are the advantages and disadvantages of the method of sealed bids?
Homework 3 due by 5 pm

Friday, September 14: The method of markers
Question: In what kind of situation does the method of markers work well?

Monday, September 17: Review
Bring in a note card with a question that you have on the exam material.
Review problems for the exam:

• pg. 30 #1, 3, 5, 7, 13, 15, 17, 19, 21,23*, 25*, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 55, 57*, 59*, 61*, 63*, 65*, 67*, 73*, 75*
• pg. 111 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 49, 51, 53, 55, 59, 61, 63, 65, 67, 69*, 75*

The problems with * are ones that are more challenging than what I would put on the exam, but are good tests of whether you've really got it.

Wednesday, September 19: EXAM 1 - Chapters 1 and 3
Homework 4 due by 5 pm

Friday, September 21: Euler circuits and graphs
READ the introduction to chapter 5 and sections 5.1-5.2
Question: Why might a graph be useful in solving a routing problem?

Monday, September 24: Graph terminology and graph models
Question: What is an example of a situation with a graph model that has NOT been mentioned in the text?
(Don't forget that your note cards should include notes and a question that you have, as well.)

Wednesday, September 26: Euler's theorems
Question: Why it is helpful to know the degrees of the vertices of a graph?
Homework 5 due by 5 pm

Friday, September 28: Fleury's algorithm
Question: Why are bridges so significant in finding an Euler path or Euler circuit?

Monday, October 1: NO CLASS

Wednesday, October 3: Eulerizing graphs
Question: What is the purpose of eulerizing a graph?
Homework 6 due by 5 pm.

Friday, October 5: Fibonacci numbers and the golden ratio
READ the introduction to chapter 9 and sections 9.1-9.2
Question: How are Fibonacci numbers and the golden ratio related?

Monday, October 8: Golden rectangles
READ the handout given in class.
Question: What is so special about golden rectangles?

Wednesday, October 10: Review
Bring in a note card with a question you have on the exam material.
Homework 7 due by 5 pm
Review questions:

• pg. 185: #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,25, 27, 29, 31, 33,35, 37, 39, 41, 43, 45, 47, 49, 51, 53*, 57*, 59*
• pg.329: #1, 3, 5, 7, 9*, 13* , 15*,  19*, 21*,  23, 25*, 27*, 29, 33*, 51, 53, 55*, 57

Friday, October 12: EXAM 2 - Chapters 5 and 9

Monday, October 15: Rigid motions and reflections
READ the introduction to Chapter 11 and sections 11.1-11.2
Question:  Draw an example of a reflection and of a rigid motion which is NOT a reflection.

Wednesday, October 17: Rotations and translations
Question: What are some real world examples of rotations and translations?

Friday, October 19: Glide reflections and symmetry
Question:  Find 3 pictures of objects with different kinds of symmetry.  What kinds of symmetry do they have?

Monday, October 22: Patterns
Question: Why do you need patterns to have symmetry given by translations and glide reflections?

Wednesday, October 24: Fractals and the Koch snowflake
READ section 12.1      **Don't worry about the reference to the geometric sum formula - we have not done this.**
Question: Explain in your own words what self-similarity is.
Homework 8 due by 5 pm

Friday, October 26: The Sierpinski gasket and the chaos game
READ sections 12.2-12.3, and observe the chaos game at the web page given at the end of 12.3.
Question: Explain how the chaos game works, and what happens if you play it thousands of times.

Monday, October 29: The twisted Sierpinski gasket
Question: What is the difference between the (ordinary) Sierpinski gasket and the twisted one?

Wednesday, October 31: The Mandelbrot set
How can you tell if the seed of a Mandelbrot sequence is in the Mandelbrot set?
Homework 9 due by 5 pm.

Friday, November 2: Review
Bring in a note card with a question you have on the exam material.
Project topics due - also bring in a note card with a short description of your topic.
Review questions:

• pg. 394: #1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53*, 55*, 57*, 59*, 65*, 67*
• pg. 434: #1, 3, 7, 9, 11, 13, 15*, 19, 21*, 25, 27, 29*, 31*, 33, 35, 37*, 39*, 41, 43, 45, 47, 49, 51, 53

Monday, November 5: EXAM 3 - Chapters 11-12

Wednesday, November 7: Population
READ the intro to chapter 13 and section 13.1
What the difference between the population and the N-value?
Homework 10 due by 5 pm

Friday, November 9: Sampling
What are some of the challenges in sampling?

Monday, November 12: Random sampling and terminology for sampling
How does random sampling work, and what are some problems that can still occur when using it?

Wednesday, November 14: The capture-recapture method and clinical studies
How do clinical studies differ from the surveys we have discussed so far?

Friday, November 16: Graphical descriptions of data and variables
READ the intro to chapter 14 and sections 14.1-14.2
What role to variables and graphical descriptions play in understanding data?

Monday, November 19: Numerical summaries of data
Question: What is the purpose of having numerical, rather than visual, representations of data?

TUESDAY, November 20: Homework 11 due by 5 pm
** Note the early due date, since there are no classes on Wednesday.

Monday, November 26: Measures of spread
Question: Why are these measures important?

Wednesday, November 28: Random experiments and sample spaces
READ the intro to chapter 15 and sections 15.1-15.2
Question: What is a sample space?
Homework 12 due

Friday, November 30: Permutations, combinations, and probability spaces
Question: What are permuations and combinations, and what do they have to do with probability?
**Projects due

Monday, December 3: Equiprobable spaces and odds
Question: What is the difference between odds and probability?

Wednesday, December 5: Review
Bring a note card with a question for review.
Homework 13 due

Friday, December 7: Review

Friday, December 14: Final exam
Review problems:

• pg. 467 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 67
• pg. 499 #1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51*, 53*, 55, 65*, 67, 69, 71*, 75*
• pg. 531 #1, 3, 5, 7, 9, 11. 13, 15, 17, 19, 21, 23, 25*, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67*, 69*, 71