Math
160, Section D

Contemporary Mathematics

Fall 2007

MWF 1:30 pm, Cardwell 130

Course syllabus

Homework assignments

Project topic ideas

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

- a question that it leads you to
ask

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

READ section 3.3.

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

READ section 3.4

Question: Which player or players have the advantage in the
lone chooser method?

Monday, September 10: The last diminisher method

READ section 3.5

Question: Do you like this method better or worse than the
two previous ones? Why?

Wednesday, September 12: The method of sealed bids

READ section 3.6

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

READ section 3.7

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

READ sections 5.3-5.4.

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

READ section 5.5

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

READ section 5.6

Question: Why are bridges so significant in finding an Euler
path or Euler circuit?

Monday, October 1: NO CLASS

Wednesday, October 3: Eulerizing graphs

READ section 5.7

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

READ sections 11.3-11.4

Question: What are some real world examples of rotations and
translations?

Friday, October 19: Glide reflections and symmetry

READ sections 11.5-11.6

Question: Find 3 pictures of objects with different
kinds of symmetry. What kinds of symmetry do they have?

Monday, October 22: Patterns

READ section 11.7

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

READ section 12.4.

Question: What is the difference between the (ordinary) Sierpinski gasket and the twisted one?

Wednesday, October 31: The Mandelbrot set

READ section 12.5

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

READ section 13.2

What are some of the challenges in sampling?

Monday, November 12: Random sampling and terminology for sampling

READ sections 13.3-13.4

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

READ sections 13.5-13.6

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

READ section 14.3

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

READ section 14.4

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

READ sections 15.3-15.4

Question: What are permuations and
combinations, and what do they have to do with probability?

**Projects due

Grading rubric to be used

Monday, December 3: Equiprobable spaces and odds

READ sections 15.5-15.6.

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

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Last
modified: 3 December 2007