Math 17, Section B

Click here to download the syllabus.

Extra help is available. See the below schedule.
Help Session Day Time Location
Math 1 - 22
MON 5:00 - 7:00 pm Perkins 200
Math 009 - 121
7:00 - 9:00 pm
Votey 254
Math 1 - 22 TUE   5:00 - 7:00 pm Kalkin 300
Math 1 - 22 WED*  5:00 - 7:00 pm Votey 254
Math 1 - 22 THU   5:00 - 7:00 pm Perkins 107
*I am at this help session.
Help Sessions are free. No appointment is necessary.
For best results, bring your textbook and some practice problems.

Course Schedule and Notes
Topics and Materials
January 17 From sections 1.1 and 1.2:
•Voters and Preference Ballots
•Elimination and Transitivity
•Preference Schedules
•The Plurality Method
•The Majority Criterion
•The Condorcet Criterion
•Head-to-head Comparisons

Here are the example ballots we used to create our preference schedule. Here is the lecture outline from today.
Ch 1 exercises:
#1-4, 11, 12
For #3, if candidate A were eliminated, who then would win according to the Plurality Method?

January 19
•Quiz on material from Jan 17

Material from section 1.3, 1.4:
•The Borda Count Method
•Plurality with Elimination Method
•The Monotonicity Criterion
Ch 1 Exercises
#17.a, 17.b, 19, 20, 23.a, 23.b, 27.a, 27.b, 29
Also, use the preference schedule in problem #33 to demonstrate that the Plurality-with-Elimination Method fails the Condorcet Criterion.
January 24
Material from section 1.5:
•The Method of Pairwise Comparisons
•The Independence of Irrelevant Alternatives Criterion
•How many pairwise comparisons are there between N candidates?

This grid shows which Voting Methods pass or fail which Fairness Criteria.

Material from section 2.1:
•Weighted Voting Systems
•Players, Wieghts, Quotas
Ch 1 Exercises
#27.c, 27.d, 30, 34, 35
Make sure you know the 4 methods and 4 criteria we have studied.

Ch 2
Read pages 44 and 45.
On Page 55 there is the story of using Weighted Voting mathematics to prove discrimination in Nassau County, NY.

Ch 2 Exercises
January 26
Quiz on Material from 1/19 and 1/24.

Material from sections 2.1 and 2.2
•Dictators, Veto Power, Dummies
•Coalitions: How many*, Winning, Losing
•Critial Players in a Coalition
•Computing the Banzhaff Power  

*I say there are 2n coalitions because I count the empty coalition. The book doesn't count the empty coalition, so it says there are 2n–1.
Ch 2 Exercises*
#7, 8, 11-18, 21, 22

Here is a real-word example of the Banzhaf Power Index used to prove that a voting system is discriminatory.

*Finding the Banzhaf Power Distribution means to find the Banzhaf Power Index for each player.
January 31
Material from sections 2.2, 3.1

•Finding the Banzhaf Power Distribution
•Definitions for Fair Division:
-S: Discrete S and Continuous S
-Player Value Systems
-Fair Shares and Fair Division
Read Section 3.1

Ch 3 Exercises*
#7, 8, 9, 10, 11, 12

*For 9 and 10: Since the values of the different shares are given as percentages, use the fact that percentages must add up to 100 for each player to figure out the values for s3.
February 2
•Quiz on material from 1/26 and 1/31

Fair Sharing continued
•The Divider-Chooser Method
Chapter 3 Exercises
February 4
Material from Chapter 3

•The Lone Divider Method
•The Method of Sealed Bids
Chapter 3 Exercises
Lone Divider: #21, 22, 31, 32
(Note that "give a Fair Division" means to list who gets which piece.

Method of Sealed Bids: #53-56
February 6
Quiz on Material from 2/2 and 2/4

•Introduction to the Method of Markers
Read Section 3.7: pages 97-100

Practice Problems for Test 1

February 14
•Finish Fair Sharing

Review for the first test
Solutions to Pratice Problems
for Test 1
February 16
Test 1:
•Voting Methods and Criteria
•Weighted Voting Systems and the Banzhaf Power Distribution
•Fair Sharing Methods

February 21
Chapter 4: Apportionment
•Population, States and Seats
•Hamilton's Method
•Alabama Paradox
•Population Paradox
•The Quota Rule
Chapter 4 Practice Problems:
#1-4, 11-18, 19, 20
Read pages 127-131.
February 23
Quiz on Material from 2/21
Bring a Calculator that is not also a phone, etc.

Apportionment, Continued
•Jefferson's Method
•Webster's Method
Chapter 4 Practice Problems
#23, 24, 25, 26 (Jefferson's)
#43, 44, 45, 46 (Webster's)

Read "Jefferson's Method and the Quota Rule"on page 137.
February 28
Chapter 10: Money and Time
•Sec. 10.1: Practice with Decimals and Percents
•Sec. 10.2: Simple Interest
•Sec. 10.3: Annual Compounding Interest
Read Ch 10.3 pages 370-371

Chapter 10 Practice Problems
#21, 22, 25, 26,
#31.a, 32

March 1
Quiz on Material from 2/23 and 2/28
Bring a Calculator that is not also a phone, etc.

Compounding interest, continued

•Sec. 10.3: General Compounding
                        (n times per year)
•Sec. 10.3 Annual Percentage Yield (APY)

Read "The Annual Percentage Yield" on pages 375-276.

Ch 10 Practice Problems
#37, 38
#41, 42 <-- these are APY questions
March 13
•Sec. 10.3: APY continued
•10.4: Geometric Sequences
      -Initial term, Common Ratio
      -Geometric Sum Formula
Ch 10 Practice Problems
#43, 44 (Skip "Daily" and "Hourly")
If the APY for any two come out the same, you are rounding too hard.

•Find the intial term and common ratio of the sequence:
32, 24, 18, 13.5, ...

•Write out the first five terms of the Geometric Sequence with initial term 10 and common ratio 3.

March 15
Quiz 7 on Material from 3/1, 3/13

Material from sections 10.3, 10.4
•APY and Geometric Sequences
•Practice the Geometric Sum Formula
Ch 10 practice & reading

Heads up! The textbook uses different letters in these formulas.

•Read section 10.4 Example 10.17, Example 10.18, and Example 10.19

•Practice Problems
#49, 50
Click here for more practice problems, including geometric sums.
March 20
Material from 10.5
•Deffered Annuities

Ch 10 Practice

Note: the book uses slightly different notation: the letters are different, and they say "G0" for the first term, "G1" for the second term, etc.

#51.a, 51.b, 52.a, 52.b, 53.a, 53.b, 54.a, 54.b.
#57.c, 57.d
#63, 64, 68
March 22
Quiz on Material from 3/19 and 3/15:
•Geomtric Sequence, Geometric Sum
•Deferred Annuities

Material from section 10.6
•Installment Loans (Amortization)
Practice Problems for Test 2
March 27
Material from Ch 13
•Definitions for Statistics
 -Sampling Methods

•Review for Test 2
Solutions to Practice Problems for Test 2

More Ch13 Practice
March 29
Test 2: Calculator Needed
•Statistics (Ch 13)

April 4
Descriptive Statistics (Ch 14)
Material from Sections 14.1, 14.2
•Data Set, Data Point, N-Value, Outliers
•Frequency Tables
•Relative Frequency Tables
•Bar Graph, Relative Frequency Bar Graph
•Range and Scale of Axes

Material from Section 14.3
•Mean of a Data Set
Ch 14 Practice Problems
#1, 2, 6, 11.a, 11.b, 12, 21,
22.a, 29.a, 30.a
April 6 Quiz 9 on Material from April 4

Material from Section 14.3, 14.4

Apr 10
Finish Chapter 14
•Practice Finding Percentiles
•5-Number Summary
•Compute the Standard Deviation of a Data Set
Chapter 14
Read about percentiles, median, quartiles, 5-number summary on pages 535-539. Read section 14.4.

Ch 14, Practice Problems:
#23, 24, 33, 34, 41, 42, 55-58

April 12
Ch 5 Graph Theory
•Edge set and Vertex Set
•Connected and Unconnected Graphs
•Adjacent Edges and Vertices
•Degree of a vertex
•Paths and Circuits
•Euler Paths and Euler Circuits
Ch 5
Read sections 5.2 and 5.3

Ch 5 Practice
April 17
Ch 5 Graph Theory
Material from Sections 5.5, 5.6, 5.7
•Euler's Circuit Theorem
•Euler's Path Theorem
•Euler's Sum of Degrees Theorem

•Fleury's Algorithm

•Eulerize a graph
Ch 5
Read sections 5.5, 5.6

Ch 5 Practice
#15, 16,
#29, 30, 33, 34
April 19
Graph Theory Quiz on:
•Vertex and Edge sets
•Connected Graphs and Bridges
•Adjacent Edges or Vertices
•Paths and Circuits
•Euler's Theorems
•Fleury's Algorithm

Graph Theory Continued:
•Representing a problem with a graph
•Practice Eulerizing a graph
Chapter 6
•Hamilton Paths and Circuits
•Different names for the same H-Circuit
Ch 6 Reading
Section 6.1

Ch 6 Practice Problems
#9, 10
April 24
Material from Ch 6

•Ore's Theorem
•Graph Kn
•Weighted Graphs
•Cost of a Circuit
•Brute Force Algorithm for the Traveling Salesman Problem
•Nearest Neighbor Algorithm
•Repetitive Nearest Neighbor Algorithm

About Kn: Section 6.2

Section 6.5:
Brute Force and
Nearest Neighbor Algorithms

Section 6.7:
Repetetive Nearest Neighbor

Chapter 6 Practice Problems
#29-31, but also do the Repetitive Nearest Neighbor Algorithm for each weighted graph.
April 26
Quiz on Material from 4/19, 4/24
(includes Eulerizing a graph)

Practice Traveling Salesman Algorithms

Begin Review for Final Exam
Click here for
Final Exam Practice Problems

Click here for solutions to the practice problems.

: FRI 05/11/2012 10:30 - 01:15 PM VOTEY 209