Help Session  Day  Time  Location 
Math 1  22 
MON  5:00  7:00 pm  Perkins 200 
Math 009  121 
MON 
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 
Dates 
Topics and Materials 
HW 
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 •Headtohead Comparisons Here are the example ballots we used to create our preference schedule. Here is the lecture outline from today. 
Ch 1 exercises: #14, 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 PluralitywithElimination 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 #14 
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 Distribution *I say there are 2^{n} coalitions because I count the empty coalition. The book doesn't count the empty coalition, so it says there are 2^{n}–1. 
Ch 2 Exercises* #7, 8, 1118, 21, 22 Here is a realword 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 Players 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 s_{3}. 
February 2 
•Quiz on material from 1/26 and 1/31 Fair Sharing continued •The DividerChooser Method 
Chapter 3 Exercises #1520 
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: #5356 
February 6 
Quiz on Material from 2/2 and 2/4 •Introduction to the Method of Markers 
Read Section 3.7: pages 97100 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: #14, 1118, 19, 20 Read pages 127131. 
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 370371 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 375276. 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 Population Sampling Methods Bias •Review for Test 2 
Solutions to Practice Problems for Test 2 More Ch13 Practice 
March 29 
Test 2: Calculator Needed •Apportionment •Finances •Statistics (Ch 13) 

April 4 
Descriptive Statistics (Ch 14) Material from Sections 14.1, 14.2 •Data Set, Data Point, NValue, Outliers •Frequency Tables •Relative Frequency Tables •Bar Graph, Relative Frequency Bar Graph •Range and Scale of Axes •Histograms 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 •5Number Summary •Compute the Standard Deviation of a Data Set 
Chapter 14 Read about percentiles, median, quartiles, 5number summary on pages 535539. Read section 14.4. Ch 14, Practice Problems: #23, 24, 33, 34, 41, 42, 5558 
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 #111 
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, #2326 #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 HCircuit 
Ch 6 Reading Section 6.1 Ch 6 Practice Problems #14 #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 
Reading: About Kn: Section 6.2 Section 6.5: Brute Force and Nearest Neighbor Algorithms Section 6.7: Repetetive Nearest Neighbor Chapter 6 Practice Problems #2931, 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. 