| 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 •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 #1-4 |
| 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 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 -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 s3. |
| February 2 |
•Quiz on material from 1/26 and 1/31 Fair Sharing continued •The Divider-Chooser Method |
Chapter 3 Exercises #15-20 |
| 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 |
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| 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 -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) |
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| 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 •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 |
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| 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 #1-11 |
| 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, #23-26 #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 #1-4 #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 #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. |