**Only choose 1 out of these 16 chapter!**!!

I also have a the information for each chapter after you pick the question

A.(Ch 1) Instant Run offImagine you are a political activist in your community. The city council is having hearings to decide if the method of instant runoff voting (plurality-with-elimination) should be adopted in our city. Choose a position (for or against) and prepare a brief to present to the city that justifies that position. Your argument should include mathematical, economic, political, and social considerations. Be sure to explain clearly.

B.(Ch 2) Johnston Power IndexIn the text they discuss the Banzaff and Shapley-Shubik power index. Explain the difference between Banzaf and the Johnston Power Index. Give at least 2 good examples of power structures and apply this index on them. (Use one of the examples in the text and show the differences between it and the Johnston method).

C.(Ch 3) Fair Division with Unequal SharesThe methods done in class were with equal shares (unequal means each person gets a different percentage). This is called an asymmetric fair division. Write a paper discussing how a method you learned can be adapted for the case of asymmetric fair division. Discuss at least one discrete and one continuous asymmetric fair-division method.

D.(Ch 4) First Apportionment of the House of Representatives2 competing bills were considered to apportion the 120 seats, one from Hamilton and one from Jefferson. Using the census from 1790 below find the apportionment using Hamilton’s Method and also fine it using Jefferson’s Method. Read their arguments (note which state each came from) and summarize each argument.

State |
Population |

Connecticut |
236,841 |

Delaware |
55,540 |

Georgia |
70,835 |

Kentucky |
68,705 |

Maryland |
278,514 |

Massachusetts |
475,327 |

New Hampshire |
141,822 |

New Jersey |
179,570 |

New York |
331,589 |

North Carolina |
353,523 |

Pennsylvania |
432,879 |

Rhode Island |
68,446 |

South Carolina |
206,236 |

Vermont |
85,533 |

Virginia |
630,560 |

Total |
3,615,920 |

E.(Ch 5) Computer Representation of a GraphIn many real-life routing problems the graphs are huge (thousands of vertices and tens of thousands of edges) In these cases it is common for the graphs to be represented in a computer by a matrix and Fleury’s algorithm (or another similar one) is used. Write a short research paper describing the use of matrices to represent graphs. Explain what a matrix is, what is the adjacency matrix of a graph and what is the incidence matrix of a graph. Illustrate some of the concepts (degrees of vertices, multiple edges, loops, etc.) in matrix terms.

F.(Ch 6) Computing with DNADNA is the basic molecule of life – encodes the genetic information that characterizes all living organisms. AT the U of Southern CA Leonard Adleman was able to encode a graph representing seven cities into asset of DNA segments and use the chemical reactions of the DNA fragments to uncover the existence of a Hamilton path in the graph. He was able to use the biochemistry of DNA to solve a graph theory problem. Write a research paper telling the story of Adleman’s landmark discovery. How did encode the graph into the DNA? How did he extract the mathematical solution (Hamilton path) from the chemical solution: What other kinds of problems might be solved using DNA computing?

G.(Ch 7) Social Networks and PrivacyThere is an inverse relation between connectedness and privacy. In general the more connected you are the less privacy you have. When you sign up for social media you are making lots of our personal information available to others. How much privacy are you losing? How are you losing it? What steps can you take to minimize invasions of your privacy from the social networks you use? Write a paper discussion these issues. Be sure to include the math of how fast your privacy is lost.

H.(Ch 8) TournamentsA tournament is a digraph whose underlying graph is a complete graph, where each vertex is connected to every other vertex by an arc. (Where the direction of the arc is from the winner to the loser). Write a paper on the mathematics of tournaments (Note: the method of pairwise comparisons is a subset of it).

I.(Ch 9) Malthusian Doctrinein 1798 Thomas Mathus wrote his famous essay on the principle of population where he put forth the principle that population grows according to an exponential growth model where food and resources grow according to a linear growth model. Based on this he thought the world was doomed to where the food supply would not be able to keep with the population growth. Write an analysis paper detailing some of the consequences of this doctrine. Can it be the explanation for the famines in sub-Saharan Africa? Discus the criticisms that can be leveled against Mathus’s doctrine. Do you agree with his doctrine?

J.(Ch 10) Many faces of eThe irrational number e has many remarkable mathematical properties. In this project you are asked to present and discuss five of the more interesting mathematical properties of e. For each property, give a historical background, a simple mathematical explanation, and a real-life application.

K.(Ch 11) 3-Dimensional Rigid motionsWe learned about the 4 basic types of rigid motion for 2-dimensional objects. For 3-dimensional objects moving in 3-dimensional space, there are 6 possible types of rigid motion. They are equivalent to a reflection, a rotation, a translation, a glide reflection, a rotary reflection, or a screw displacement. Prepare a presentation on the 6 possible types of rigid motion in 3-dimensional space. For each give a precise definition of the rigid motion, describe its most important properties, and give illustrations as well as real-world examples.

L.(Ch 12) Book Review: The Fractal MurdersThe Fractal Murders by Mark Cohen (2002) is a whodunit with a mathematical backdrop. It is a classic murder mystery with a fractal twist where all the victims are mathematicians doing research in the field of fractal geometry. Read the novel and write a review of it. Include a critique of the mathematical merits of the book.

M.(Ch 13) The Golden Ratio in Art, Architecture, and MusicMany artists, architects, and musicians have been fascinated by the golden ratio. Choose one of the 3 fields (art, architecture, or music) and write a paper discussing the history of the golden ratio in that field. Describe famous works of art, architecture or music in which the golden ratio is alleged to have been used. Who were the artists, architects, and composers?

N.(Ch 14) Recent StudyDo an in-depth report on a recent study from an article in a newspaper or magazine (can find online) discussing the results of a major study and write an analysis of the study. Discuss if the article gives enough information to assess the validity of the study’s conclusions. In your opinion is there information missing in the article, generate a list of questions that would help you further assess? Pay particular attention to the ideas and concepts discussed in this chapter, including the target population, sample size, sampling bias, randomness, controls, and so on.

O.(Ch 15) Lies, Damn Lies, and StatisticsStatistics are often used to exaggerate, distort and misinform, and this is the most commonly done by the misuse of graphs and charts. Discuss the different graphical tricks that can be used to mislead or slant the information presented ina pictures. Include items from recent newspapers, magazines, and other media.

P.(Ch 16) History of GamblingGames of chance can be traced all the way back to some of the earliest civilizations. Write a paper discussing the history of gambling and the historical role of games of chance in the development of the probability theory.