Math 1010 Projects As explained in the course outline, you are required to complete one project during the semester. A project is a 3-4 (page paper that explores an application of mathematics to a practical everyday problem. It must be typed, fully documented, well organized, and detailed in explanations and conclusions. It should contain any graphs, diagrams, figures, or data that are needed for a full exposition. Most important, the project must have mathematical content. The project must have a cover page showing the title and authors. It must have an introduction that explains the problem and gives relevant background information. The main body should explain in detail the procedures used to solve the problem and present interesting observations that you made. The conclusion must give a concise summary of your results and give possibilities for future work on the problem. The project must include at least three references (books, papers from the literature, or web sources). You may work in groups of 2-3 people; everyone in a group gets the same grade. How do you find a project topic? You may (i) choose a topic from the list below or (ii) work on a topic of your own choice with instructor approval. You should get started on your project as soon as possible and consult me whenever necessary. Suggested Projects The following project ideas are meant to be only starting points. You should go beyond the given suggestions by posing related questions, carrying out interesting experiments, and extending the stated questions. Supporting units from the text are also given below. Remember your project must focus on the mathematical aspects of the topic. 1. Lotteries. Discuss how your state lottery works. For example: On average how many people play each week and how much do they spend? What are the theoretical chances of winning the grand prize and the smaller prizes? Do the theoretical chances agree closely with the observed number of winners? Do the theoretical chances agree closely with the advertised chances? Exactly how are lottery funds distributed? Is there? What are the advantages of an annuity vs. lump sum option for the grand prize winner? 2. The Golden Ratio and the Arts. Investigate the golden ratio as it appears in either the visual arts (architecture and painting) or music. Explain the golden ratio and the golden rectangle, and discuss their history. Give examples of apparent uses of the golden ratio and the golden rectangle, and give your opinion about whether these uses are designed or coincidental. Cite at least one reference that debunks theories of the golden ratio and the arts. 3. Pollution in Denver. If you have lived in Denver for a few years, you probably know that the city is constantly at risk of violating federal air quality standards (particularly in the winter). Give an argument either for or against the statement: Denver’s air quality has improved over the past ten years. 4. Nielsen Ratings. The Nielsen Company has been conducting ratings of radio and TV programs since about 1920. Give some history of the company and its methods. Discuss how ratings are conducted today. Give examples of the results of the ratings. Discuss issues of sampling, margins of errors, and confidence intervals. 5. Reducing Class Size. Suppose that CU-Denver made the decision to limit all class sizes to 25 students or less. Collect all necessary facts and data to determine the cost of such a proposal. Is it feasible? How would you present the proposal to the chancellor of the university? 6. Improving Recycling. Choose a specific community for which you can find data on garbage disposal and recycling. Estimate the total garbage production for this community (are you considering residential, commercial, or both?). What is the current rate of recycling in this community? Discuss what would be needed to attain a 50% recycling rate; a 75% recycling rate. Make a proposal for attaining these levels in the next ten years. 7. Retirement Planning. Suppose you are planning on retirement at age 65 and you want to begin investing now to be sure that you have a comfortable income. Specifically, suppose that you want an annual income of $50,000 every year after you turn 65. How much would you need to invest (i) as a single lump sum and (ii) on a monthly basis beginning today to insure this retirement income? You will have to do some research about various forms of investment and then choose real investment plans (mutual funds, bonds, or stocks). What assumptions have you made, particularly about interest rates? Are there federal tax implications in this scheme? Experiment with the various parameters in this problem: What is the effect of changing the interest rates by plus or minus 1%? What is the effect of changing the target income to $60,000? What is the effect of delaying your investment by ten years? 8. Voting Systems. Find at least three situations in which voting methods other than the plurality method is used (for example, Academy Awards, Heisman Trophy, other governments, United Nations). Give a thorough explanation of how the voting works in these situations. Give some history and results of the voting. Does the system seem fair to you in each case? 9. Bar Codes. How do bar codes work?? You must include the mathematics! 10. Why Do (Good) Paintings Look Three-Dimensional? Discuss the mathematics of perspective. 11. Prime numbers and security systems. Prime numbers are the fundamental building blocks of arithmetic, but until recently, they had only mathematical interest. Now they are used to design sophisticated coding and security systems. How do these systems work? 12. Mathematics and Controversy. Choose one on the many controversial social, medical, or economic issues that face us: gun control, abortion, capital punishment, health care, mammograms, to name a few. Investigate the mathematics behind these issues, specifically, how both sides use quantitative arguments in different ways. Discuss how mathematics shapes the debate on both sides. 13. Mathematical Modeling for the Environment. Choose a policy initiative that could theoretically be implemented by CU-Denver to help our planet (i.e. Eliminating single use plastic from campus in vending machines, markets, etc.; Implementing ‘Meatless Monday’s on campus and in dining halls; Incentivizing bike/walk to work programs, etc.). Investigate the mathematics behind these issues including the potential cost of implementation and potential positive impact on the environment. Discuss how mathematics could be used to help pitch your idea to the Chancellor.
