Math 1010 Projects
As explained in the course outline, you are required to complete one project during the semester. A project is a 68 page paper that explores an application of mathematics to a practical everyday sort of problem. It must be typed neatly with perfect spelling and grammar, 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 at most three people; everyone in a group gets the same grade. An outline and bibliography for the project are due no later than March 1 and the final project is due no later than April 24.
How do you find a project topic? You may (i) choose a topic from the list below, (ii) choose a project from the end-of-unit problems in the book, or (iii) 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.
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? (Unit 6D)
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. (Unit 8C)
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. Analysis of a Statistical Study. Choose a very specific statistical study that has been recently published (for example, overhead power lines and the incidence of cancer or car phones and accident rates). Give a thorough analysis of the study based on the guidelines of Unit 5B.
5. Conducting a Statistical Study. Choose a very specific issue that can be explored using a survey or statistical study. Carry out a statistical study that accounts for the issues discussed in Unit 5A and 5B. Present your data, the analysis of your data, and your conclusions.
6. 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. (Unit 5A, 5B)
7. Currency Exchanges. Make a table of currency exchange rates for at least ten different international currencies. First assume that “buy rates” and “sell rates” are equal. Is it possible to actually make money by buying and selling several different currencies in succession? Can you propose a general strategy that works for making money in such a way? Explore the problem in the case that “buy rates” and “sell rates” are not equal. (Unit 2A, 2B)
8. 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?
9. 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.
10. 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? (Chapter 4)
11. U.S. Census. As you know, the United States conducted a census (as stipulated by the Constitution) in 2000. Give a brief history of the U.S. Census, its methods, and its results. How accurate are the traditional methods for the census? What are the issues and results associated with Census 2000?
12. Consumer Price Index. The federal government keeps track of the cost of living in this country by measuring the Consumer Price Index (CPI). Give a brief history of the CPI, including CPI data for at least the last 30 years. Discuss the various indices within the CPI. What sampling issues arise in measuring the CPI. Discuss the claim: the CPI has been increasing exponentially for the last 30 years and is likely to continue doing so.
13. 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? (Unit 9A)
14. Sports Records. Choose a timed athletic event for which you can find both men’s and women’s records for at least 30 years (for example, running or swimming events). Present the data in graphical form. Carry out a linear regression on both the men’s and women’s data sets, either exactly or visually. Discuss, compare, and project future records.
15. Tax cuts. The Bush administration passed a tax cut in 2002 (you could also choose one of many recent tax cuts at the state of federal level). Why are there different theories about who will benefit from this tax cut? In your analysis, which income groups will benefit the most and the least from this tax cut?
16. Bar Codes. How do bar codes work?? You must include the mathematics!
17. Election 2000. Explore the mathematics, politics, and legal aspects of the 2000 presidential election.
18. Why Do (Good) Paintings Look Three-Dimensional? Discuss the mathematics of perspective (Unit 8B).
19. 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?
20. 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.