**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.*

**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? (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.