Math 408 (Prof. Hildebrand), Spring 2008
Honors Credit Projects for James Scholars
The projects are open to students in the James Scholar program who have
submitted an appropriate online application, called Honors Credit
Learning Agreement (HCLA), earlier in the semester. (The deadline for
HCLA applications has long passed, so if you haven't applied yet, it's
too late to do it now.)
According to the general guidelines of James Scholar program, the work
required to earn James Scholar Honors Credit must be substantial (it
should take at least 15 hours to complete); it must go well beyond
homework type assignments; and it must be related to the subject of the
course (which in our case is statistics/probability, in a rather broad
sense). A list of suitable projects is given below.
What you need to do
- Collect source materials: Articles in newspapers and
magazines, scientific journal articles, websites, etc.
For each of the projects below
I have given some links that can serve as starting points. In some cases
this may be all you need, in others you should try to find and locate
additional appropriate sources. With search tools like google available,
this isn't too hard these days.
Try to use nontechnical articles, such as articles published in
mainstream newspapers and magazines, or expository science journals;
papers published in research-level mathematics and statistics journals
are likely too technical.
(The projects below are all such that there is
plenty of nontechnical material available.)
While some materials may be readily available on the web, for others you
may have to do some legwork, make a trip to the Main Library or to one of the
branch libraries (such as the law library for legal documents), and
check out or make copies of the document you need. This in itself can be
interesting and fun; if you have never been to the main library stacks,
it's worth a trip! Librarians are a great resource and can often
quickly direct you to the right place; don't be shy asking for assistance.
For example, if you don't know where to start at all, the reference
desk at the Main Library is a good place to start.
Read the material.
This goes without saying. The principal source(s) you should read in
full. With auxiliary materials, you may be able to focus on the most
relevant portions, and skim the rest of the document.
While every source that you use in some form should be cited, citing a
paper doesn't necessarily mean that you have to read every sentence of
Prepare a paper.
The paper should be self-contained (i.e., one should be able to read and
understand it without having to consult the source(s)).
It should be neatly written up (preferably
typed up), with complete sentences, in grammatical English, and well
organized (i.e., subdivided into sections, and possibly subsections,
rather than an uninterrupted stream of prose).
Needless to say, the writing should be your own;
it should summarize the source material in your own words, and
not be simply a copy or an excerpt.
The length of your paper depends on the nature of the
project, and such things as font size, etc.;
Papers from past James Scholar projects I have given have ranged from
about 5 to more than 15 typed pages.
The paper should include the following:
The paper (and attachments) must be turned in as hard copy.
- Title matter: Your name, the title of the project, the course
(Math 408), the date or semester.
At the end of the paper provide full citations of all sources
that you have used in preparing the paper. Be specific in your
references; if it's an online document, provide a URL.
- Attachments: Attach copies/printouts of all main sources
(columns, articles, webpages, etc.) you used. (In case of very long
documents, a reference (URL, etc.) is sufficient.)
- Friday, April 11: Deadline for selection of projects.
By Friday, April 11, you should have selected project that you are
going to do, and let me know which one you chose.
Feel free to discuss the selection with me!
- Friday, April 25: Deadline for preliminary draft.
Aim at completing your work and showing it to me by that
deadline. In most cases I can tell you right away whether
it is sufficient for honors credit. In case it is not satisfactory,
you'd have a couple of days to correct any problems and turn in a
revised version by the final deadline of April 30 (the last day of class).
- Wednesday, April 30 (last day of class): Final deadline.
This is the deadline for turning in the final version.
- Group work.
I have no objection to group work, provided you (and any other members
of the group) discuss this with me and get my permission beforehand.
Honors credit work and course grade:
Doing an honors credit project has no effect on your course grade; it
only serves to satisfy the James Scholar Honors Credit requirement. In
particular, an honors credit project - no matter how impressive it is -
does not justify "bumping up" a grade.
Below is the list of projects. Take a look at the descriptions and
links provided, and pick the one that suits you best. I have selected
these projects since they are at a level and length appropriate for a
James Scholar project, and I have had students in years past
successfully complete the project as part of a James Scholar or EC
assignment. I might consider other project ideas, but you should
first consider the projects below. Project ideas that might sound
great at first glance may turn out to be either way above the scope and
level of a James Scholar project, or too little or too shallow for such
a project. The projects below are all tried and proven, and at just the
right level. If you have questions about any of these, talk to me!
In its simplest form, a standard lottery is easy to analyze, Also, if
the prizes to be won are fixed and not shared (e.g., if everyone who
gets all 6 numbers right in a 6 number lottery wins a million dollars),
then the expected win at
a single drawing, and hence the fair price of a lottery ticket, can
easily be computed. However, things get more complicated if the prizes
may have to be shared, or are variable,
as in the case of a "jackpot" that accumulates if
there are no winners at a given drawing. Occasionally, such jackpots
reach almost astronomical numbers and then make headlines and cause a
big rush at convenience stores by people wanting to buy tickets.
One can ask if it is advantageous to buy lottery tickets during such
periods of high jackpots. (The answer is not clear: On the one hand,
a high jackpot means that the potential winnings are larger, but on the
other hand, a high jackpot attracts a greater number of lottery
players, so there is also a greater chance of having to share a prize.)
The above article analyzes this situation for the Powerball lottery.
Probability and the Law: The People vs. Collins case
This project deals with a famous court case from the 1960s in which a
was convicted based on flimsy probabilistic reasoning, and the
conviction was overturned in appeal, after the probabilistic argument
was shown to be seriously flawed. This project is less mathematical than
the others, and involves more old-fashioned literature search,
legwork (e.g., a trip to the law library), and digging out and
reading legal documents. (Since the case occurred nearly 40 years ago,
well before the internet age, most of the relevant literature is only
available in print form.)
Doing such research in itself can
be fun, interesting, and educating (have you even seen an official court
opinion?), especially for those who have an interest in public policy,
politics, and the legal system.
This is a case where you should definitely avail yourself of the vast
resources of the University Library. A good starting point for a
literature search is the Reference Library, located at the second floor
of the Main Library. Don't be shy asking one of the reference
librarians there; they are there to help!
Below are some sources that I am familiar with. You should get all of
these; if you find others, great, but make sure you cite all sources you
use, and copies of the source documents to your paper.
I have intentionally
been vague in the references, so you'll have to find exact citations,
and library locations, etc., yourself (or, better, ask a librarian to
How many times do you have to shuffle a standard deck of card in order
to mix them reasonably well? The correct answer is seven, according to
Persi Diaconis, a well-known Professor of Statistics and Mathematics
at Stanford and former professional magician. Diaconis' work, which
appeared in the early 1990s, made headlines at the time,
and was written up in the New York Times and other
main stream media. The above article by Brad Mann gives an exposition
of Diaconis' work and the underlying mathematics. Compared to the other
projects, this project involves deeper (and probably more interesting)
mathematics (but still well within the level of a basic undergraduate
probability course). On the other hand, it requires little or no
literature search, trips to the library, etc., as it can be based almost
exclusively on the Mann article. (You might still want to look at the
NY Times article referenced in the Mann paper, or other, secondary,
sources, if only to get a different, nontechnical, perspective.)
- Articles in Times Magazine: There are two,
one on the original conviction, and the other one on the
overturning of the verdict on appeal. Those are the least technical
sources. They are good for a quick overview, but you should definitely read
the more technical papers below, and base your write-up mainly on those
- Court Opinion: The official Court Opinion by Judge Raymond
Sullivan of the California Supreme Court. Definitely not a light read,
but I found it fascinating in its own way. (For example, it is
interesting to see how fairly simple mathematical arguments read
after being translated into legalese ...)
- Articles by William B. Fairley and Frederick Mosteller.
Fairley, a legal scholar, and Mosteller, a well-known statistician,
have collaborated on several articles related to the
People vs. Collins case. One appeared in the University of Chicago Law
Review, and another in a book titled "Statistics and the Law".
For those who have strong programming skills, I could provide suitable
projects. If you are interested, talk to me. (In my Math 461 classes,
the programming projects tend to be by far the most popular. This is no
surprise, since those classes are populated by students in Engineering
and Computer Science for whom programming is second nature. By contrast,
in all of my Math 408 classes I have had only one student take on a
programming project. Superficial familiarity with a programming
language is not enough; you should have a very solid knowledge in at
least one of the major programming languages (e.g., C, C++, Java) as
well as hands-on experience in writing programs before considering a
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