Below is a small sampling of topics that are possible. Some have been done in previous semesters, some have not. The most fun topics also often require the most time: often you'll need to find a little bit of information from several different sources, or request a copy of an article or book through inter-library loan. So I suggest you start thinking of a topic now. If you only allow yourself a week, your lack of foresight will force you into doing a less interesting topic, and often will also prevent you from finding the connections or learning the math that get the most points.

• Art and/or architecture: This is a huge topic. Some possibilities:
  • How mathematics affected Leonardo Da Vinci's life and work, with specific examples, on slides.
  • How the mathematical ideas of tiling a plane relate to quilts and/or wallpaper.
  • The history of mathematical perspective in art, and how it affected areas beyond art by allowing detailed drawings of 3 dimensional objects to be included in books. This helped spawn the spread of information on building machines and buildings.
  • The use of symmetry, or a-symmetry, in creating art or architecture.
  • The use of the Golden Mean in composing works of art or architecture.
  • The connection between science and art, with a focus on math.
  • Mathematical art--fractals, symmetry, tilings, etc.
  • Visualizing the 4th dimension.
  • The Shroud of Turin--see History
  • The 4 color problem--you can color any map, or in fact, any picture in a coloring book in only 4 colors, and not two pieces of the same color share a side. Investigate this, what it has to do with graph theory. This could be part of a talk on math in art, math in children's lives, or math in geography (maybe), or it could be a whole commercial.
• Business--beyond the obvious
  • The use of mathematics in marketing, from surveys to choosing the shape of the container, to using logic (or false logic) to persuade people they need it. Videotape several TV ads, or cut out magazine ads, and discuss the fallacies in their arguments.
  • Scheduling
  • UPC codes--how they work, what they really are. (They're all math).
• Health and Medicine
  • The connection between math and medicine--how much medicine should be prescribed? How fast is a drug eliminated from a person's body? Clinical drug studies. Etc.
  • Using math to discuss our culture's ideal body images (with Barbie or GI Joe as possible examples), and/or comparing to historical ideals.
• History and/or Archaeology
  • The Shroud of Turin, thought by millions to be the shroud of Jesus: is it real, or is it a fraud? Mathematics can be used to argue either side.
  • How do archaeologists/paleontologists determine how old items are? How effective are these techniques? (There's carbon-dating, tree-ring counting, etc)
  • How did ancient cultures determine what was aesthetically pleasing? (The Greeks used math. How? Did other cultures?)
  • What field techniques do archaeologists use? Do they use math?
  • How were mathematicians some of the real heroes of WWII?
  • The advanced mathematics of the Mayans: their numeration system they were one of the first cultures to more or less have a zero), their calendar, and/or breaking the code--trying to figure out how to read Mayan.
  • The history of European numeration: those wild and wacky Babylonians, the advanced Greeks, the primitive Romans who set back mathematics, and the introduction of the Hindu-Arabic system we use today, ranked by Scientific American as one of the top 10 scientific ``advances'' of the millenium.
  • Historic mathematicians:
    • The epic adventure of the solving of Fermat's Last Theorem.
    • The brilliant but bizarre mathematician Paul Erdos.
    • The tragic tale of the mathematical prodigy Ramanujan, a member of one of the lower castes in India who taught himself mathematics, and was ``discovered'' by an English mathematician, only to die at a young age after being brought to England.
    • The unabomer and other crazy mathematicians.
• Law and Order
  • Using math to solve crimes: ballistics, comparing DNA, rates of cooling, rates of larval growth, rates of decay, determining the size of perimeter, determining whether a car was speeding by the length of skid marks and the weather conditions, etc.
  • Using math (statistics) to analyze juries and decide whether a person really has been tried by ``a jury of his peers'' (or hers, of course).
  • Using math to argue a case. One possible source: the book (not the movie) ``A Civil Contract'': both sides used statistics to make their points.
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• Literature: I think there's a lot to do here, but I've had trouble thinking of things. Please share any ideas you have with me.
  • Using the relative frequency certain words appear to make an educated guess as to whether Shakespeare (or some other famous and prolific author) actually wrote a certain work.
  • Similar to the Bible code, some people have claimed that some author's works contain coded messages.
  • Read Flatlands by Edwin Abbott or The Difference Engine by Willian Gibson and Bruce Sterling, or any other book that's about math or math people.
  • The most obvious other is to look into the use of logic in Alice in Wonderland, and/or the Multiplication Tables when she first gets there and wonders if she still is who she was that morning--alternate bases.
• Movies:
  • The math behind the special effects and/or graphics and/or computer animation
  • The math/physics of star trek
  • The mathematics of your favorite superhero (this can be done with superman, don't know about others. And it's not necessarily easy, but could be fun.)
  • The math in various movies. Some possibilities
    • Good Will Hunting, and the math in it. Why did they choose that particular branch of math? Were the problems as difficult as they were supposed to be? Did the math form a coherent sensible mix?
    • Pi
    • The Mirror has Two Faces
    • Jurassic Park
• Music: another huge topic
  • The broad concept of the relationship between music and math.
  • Ringing changes on bells (a primarily English amusement; Dorothy Sayers devoted an entire mystery to it) is highly mathematical. How?
  • Mozart's sonatas are said to be the most beautiful. The golden mean appears in them: how? was it intentional? Compare to other sonatas. (I have a reference for a paper; you also need to learn how sonatas are divided into sections.)
  • Bartok, Debussy, and Beethoven are also possibilities.
  • Does your favorite group use the golden mean (or other mathematical notions), whether conciously or no, in their compositions. (This is risky--you might be left with not much to say if your group of choice doesn't use it--depending on whether anyone else has already talked about math and music.)
  • One student wanted to either investigate the significance of a particular number that had always had meaning to him or ways that math is involved in music. He ended up discovering a musician who created a scale that involved his special number, using mathematics.
  • Another student used $\pi$ to compose an original piece of music, played a recording of the music, and discussed how he composed it.
• Politics, International Relations, and political issues
  • Using the same information to argue two different sides of an issue--abortion and gun control are the ones which are obvious to me, but I'm sure there are endless possiblities.
  • How Lani Guinier's views on voting theory spelled the end to her nomination as Assistant Attorney General for Affirmative Action (or some such position).
  • How misapportionment or a choice of voting method has affected historical outcomes.
  • Game Theory, and its use in analyzing tricky situations in international relations (like the Cuban Missile Crisis).
  • In certain situations in the European Union, each country votes, and each country has a different number of votes. Right now, those votes are distributed fairly randomly, only loosely based on population. How much power does each country have now? And/or use an apportionment method to redistribute the votes in a more logical manner. How does that change the distribution of power?
  • The 2000 Census is here. Sampling vs only counting. The affect it will have on states' and/or various groups power. Redistricting. Etc. This is a huge area with lots of possibilities.
  • There are several other voting methods that we didn't/ aren't going to study. Look into one or some. (One was devised by Charles Dodgson, aka Lewis Carroll--he thought it would be a good way for Oxford faculty to vote on the various issues that came before them.)
• Religion
  • The Bible Code: an example of how a little knowledge is a dangerous thing. The ideas behind the bible code, and how it was debunked (by people who knew more.)
  • The Shroud of Turin--see History
  • Some famous mathematicians and their interesting religious viewpoints (esp. Erdos and \ldots maybe it's Whitehead I'm thinking of? See The Man Who Loved Only Numbers for some ideas.)
  • The Pythagorean Cult
• Science
  • Patterns in Plants
  • Patterns in Nature (there are many, but the reproduction of rabbits and honeybees, the patterns in some shells, the rates of population growth, the relationships between the populations of prey and predator are all possibilities).
  • Using Fractals to model patterns
  • Astronomy--the size of the numbers involved, the number of coincidences involved in Earth having full solar eclipses, the speeds involved, how astronomy and math have advanced in step, etc. Also possible: arguing the probability of extraterrestial life.
  • Bucky Balls
• Sports: Many people want to do sports, but it's hard. Some ideas.
  • Using math to improve performance in ice skating, yachting, tennis, etc. See Life by the Numbers video series. Parabolic skis are also possible, but there's as with a lot of sports, there's little or no written material, so it would be a lot of your own calculations.
  • Using math to analyze games--bounces are reflections, etc
  • Using math to figure out placement for catching pop fly
• Warfare
  • How were mathematicians some of the heroes of WWII (as in history)?
  • A history of math in warfare--you can go at least as far back as archimedes and how and why he died
  • codes and code-breaking