Note: do not do outside research unless the topic is specifically identified as a research topic. For those, you should use standard procedures for acknowledging sources.
Consider whether or not two-dimensional numbers can be divided.
Look for equilibrium values using the recursion rule zn+1 = zn2 + c
Continue exploring the cubic recursion model from the exam. Come see me to learn the calculus that will allow you to find the height of the hump.
Learn about four-dimensional numbers (quaternions) and the dynamical systems made with them. This is a research topic.
Make a detailed map of the Mandelbrot set, showing where various types of Julia sets are located. (For example, the five-cycle Julia sets are in this region, seven-cycles are here, etc.)
Read Thomas Kuhn’s The Structure of Scientific Revolutions to learn more about the concept of paradigm. This is a research topic.
Use the Randomania program to look at the difference between randomness and chaos.
When the computer generates a random number, it’s actually a pseudo-random number. Find out how computers generate these numbers. The most common method is based on modular arithmetic!
Analyze the probabilities involved in Yahtzee or poker or some other game that involves chance. Is the scoring for the game fair?
Analyze the card game called "War," which is played purely on the basis of chance. How long should the average game last?
Record a sporting event and analyze the commentary of the sportscasters. Do you feel they demonstrate an understanding of probability? You may need to make several recordings before you get some good examples.
A current political debate concerns the United States census. Some people are advocating that the government should use sampling to count the population, while others insist that we should stick with the current method of attempting to find every single person and count heads one by one. Find out what they’re arguing about and why it has political significance.
Part of the debate about evolution involves probability. Creation theorists argue that there hasn’t been enough time for development of complicated organisms to have occurred by random mutations. Check into the debate. One possible source is Climbing Mount Improbable by Richard Dawkins.
Look into the application of probability theory to the stock market. The work of Nassim Taleb is especially interesting. There is a link on our chance page to an article by Malcolm Gladwell about Taleb and Taleb has his own web site. There is also a famous book by Malkiel, A Random Walk Down Wall Street, which has been out since I was in college.