1. What is RSA cryptography, and what mathematical ideas are used to implement it?
2. Describe a one-to-one correspondence between two sets of objects in everyday life. Then, describe two sets of objects which do NOT have a one-to-one correspondence.
3. Describe a one-to-one correspondence between the infinite sets andWhat does this tell you about the cardinality of these two sets?
4. What is Cantor's Diagonalization Argument and what is it used for?
5. What is dimension? Use this idea of dimension to explain what the 4thdimension is and what 4thdimensional objects are like.
6. Topology is also known as "rubber sheet geometry." How is topology different from traditional (high school) geometry? Give an example of two shapes which are equivalent in topology, but are different in traditional geometry.
7. Explain what is meant by the phrase "a topologist can't tell the difference between a doughnut and a coffee cup." How are a doughnut and a coffee cup related?
8. Describe one real-world application of graph theory. What would the vertices represent, and what would the edges represent?
9. What is Conway's Game of Life? Explain what it is used for and describe ONE of the rules of the game.
10. Suppose 4 people are in a race. How many different 1stplace, 2ndplace, and 3rdplace finishes can there be? Explain your reasoning.
11. Describe the two different ways to measure the center of a data set. How do you calculate each one?
12. Thedistributionof a data set refers to the different values of the data, and how many data points take on those values. Give an example of a type of data which isnormally distributedand describe the shape of this distribution (when graphed).
13. Explain how probability played a role in Gregor Mendel's experiments with peas and his theory of genetics.
14. Suppose that airlines want to reduce the number of airplane deaths. They spend money to increase airplane safety to effectively decrease the number of airplane deaths per year. What could be an unintended consequence? Explain.